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Sample records for boltzmann collision integral

  1. Collision group and renormalization of the Boltzmann collision integral

    Science.gov (United States)

    Saveliev, V. L.; Nanbu, K.

    2002-05-01

    On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

  2. Nonlinear moments method for the isotropic Boltzmann equation and the invariance of collision integral

    International Nuclear Information System (INIS)

    Ehnder, A.Ya.; Ehnder, I.A.

    1999-01-01

    A new approach to develop nonlinear moment method to solve the Boltzmann equation is presented. This approach is based on the invariance of collision integral as to the selection of the base functions. The Sonin polynomials with the Maxwell weighting function are selected to serve as the base functions. It is shown that for the arbitrary cross sections of the interaction the matrix elements corresponding to the moments from the nonlinear integral of collisions are bound by simple recurrent bonds enabling to express all nonlinear matrix elements in terms of the linear ones. As a result, high-efficiency numerical pattern to calculate nonlinear matrix elements is obtained. The presented approach offers possibilities both to calculate relaxation processes within high speed range and to some more complex kinetic problems [ru

  3. A temperature and mass dependence of the linear Boltzmann collision operator from group theory point of view

    International Nuclear Information System (INIS)

    Saveliev, V.

    1996-01-01

    The Lie group of the transformations affecting the parameters of the linear Boltzmann collision operator such as temperature of background gas and ratio of masses of colliding particles and molecules is discovered. The group also describes the conservation laws for collisions and main symmetries of the collision operator. New algebraic properties of the collision operator are derived. Transformations acting on the variables and parameters and leaving the linear Boltzmann kinetic equation invariant are found. For the constant collision frequency the integral representation of solutions for nonuniform case in terms of the distribution function of particles drifting in a gas with zero temperature is deduced. The new exact relaxation solutions are obtained too. copyright 1996 American Institute of Physics

  4. Some properties of the Boltzmann elastic collision operator; Quelques proprietes particulieres de l'operateur de collision elastique de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Delcroix, J. L. [Ecole Normale Superieure (France); Salmon, J. [Commissariat a l' energie atomique et aux energies alternatives - CEA (France)

    1959-07-01

    The authors point out some properties (an important one is a variational property) of the Boltzmann elastic collision operator, valid in a more general framework than that of the Lorentz gas. Reprint of a paper published in 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596 [French] Les auteurs mettent en evidence quelques proprietes (dont notamment une propriete variationnelle) de l'operateur de collision elastique de Boltzmann valables dans un cadre plus general que celui du gaz de Lorentz. Reproduction d'un article publie dans 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596.

  5. An integrated Boltzmann+hydrodynamics approach to heavy ion collisions

    International Nuclear Information System (INIS)

    Petersen, Hannah

    2009-01-01

    In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v 2 values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E lab =2-160 A GeV. The HBT correlation of the negatively charged pion source created in

  6. An integrated Boltzmann+hydrodynamics approach to heavy ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Petersen, Hannah

    2009-04-22

    In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v{sub 2} values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E{sub lab}=2-160 A GeV. The HBT correlation of the negatively charged pion source

  7. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Haack, Jeffrey R.

    2014-01-01

    We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

  8. Applications of Boltzmann Langevin equation to nuclear collisions

    International Nuclear Information System (INIS)

    Suraud, E.; Belkacem, M.; Stryjewski, J.; Ayik, S.

    1991-01-01

    An approximate method for obtaining numerical solutions of the Boltzmann-Langevin equation is proposed. The method is applied to calculate the time evolution of the mean value and dispersion of the quadrupole and octupole moments of the momentum distribution in nucleus-nucleus collisions, and some consequences are discussed

  9. Boltzmann Solver with Adaptive Mesh in Velocity Space

    International Nuclear Information System (INIS)

    Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.

    2011-01-01

    We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

  10. Some properties of the Boltzmann elastic collision operator

    International Nuclear Information System (INIS)

    Delcroix, J. L.; Salmon, J.

    1959-01-01

    The authors point out some properties (an important one is a variational property) of the Boltzmann elastic collision operator, valid in a more general framework than that of the Lorentz gas. Reprint of a paper published in 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596 [fr

  11. Transition flow ion transport via integral Boltzmann equation

    International Nuclear Information System (INIS)

    Darcie, T.E.

    1983-10-01

    A new approach is developed to solve the Integral Boltzmann Equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion/neutral mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion beam extractions from high pressure sources. Theoretical predictions are tested through an experiment in which an atmospheric pressure ion source is coupled to a high vacuum energy analyser. Excellent agreement results for configurations in which the radial velocity remains small. Velocity distributions are applied to predicting the efficiency of coupling an atmospheric pressure ion source to a quadrupole mass spectrometer and results clearly indicate the most desirable extracting configuration. A method is devised to calculate ion-molecule hard sphere collision cross sections for easily fragmented organic ions

  12. Lattice Boltzmann Simulation of Collision between 2D Circular Particles Suspension in Couette Flow

    Directory of Open Access Journals (Sweden)

    Li-Zhong Huang

    2013-01-01

    Full Text Available Collision between 2D circular particles suspension in Couette flow is simulated by using multiple-relaxation-time based lattice Boltzmann and direct forcing/fictitious domain method in this paper. The patterns of particle collisions are simulated and analyzed in detail by changing the velocity of top and bottom walls in the Couette flow. It can be seen from the simulation results that, while the velocity is large enough, the number of collisions between particles will change little as this velocity varies.

  13. A fast conservative spectral solver for the nonlinear Boltzmann collision operator

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Haack, Jeffrey R.; Hu, Jingwei

    2014-01-01

    We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M 2 N 4 logN) from the O(N 6 ) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results

  14. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis; Mouhot, Clé ment

    2011-01-01

    The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

  15. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis

    2011-04-01

    The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

  16. All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

    International Nuclear Information System (INIS)

    Fillion-Gourdeau, F.; Gagnon, J.-S.; Jeon, S.

    2007-01-01

    We summarize our main findings in deriving the Boltzmann collision term from the Kadanoff-Baym relativistic transport equation and the multiple scattering expansion of the self-energy within a quasi-particle approximation. Our collision term is valid to all orders in perturbation theory and contains processes with any number of participating particles. This work completes a program initiated by Carrington and Mrowczynski and developed further by present authors and Weinstock in recent literature

  17. Solution of the non-stationary electron Boltzmann equation for a weakly ionized collision dominated plasma

    International Nuclear Information System (INIS)

    Winkler, R.; Wilhelm, J.

    A detailed description is presented of calculating the nonstationary electron distribution function in a weakly ionized collision-dominated plasma from the Boltzmann kinetic equation respecting the effects of the time-dependent electric field, collision processes and the electron formation and loss. The finite difference approximation was used for numerical solution. Using the Crank-Nicolson method and parabolic interpolation between the grid points the Boltzmann equation was transformed to a system of linear equations which was then solved by iterations at a preset accuracy. Using the calculated distribution function values, the macroscopic plasma parameters were determined and the balance of electron density and energy checked in each time step. The mathematical procedure is illustrated using a neon plasma perturbed by a rectangular electric pulse. The time development shown of the distribution function at moments when the pulse was switched on and off demonstrates the great stability of the numerical solution. (J.U.)

  18. Intensity-interferometric test of nuclear collision geometries obtained from the Boltzmann-Uehling-Uhlenbeck equation

    International Nuclear Information System (INIS)

    Gong, W.G.; Bauer, W.; Gelbke, C.K.; Carlin, N.; de Souza, R.T.; Kim, Y.D.; Lynch, W.G.; Murakami, T.; Poggi, G.; Sanderson, D.P.; Tsang, M.B.; Xu, H.M.; Pratt, S.; Fields, D.E.; Kwiatkowski, K.; Planeta, R.; Viola, V.E. Jr.; Yennello, S.J.

    1990-01-01

    Two-proton correlation functions measured for the 14 N+ 27 Al reaction at E/A=75 MeV are compared to correlation functions predicted for collision geometries obtained from numerical solutions of the Boltzmann-Uehling-Uhlenbeck (BUU) equation. The calculations are in rather good agreement with the experimental correlation function, indicating that the BUU equation gives a reasonable description of the space-time evolution of the reaction

  19. A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

    International Nuclear Information System (INIS)

    Green, B I; Vedula, Prakash

    2013-01-01

    An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)

  20. Flavored quantum Boltzmann equations

    International Nuclear Information System (INIS)

    Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

    2010-01-01

    We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

  1. Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

    International Nuclear Information System (INIS)

    Bianchi, M.P.

    1991-01-01

    The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

  2. From Newton's Law to the Linear Boltzmann Equation Without Cut-Off

    Science.gov (United States)

    Ayi, Nathalie

    2017-03-01

    We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. More particularly, we will describe the motion of a tagged particle in a gas close to global equilibrium. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated with the long-range interaction, leading to some explicit weak estimates.

  3. Large Eddy Simulation of Wall-Bounded Turbulent Flows with the Lattice Boltzmann Method: Effect of Collision Model, SGS Model and Grid Resolution

    Science.gov (United States)

    Pradhan, Aniruddhe; Akhavan, Rayhaneh

    2017-11-01

    Effect of collision model, subgrid-scale model and grid resolution in Large Eddy Simulation (LES) of wall-bounded turbulent flows with the Lattice Boltzmann Method (LBM) is investigated in turbulent channel flow. The Single Relaxation Time (SRT) collision model is found to be more accurate than Multi-Relaxation Time (MRT) collision model in well-resolved LES. Accurate LES requires grid resolutions of Δ+ LBM requires either grid-embedding in the near-wall region, with grid resolutions comparable to DNS, or a wall model. Results of LES with grid-embedding and wall models will be discussed.

  4. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

    Barrachina, R.O.

    1985-01-01

    The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

  5. Relativistic Boltzmann theory for a plasma

    International Nuclear Information System (INIS)

    Erkelens, H. van.

    1984-01-01

    This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)

  6. Boltzmann equation analysis of electron-molecule collision cross sections in water vapor and ammonia

    International Nuclear Information System (INIS)

    Yousfi, M.; Benabdessadok, M.D.

    1996-01-01

    Sets of electron-molecule collision cross sections for H 2 O and NH 3 have been determined from a classical technique of electron swarm parameter unfolding. This deconvolution method is based on a simplex algorithm using a powerful multiterm Boltzmann equation analysis established in the framework of the classical hydrodynamic approximation. It is well adapted for the simulation of the different classes of swarm experiments (i.e., time resolved, time of flight, and steady state experiments). The sets of collision cross sections that exist in the literature are reviewed and analyzed. Fitted sets of cross sections are determined for H 2 O and NH 3 which exhibit features characteristic of polar molecules such as high rotational excitation collision cross sections. The hydrodynamic swarm parameters (i.e., drift velocity, longitudinal and transverse diffusion coefficients, ionization and attachment coefficients) calculated from the fitted sets are in excellent agreement with the measured ones. These sets are finally used to calculate the transport and reaction coefficients needed for discharge modeling in two cases of typical gas mixtures for which experimental swarm data are very sparse or nonexistent (i.e., flue gas mixtures and gas mixtures for rf plasma surface treatment). copyright 1996 American Institute of Physics

  7. Long-range correlations in Boltzmann-Langevin model

    International Nuclear Information System (INIS)

    Ayik, S.

    1994-01-01

    The average phase-space density described by the Boltzmann-Langevin model can largely deviate from the one provided by the Boltzmann-Uhling-Uhlenbeck model, due to the non-linear evolution of density fluctuations. This aspect is investigated for long-wavelength, small density fluctuations in the framework of a memory incorporated Boltzmann-Langevin model. It is shown that the correlations associated with density fluctuations yield a collision term describing coupling between the collective vibrations and the single-particle degrees of freedom, which may play an important role in damping of collective motion in both the stable and unstable regions. (orig.)

  8. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  9. Measurement of the Boltzmann constant by Johnson noise thermometry using a superconducting integrated circuit

    Science.gov (United States)

    Urano, C.; Yamazawa, K.; Kaneko, N.-H.

    2017-12-01

    We report on our measurement of the Boltzmann constant by Johnson noise thermometry (JNT) using an integrated quantum voltage noise source (IQVNS) that is fully implemented with superconducting integrated circuit technology. The IQVNS generates calculable pseudo white noise voltages to calibrate the JNT system. The thermal noise of a sensing resistor placed at the temperature of the triple point of water was measured precisely by the IQVNS-based JNT. We accumulated data of more than 429 200 s in total (over 6 d) and used the Akaike information criterion to estimate the fitting frequency range for the quadratic model to calculate the Boltzmann constant. Upon detailed evaluation of the uncertainty components, the experimentally obtained Boltzmann constant was k=1.380 6436× {{10}-23} J K-1 with a relative combined uncertainty of 10.22× {{10}-6} . The value of k is relatively -3.56× {{10}-6} lower than the CODATA 2014 value (Mohr et al 2016 Rev. Mod. Phys. 88 035009).

  10. Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method

    Directory of Open Access Journals (Sweden)

    Muneki Yasuda

    2018-04-01

    Full Text Available The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning problems in the Boltzmann machine are NP-hard. The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning. In this paper, we study Boltzmann machine learning based on the (first-order spatial Monte Carlo integration method, referred to as the 1-SMCI learning method, which was proposed in the author’s previous paper. In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is more effective than the MPLE. In the latter part, we compare the 1-SMCI learning method with other effective methods, ratio matching and minimum probability flow, using a numerical experiment, and show the 1-SMCI learning method outperforms them.

  11. EPOSHQ–a new approach to describe charmed mesons in pp, pA and AA collisions

    Energy Technology Data Exchange (ETDEWEB)

    Aichelin, J.; Guiot, B.; Ozvenschuck, V. [SUBATECH, UMR 6457, Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS. 4 rue Alfred Kastler, 44307 Nantes cedex 3 (France); Nahrgang, M. [Department of Physics, Duke University, Durham, NC 27708-0305 (United States); Gossiaux, P.B.; Werner, K. [SUBATECH, UMR 6457, Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS. 4 rue Alfred Kastler, 44307 Nantes cedex 3 (France)

    2016-12-15

    We present first results of a new approach, EPOSHQ, which combines the EPOS3 event generator with the heavy quarks physics. In this approach light and heavy quarks are simultaneously created in the elementary collisions. The heavy quarks interact by elastic and radiative collisions with the plasma constituents, given by the EPOS3 approach, employing the full Boltzmann collision integral. This approach will allow for the description of correlations between light and heavy mesons.

  12. Nonequilibrium phenomena in QCD and BEC. Boltzmann and beyond

    Energy Technology Data Exchange (ETDEWEB)

    Stockamp, T.

    2006-12-22

    In chapter 2 we chose the real time formalism to discuss some basic principles in quantum field theory at finite temperature. This enables us to derive the quantum Boltzmann equation from the Schwinger-Dyson series. We then shortly introduce the basic concepts of QCD which are needed to understand the physics of QGP formation. After a detailed account on the bottom-up scenario we show the consistency of this approach by a diagramatical analysis of the relevant Boltzmann collision integrals. Chapter 3 deals with BEC dynamics out of equilibrium. After an introduction to the fundamental theoretical tool - namely the Gross-Pitaevskii equation - we focus on a generalization to finite temperature developed by Zaremba, Nikuni and Griffin (ZNG). These authors use a Boltzmann equation to describe the interactions between condensed and excited atoms and manage in this way to describe condensate growth. We then turn to a discussion on the 2PI effective action and derive equations of motion for a relativistic scalar field theory. In the nonrelativistic limit these equations are shown to coincide with the ZNG theory when a quasiparticle approximation is applied. Finally, we perform a numerical analysis of the full 2PI equations. These remain valid even at strong coupling and far from equilibrium, and thus go far beyond Boltzmann's approach. For simplicity, we limit ourselves to a homogeneous system and present the first 3+1 dimensional study of condensate melting. (orig.)

  13. Stabilizing the thermal lattice Boltzmann method by spatial filtering.

    Science.gov (United States)

    Gillissen, J J J

    2016-10-01

    We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

  14. Dynamics of density fluctuations in a non-Markovian Boltzmann- Langevin model

    International Nuclear Information System (INIS)

    Ayik, S.

    1996-01-01

    In the course of the past few years, the nuclear Boltzmann-Langevin (BL)model has emerged as a promising microscopic model for nuclear dynamics at intermediate energies. The BL model goes beyond the much employed Boltzmann-Uehling-Uhlenbeck (BUU) model, and hence it provides a basis for describing dynamics of density fluctuations and addressing processes exhibiting spontaneous symmetry breaking and catastrophic transformations in nuclear collisions, such as induced fission and multifragmentation. In these standard models, the collision term is treated in a Markovian approximation by assuming that two-body collisions are local in both space and time, in accordance with Boltzmann's original treatment. This simplification is usually justified by the fact that the duration of a two-body collision is short on the time scale characteristic of the macroscopic evolution of the system. As a result, transport properties of the collective motion has then a classical character. However, when the system possesses fast collective modes with characteristic energies that are not small in comparision with the temperature, then the quantum-statistical effects are important and the standard Markovian treatment is inadequate. In this case, it is necessary to improve the one-body transport model by including the memory effect due to the finite duration of two-body collisions. First we briefly describe the non-Markovian extension of the BL model by including the finite memory time associated with two-body collisions. Then, using this non-Markovian model in a linear response framework, we investigate the effect of the memory time on the agitation of unstable modes in nuclear matter in the spinodal zone, and calculate the collisional relaxation rates of nuclear collective vibrations

  15. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  16. A fast iterative scheme for the linearized Boltzmann equation

    Science.gov (United States)

    Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

    2017-06-01

    Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

  17. Comparison of heavy-ion transport simulations: Collision integral in a box

    Science.gov (United States)

    Zhang, Ying-Xun; Wang, Yong-Jia; Colonna, Maria; Danielewicz, Pawel; Ono, Akira; Tsang, Manyee Betty; Wolter, Hermann; Xu, Jun; Chen, Lie-Wen; Cozma, Dan; Feng, Zhao-Qing; Das Gupta, Subal; Ikeno, Natsumi; Ko, Che-Ming; Li, Bao-An; Li, Qing-Feng; Li, Zhu-Xia; Mallik, Swagata; Nara, Yasushi; Ogawa, Tatsuhiko; Ohnishi, Akira; Oliinychenko, Dmytro; Papa, Massimo; Petersen, Hannah; Su, Jun; Song, Taesoo; Weil, Janus; Wang, Ning; Zhang, Feng-Shou; Zhang, Zhen

    2018-03-01

    Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within 1 % or better) with analytical results, or completely controlled results of a basic cascade code. In orderto reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients

  18. An Eulerian description of the streaming process in the lattice Boltzmann equation

    CERN Document Server

    Lee Tae Hun

    2003-01-01

    This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...

  19. Boltzmann-Langevin equation, dynamical instability and multifragmentation

    International Nuclear Information System (INIS)

    Feng-Shou Zhang

    1993-02-01

    By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40 Ca + 40 Ca system, we recover some trends of recent multifragmentation data

  20. Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

    Science.gov (United States)

    Agarwal, Ramesh; Chen, Rui; Cheremisin, Felix G.

    2006-11-01

    Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.

  1. MRT Lattice Boltzmann schemes for confined suspension flows

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2010-01-01

    We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been

  2. Transverse-momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV

    Energy Technology Data Exchange (ETDEWEB)

    Tripathy, Sushanta; Khuntia, Arvind; Tiwari, Swatantra Kumar; Sahoo, Raghunath [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Sciences, Indore (India)

    2017-05-15

    In the continuation of our previous work, the transverse-momentum (p{sub T}) spectra and nuclear modification factor (R{sub AA}) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial p{sub T}-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the p{sub T}-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, K{sup *0} and φ. It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in p{sub T} for all these particles except for protons. R{sub AA} is found to be independent of the degree of non-extensivity, q{sub pp} after p{sub T} ∝ 8 GeV/c. (orig.)

  3. Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

    Science.gov (United States)

    De Rosis, Alessandro; Lévêque, Emmanuel; Chahine, Robert

    2018-06-01

    Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar-Gross-Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.

  4. Lattice Boltzmann method with the cell-population equilibrium

    International Nuclear Information System (INIS)

    Zhou Xiaoyang; Cheng Bing; Shi Baochang

    2008-01-01

    The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman–Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions

  5. Nonlocal Boltzmann theory of plasma channels

    International Nuclear Information System (INIS)

    Yu, S.S.; Melendez, R.E.

    1983-01-01

    The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents

  6. On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

    Science.gov (United States)

    Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

    2018-03-01

    The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

  7. Boltzmann hierarchy for interacting neutrinos I: formalism

    International Nuclear Information System (INIS)

    Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y.Y.

    2015-01-01

    Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c eff 2 ,c vis 2 )-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles

  8. Analysis of a bubble coalescence in the multiphase lattice Boltzmann method

    International Nuclear Information System (INIS)

    Ryu, Seung Yeob; Park, Cheon Tae; Lee, Chung Chan; Kim, Keung Koo

    2008-01-01

    Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. To study the effect of the mobility coefficient Γ and the width of the interface layer, two stationary bubbles without a collision are considered. The gap of the two bubbles is taken as 4, while the width of the interface (w) and the mobility coefficient Γ are varied. In the present work, the lattice Boltzmann model for multiphase flows proposed by Zheng et al. is used for simulating two stationary bubbles without a collision. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made smaller. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

  9. Boltzmann equation for a mixture of gases with non-conservative processes

    International Nuclear Information System (INIS)

    Martiarena, M.L.

    1989-01-01

    The nonlinear and non-isotropic Boltzmann equation (NLBE) including several molecular species, non-conservative channels and external forces. The general solution of that equation is obtained for a spatially homogeneous mixture of L gases, consisting of Maxwell particles, as a Generalized Laguerre expansion, within a Hilbert space. Removal and self-generation effects are included in presence of a time-dependent external force. An exact particular solution is studied generalizing the well-known BKW-mode for a mixture of L gases with inelastic processes. An homogeneous gas of test particles, in d dimension, is considered which interacts with a background host medium in the presence of an external space and time dependent force. Scattering, removal and self-generation collisions are included. The inhomogeneous Boltzmann equation for this system to an homogeneous one is reduced without background or external forces, using a generalized Nilkoskii transform. It is shown that a background of field particles can confine the test gas, even in absence of external forces. Furthermore, the solution of NLBE with non-isotropic singular initial conditions, is analyzed. The NLBE is transformed into an integral equation which is solved iteratively. The evolution of delta and step singularities in the distribution function is discussed during the initial layer and compared with the isotropic case. As an application of the methods abovementioned, the collision of a beam of ions or neutral atoms with a carbon-foil is considered. The electron experimental spectra from a transport equation is described. It is supposed that convoy electron may be produced inside the solid by single ion-atom collisions as ELC or ECC. The produced electrons lost energy by collision with the atoms of the material, which are considered at rest. The electron distribution function is numerically calculated. The ratio between the intrinsic convoy electron peak height to the background electron intensity

  10. Painleve test and discrete Boltzmann equations

    International Nuclear Information System (INIS)

    Euler, N.; Steeb, W.H.

    1989-01-01

    The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

  11. Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

    International Nuclear Information System (INIS)

    Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin

    2014-01-01

    Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body

  12. CMB spectral distortions as solutions to the Boltzmann equations

    Energy Technology Data Exchange (ETDEWEB)

    Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

    2017-01-01

    We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

  13. Towards a physical interpretation of the entropic lattice Boltzmann method

    Science.gov (United States)

    Malaspinas, Orestis; Deville, Michel; Chopard, Bastien

    2008-12-01

    The entropic lattice Boltzmann method (ELBM) is one among several different versions of the lattice Boltzmann method for the simulation of hydrodynamics. The collision term of the ELBM is characterized by a nonincreasing H function, guaranteed by a variable relaxation time. We propose here an analysis of the ELBM using the Chapman-Enskog expansion. We show that it can be interpreted as some kind of subgrid model, where viscosity correction scales like the strain rate tensor. We confirm our analytical results by the numerical computations of the relaxation time modifications on the two-dimensional dipole-wall interaction benchmark.

  14. A Boltzmann equation approach to the damping of giant resonances in nuclei

    International Nuclear Information System (INIS)

    Schuck, P.; Winter, J.

    1983-01-01

    The Vlasov equation plus collision term (Boltzmann equation) represents an appropriate frame for the treatment of giant resonances (zero sound modes) in nuclei. With no adjustable parameters we obtain correct positions and widths for the giant quadrupole resonances. (author)

  15. Weighted particle method for solving the Boltzmann equation

    International Nuclear Information System (INIS)

    Tohyama, M.; Suraud, E.

    1990-01-01

    We propose a new, deterministic, method of solution of the nuclear Boltzmann equation. In this Weighted Particle Method two-body collisions are treated by a Master equation for an occupation probability of each numerical particle. We apply the method to the quadrupole motion of 12 C. A comparison with usual stochastic methods is made. Advantages and disadvantages of the Weighted Particle Method are discussed

  16. Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations

    International Nuclear Information System (INIS)

    Xu Kun; He Xiaoyi

    2003-01-01

    Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented

  17. The Boltzmann equation in the difference formulation

    Energy Technology Data Exchange (ETDEWEB)

    Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-05-06

    First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

  18. Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

    International Nuclear Information System (INIS)

    Sherrill, M.E.; Abdallah, J. Jr.; Csanak, G.; Kilcrease, D.P.; Dodd, E.S.; Fukuda, Y.; Akahane, Y.; Aoyama, M.; Inoue, N.; Ueda, H.; Yamakawa, K.; Faenov, A.Ya.; Magunov, A.I.; Pikuz, T.A.; Skobelev, I.Yu.

    2006-01-01

    In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He α spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model

  19. Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

    Energy Technology Data Exchange (ETDEWEB)

    Sherrill, M.E. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States)]. E-mail: manolo@t4.lanl.gov; Abdallah, J. Jr. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Csanak, G. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Kilcrease, D.P. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Dodd, E.S. [Los Alamos National Laboratory, X-1, Los Alamos, NM 87545 (United States); Fukuda, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Akahane, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Aoyama, M. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Inoue, N. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Ueda, H. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Yamakawa, K. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Faenov, A.Ya. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Magunov, A.I. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Pikuz, T.A. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Skobelev, I.Yu. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation)

    2006-05-15

    In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He{sub {alpha}} spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model.

  20. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    EL Safadi, M

    2007-03-15

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  1. Open heavy flavor and other hard probes in ultra-relativistic heavy-ion collisions

    OpenAIRE

    Uphoff, Jan

    2014-01-01

    In this thesis hard probes are studied in the partonic transport model BAMPS (Boltzmann Approach to MultiParton Scatterings). Employing Monte Carlo techniques, this model describes the 3+1 dimensional evolution of the quark gluon plasma phase in ultra-relativistic heavy-ion collisions by propagating all particles in space and time and carrying out their collisions according to the Boltzmann equation. Since hard probes are produced in hard processes with a large momentum transfer, the value of...

  2. Recent applications of the Boltzmann master equation to heavy ion precompound decay phenomena

    International Nuclear Information System (INIS)

    Blann, M.; Remington, B.A.

    1988-06-01

    The Boltzmann master equation (BME) is described and used as a tool to interpret preequilibrium neutron emission from heavy ion collisions gated on evaporation residue or fission fragments. The same approach is used to interpret neutron spectra gated on deep inelastic and quasi-elastic heavy ion collisions. Less successful applications of BME to proton inclusive data with 40 MeV/u incident 12 C ions are presented, and improvements required in the exciton injection term are discussed

  3. The Lattice Boltzmann Method applied to neutron transport

    International Nuclear Information System (INIS)

    Erasmus, B.; Van Heerden, F. A.

    2013-01-01

    In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

  4. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  5. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

    2016-06-01

    Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

  6. Observation of distorted Maxwell-Boltzmann distribution of epithermal ions in LHD

    Science.gov (United States)

    Ida, K.; Kobayashi, T.; Yoshinuma, M.; Akiyama, T.; Tokuzawa, T.; Tsuchiya, H.; Itoh, K.; LHD Experiment Group

    2017-12-01

    A distorted Maxwell-Boltzmann distribution of epithermal ions is observed associated with the collapse of energetic ions triggered by the tongue shaped deformation. The tongue shaped deformation is characterized by the plasma displacement localized in the toroidal, poloidal, and radial directions at the non-rational magnetic flux surface in toroidal plasma. Moment analysis of the ion velocity distribution measured with charge exchange spectroscopy is studied in order to investigate the impact of tongue event on ion distribution. A clear non-zero skewness (3rd moment) and kurtosis (4th moment -3) of ion velocity distribution in the epithermal region (within three times of thermal velocity) is observed after the tongue event. This observation indicates the clear evidence of the distortion of ion velocity distribution from Maxwell-Boltzmann distribution. This distortion from Maxwell-Boltzmann distribution is observed in one-third of plasma minor radius region near the plasma edge and disappears in the ion-ion collision time scale.

  7. Studies of fluctuation processes in nuclear collisions

    International Nuclear Information System (INIS)

    Ayik, S.

    1992-02-01

    This report discusses the following topics: Relativistic Boltzmann-Langevin model for heavy-ion collision; K+ production far below free neucleon-nucleon threshold and damping of collective vibrations in a memory-dependent transport model

  8. Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants

    Science.gov (United States)

    Bernhoff, Niclas

    2018-05-01

    An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.

  9. Effects of nanoparticles on melting process with phase-change using the lattice Boltzmann method

    Directory of Open Access Journals (Sweden)

    Ahmed M. Ibrahem

    Full Text Available In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM enthalpy-based is employed. The collision model of lattice Bhatnagar-Gross-Krook (LBGK is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0–2% added to water-base fluid and Rayleigh numbers of 103–105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied. Keywords: Lattice Boltzmann method, Nanofluids, Conduction melting, Convection melting, BGK collision model

  10. A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma

    Directory of Open Access Journals (Sweden)

    Dongxin Pan

    2018-05-01

    Full Text Available In this study, the Boltzmann equation with electric acceleration term is discretized and solved by the unified gas-kinetic scheme (UGKS. The charged particle transport driven by electric field is included in the electric acceleration term. To capture non-equilibrium distribution function, the probability distribution functions of gas is discretized in a discrete velocity space. After discretization, the numerical flux for distribution function is computed to update the microscopic and macroscopic states. The flux is decided by an integral solution of Boltzmann equation based on characteristic problem. An electron-ion collision model is introduced in the Boltzmann Bhatnagar-Gross-Krook (BGK equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. For simplicity, the electric field induced by charged particles is controlled by the Poisson’s equation, which is solved using the Green’s function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical cases, linear Landau damping and Gaussian beam, are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Comparison results show good accuracy and higher efficiency than particle based methods. Difference between Poisson’s equation and complete electromagnetic Maxwell equation is presented by numerical results based on the two models. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily. The UGKS-Poisson model is proved to be promising in plasma flow simulation.

  11. Classifying images using restricted Boltzmann machines and convolutional neural networks

    Science.gov (United States)

    Zhao, Zhijun; Xu, Tongde; Dai, Chenyu

    2017-07-01

    To improve the feature recognition ability of deep model transfer learning, we propose a hybrid deep transfer learning method for image classification based on restricted Boltzmann machines (RBM) and convolutional neural networks (CNNs). It integrates learning abilities of two models, which conducts subject classification by exacting structural higher-order statistics features of images. While the method transfers the trained convolutional neural networks to the target datasets, fully-connected layers can be replaced by restricted Boltzmann machine layers; then the restricted Boltzmann machine layers and Softmax classifier are retrained, and BP neural network can be used to fine-tuned the hybrid model. The restricted Boltzmann machine layers has not only fully integrated the whole feature maps, but also learns the statistical features of target datasets in the view of the biggest logarithmic likelihood, thus removing the effects caused by the content differences between datasets. The experimental results show that the proposed method has improved the accuracy of image classification, outperforming other methods on Pascal VOC2007 and Caltech101 datasets.

  12. Celebrating Cercignani's conjecture for the Boltzmann equation

    KAUST Repository

    Villani, Cédric

    2011-01-01

    Cercignani\\'s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann\\'s nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.

  13. On the Stability of the Finite Difference based Lattice Boltzmann Method

    KAUST Repository

    El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad

    2013-01-01

    This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

  14. On the Stability of the Finite Difference based Lattice Boltzmann Method

    KAUST Repository

    El-Amin, Mohamed

    2013-06-01

    This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

  15. Chaotic Boltzmann machines

    Science.gov (United States)

    Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

    2013-01-01

    The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425

  16. Transport in partially degenerate, magnetized plasmas. Pt. 1. Collision operators

    International Nuclear Information System (INIS)

    Brown, S.R.; Haines, M.G.

    1997-01-01

    The quantum Boltzmann collision operator is expanded to yield a degenerate form of the Fokker-Planck collision operator. This is analyzed using Rosenbluth potentials to give a degenerate analogue of the Shkarofsky operator. The distribution function is then expanded about an equilibrium Fermi-Dirac distribution function using a tensor perturbation formulation to give a zeroth-order and a first-order collision operator. These equations are shown to satisfy the relevant conservation equations. It is shown that the distribution function relaxes to a Fermi-Dirac form through electron-electron collisions. (Author)

  17. On transient effects in violent nuclear collisions

    International Nuclear Information System (INIS)

    Suraud, E.; Belkacem, M.; Feng-Shou Zhang; Academia Sinica, Lanzhou, GS

    1993-01-01

    It is shown that the numerical simulations of the recently developed Boltzmann-Langevin model exhibit large dynamical fluctuations in momentum space during the early stages of heavy-ion collisions, which arise from an interplay between the nuclear meanfield and binary collisions. It is pointed out that this transient behaviour provides an initial seed for the development of density fluctuations, and could strongly influence the particle production cross-sections at subthreshold energies. (author) 13 refs.; 3 figs

  18. Microscopic descriptions of high-energy heavy-ion collisions

    International Nuclear Information System (INIS)

    Bodmer, A.R.

    1977-01-01

    The essentials of the equation-of-motion (EOM) approach are given and some of its significant and interesting results are described. A framework for the theoretical description of high-energy heavy-ion (HE-HI) collisions is presented; specifically included are a critical assessment of various approaches--EOM calculations, Boltzmann equations/cascade calculations, and hydrodynamics--their relationships and their respective domains of applicability, if any, to HE-HI collisions. 11 figures, 3 tables

  19. Perturbation theory and collision probability formalism. Vol. 2

    Energy Technology Data Exchange (ETDEWEB)

    Nasr, M [National Center for Nuclear Safety and Radiation Control, Atomic Energy Authority, Cairo (Egypt)

    1996-03-01

    Perturbation theory is commonly used in evaluating the activity effects, particularly those resulting from small and localized perturbation in multiplying media., e.g. in small sample reactivity measurements. The Boltzmann integral transport equation is generally used for evaluating the direct and adjoint fluxes in the heterogenous lattice cells to be used in the perturbation equations. When applying perturbation theory in this formalism, a term involving the perturbation effects on the special transfer kernel arises. This term is difficult to evaluate correctly, since it involves an integration all over the entire system. The main advantage of the perturbation theory which is the limitation of the integration procedure on the perturbation region is found to be of no practical use in such cases. In the present work, the perturbation equation in the collision probability formalism is analyzed. A mathematical treatment of the term in question is performed. A new mathematical expression for this term is derived. The new expression which can be estimated easily is derived.

  20. Adaptive time-stepping Monte Carlo integration of Coulomb collisions

    Science.gov (United States)

    Särkimäki, K.; Hirvijoki, E.; Terävä, J.

    2018-01-01

    We report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell-Jüttner statistics. The implementation is based on the Beliaev-Budker collision integral which allows both the test particle and the background plasma to be relativistic. The integration method supports adaptive time stepping, which is shown to greatly improve the computational efficiency. The Monte Carlo method is implemented for both the three-dimensional particle momentum space and the five-dimensional guiding center phase space. Detailed description is provided for both the physics and implementation of the operator. The focus is in adaptive integration of stochastic differential equations, which is an overlooked aspect among existing Monte Carlo implementations of Coulomb collision operators. We verify that our operator converges to known analytical results and demonstrate that careless implementation of the adaptive time step can lead to severely erroneous results. The operator is provided as a self-contained Fortran 95 module and can be included into existing orbit-following tools that trace either the full Larmor motion or the guiding center dynamics. The adaptive time-stepping algorithm is expected to be useful in situations where the collision frequencies vary greatly over the course of a simulation. Examples include the slowing-down of fusion products or other fast ions, and the Dreicer generation of runaway electrons as well as the generation of fast ions or electrons with ion or electron cyclotron resonance heating.

  1. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    International Nuclear Information System (INIS)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki

    2011-01-01

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3–6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3–4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: ► This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. ► A Boltzmann distribution is studied among iron lines of various excitation levels. ► We find an overpopulation of the high-lying energy levels from the normal distribution. ► It is caused through Penning-type collision of iron atom with argon metastable atom.

  2. Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

    Science.gov (United States)

    Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

    2014-04-01

    The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

  3. Singularities in the nonisotropic Boltzmann equation

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

    1987-09-01

    We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

  4. Boltzmann

    International Nuclear Information System (INIS)

    Lin, X.

    1991-01-01

    This paper reports the development of an object-oriented programming methodology for particle simulations. It is established on the [m reductionist] view that many physical phenomena cana be reduced to many-body problems. By doing the reduction, many seemly unrelated physical phenomena can be simulated in a systematic way and a high-level programming system can be constructed to facilitate the programming and the solution of the simulations. In the object-oriented particle simulation methodology, a hierarchy of abstract particles is defined to represent a variety of characteristics in physical system simulations. A simulation program is constructed from particles derived from the abstract particles. The object- oriented particle simulation methodology provides a unifying modeling and simulation framework for a variety of simulation applications with the use of particle methods. It allows easy composition of simulation programs from predefined software modules and facilitates software reusability. It greatly increase the productivity of simulation program constructions. Boltzmann (after Ludwig Boltzmann, 1844-1906) is a prototype programming system in the object-oriented particle simulation methodology. Boltzmann is implemented in C++ and the X Window System. It contains a library of data types and functions that support simulations in particle methods. Moreover, it provides a visualization window to support friendly user-computer interaction. Examples of the application of the Boltzmann programming system are presented. The effectiveness of the object-oriented particle simulation methodology is demonstrated. A user's manual is included in the appendix

  5. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp

    2011-11-15

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3-6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3-4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: Black-Right-Pointing-Pointer This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. Black-Right-Pointing-Pointer A Boltzmann distribution is studied among iron lines of various excitation levels. Black-Right-Pointing-Pointer We find an overpopulation of the high-lying energy levels from the normal distribution. Black-Right-Pointing-Pointer It is caused through Penning-type collision of iron atom with argon metastable atom.

  6. Three-dimensional lattice Boltzmann model for compressible flows.

    Science.gov (United States)

    Sun, Chenghai; Hsu, Andrew T

    2003-07-01

    A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.

  7. Infrared and dc conductivity in metals with strong scattering: Nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects

    International Nuclear Information System (INIS)

    Allen, P.B.; Chakraborty, B.

    1981-01-01

    Metals with high resistivity (approx.100 μΩ cm) seem to show weaker variation of resistivity (as a function of temperature and perhaps also static disorder) than predicted by semiclassical (Bloch-Boltzmann) theory (SBT). We argue that the effect is not closely related to Anderson localization, and therefore does not necessarily signify a failure of the independent collision approximation. Instead we propose a failure of the semiclassical acceleration and conduction approximations. A generalization of Boltzmann theory is made which includes quantum (interband) acceleration and conduction, as well as a complete treatment of interband-collision effects (within the independent-collision approximation). The interband terms enhance short-time response to E fields (because the theory satisfies the exact f-sum rule instead of the semiclassical approximation to it). This suggests that the additional conductivity, as expressed phenomenologically by the shunt resistor model, is explained by interband effects. The scattering operator is complex, its imaginary parts being related to energy-band renormalization caused by the disorder. Charge conservation is respected and thermal equilibrium is restored by the collision operator. The theory is formally solved for the leading corrections to SBT, which have the form of a shunt resistor model. At infrared frequencies, the conductivity mostly obeys the Drude law sigma(ω)approx.sigma(0)(1-iωtau) -1 , except for one term which goes as (1-iωtau) -2

  8. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2006-01-01

    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

  9. Memory effects in relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Greiner, C.; Wagner, K.; Reinhard, P.

    1994-01-01

    We consider equilibration in relativistic nuclear dynamics starting from a nonequilibrium Green's-functions approach. The widely used Boltzmann-Uehling-Uhlenbeck equation is obtained only as the Markovian limit (i.e., negligible memory time). The actual memory time in energetic nuclear collisions turns out to be ∼2--3 fm/c, which interferes substantially with the time scale of the relaxation process. The memory kernels of the collision process will be presented. Because of their more involved structure, depending sensitively on the kinematical regime, both less and more stopping power is observed in the reaction compared to the Markovian description

  10. On the relativistic large-angle electron collision operator for runaway avalanches in plasmas

    Science.gov (United States)

    Embréus, O.; Stahl, A.; Fülöp, T.

    2018-02-01

    Large-angle Coulomb collisions lead to an avalanching generation of runaway electrons in a plasma. We present the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator. The relation to previous models for large-angle collisions is investigated, and their validity assessed. We present a form of the generalized collision operator which is suitable for implementation in a numerical kinetic equation solver, and demonstrate the effect on the runaway-electron growth rate. Finally we consider the reverse avalanche effect, where runaways are slowed down by large-angle collisions, and show that the choice of operator is important if the electric field is close to the avalanche threshold.

  11. Deviation from Boltzmann distribution in excited energy levels of singly-ionized iron in an argon glow discharge plasma for atomic emission spectrometry

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp

    2012-01-15

    A Boltzmann plot for many iron ionic lines having excitation energies of 4.7-9.1 eV was investigated in an argon glow discharge plasma when the discharge parameters, such as the voltage/current and the gas pressure, were varied. A Grimm-style radiation source was employed in a DC voltage range of 400-800 V at argon pressures of 400-930 Pa. The plot did not follow a linear relationship over a wide range of the excitation energy, but it yielded a normal Boltzmann distribution in the range of 4.7-5.8 eV and a large overpopulation in higher-lying excitation levels of iron ion. A probable reason for this phenomenon is that excitations for higher excited energy levels of iron ion would be predominantly caused by non-thermal collisions with argon species, the internal energy of which is received by iron atoms for the ionization. Particular intense ionic lines, which gave a maximum peak of the Boltzmann plot, were observed at an excitation energy of ca. 7.7 eV. They were the Fe II 257.297-nm and the Fe II 258.111-nm lines, derived from the 3d{sup 5}4s4p {sup 6}P excited levels. The 3d{sup 5}4s4p {sup 6}P excited levels can be highly populated through a resonance charge transfer from the ground state of argon ion, because of good matching in the excitation energy as well as the conservation of the total spin before and after the collision. An enhancement factor of the emission intensity for various Fe II lines could be obtained from a deviation from the normal Boltzmann plot, which comprised the emission lines of 4.7-5.8 eV. It would roughly correspond to a contribution of the charge transfer excitation to the excited levels of iron ion, suggesting that the charge-transfer collision could elevate the number density of the corresponding excited levels by a factor of ca.10{sup 4}. The Boltzmann plots give important information on the reason why a variety of iron ionic lines can be emitted from glow discharge plasmas.

  12. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

    International Nuclear Information System (INIS)

    Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.

    2016-01-01

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

  13. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

    Science.gov (United States)

    Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

    2016-01-07

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

  14. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

    Energy Technology Data Exchange (ETDEWEB)

    Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

    2016-01-07

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

  15. Electron kinetics with attachment and ionization from higher order solutions of Boltzmann's equation

    International Nuclear Information System (INIS)

    Winkler, R.; Wilhelm, J.; Braglia, G.L.

    1989-01-01

    An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF 6 . The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation. (author)

  16. Ludwig Boltzmann, mechanics and vitalism

    International Nuclear Information System (INIS)

    Broda, E.

    1990-01-01

    During most of his life Boltzmann considered classical mechanics, based on the ideas of material points and central forces, as the fundament of physics. On this basis he became one of the founders of Statistical Mechanics, through which thermodynamics was interpreted on an atomistic basis. In this work, Boltzmann was opposed by his colleague, Ernst Mach. Boltzmann also devoted much work to attempts to interpret Maxwell's theory of the electromagnetic field, of which he was a main protagonist in Central Europe, through mechanics. However, as a supporter of mechanics Boltzmann was by no means dogmatic. While he was adamant in his rejection of Wilhelm Ostwald's energism, he was openminded in respect to the relationship of mechanics, electromagnetism and atomistics. Personally, Boltzmann wanted to conserve and transmit the enormous achievements of mechanics, especially in connection with the mechanical theory of heat, so that these results should not be lost to future generations, but he encouraged attempts to proceed in new directions. While within the framework of statistical mechanics the atoms were treated like the material points of classical mechanics, Boltzmann resisted the initial, unwarranted, ideas about the structure and the properties of the atoms. When later valid ideas were evolved, Boltzmann warmly welcomed this progress, without however personally taking part in the new developments. In his later years, Boltzmann took an intense interest in biology. He supported Darwin's theories, and he contributed to them. He may be called an 'absolute Darwinist'. In his search for a natural explanation of the phenomena of life, he used the term 'mechanical', without meaning to limit them to the realm of classical mechanics. This terminological laxity is considered as unfortunate. Extending his application of Darwinian principles to advanced species, including man, Boltzmann put forward 'mechanical' explanations of thought, of morality, of the sense of beauty, and of

  17. Ludwig Boltzmann - pioneer of atomistics and evolution

    International Nuclear Information System (INIS)

    Stiller, W.

    1986-01-01

    At first a short introduction to Ludwig Boltzmann's life (1844 - 1906) and work is given. Some theoretical results of his work (H-theorem, classical Boltzmann statistics, Boltzmann's kinetic equation) are treated in detail. His experimental work is briefly discussed. In addition Boltzmann's philosophical work is characterized. Finally, the influence of Boltzmann's ideas on our time is investigated. (author)

  18. Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework

    KAUST Repository

    Neumann, Philipp

    2015-09-01

    © 2014 Elsevier Inc. All rights reserved. We present a dynamically adaptive Lattice Boltzmann (LB) implementation for solving the shallow water equations (SWEs). Our implementation extends an existing LB component of the Peano framework. We revise the modular design with respect to the incorporation of new simulation aspects and LB models. The basic SWE-LB implementation is validated in different breaking dam scenarios. We further provide a numerical study on stability of the MRT collision operator used in our simulations.

  19. Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

    International Nuclear Information System (INIS)

    Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.

    2015-01-01

    This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

  20. Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

    2015-07-01

    This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

  1. A new scheme for solving inhomogeneous Boltzmann equation for electrons in weakly ionised gases

    International Nuclear Information System (INIS)

    Mahmoud, M.O.M.; Yousfi, M.

    1995-01-01

    In the case of weakly ionized gases, the numerical treatment of non-hydrodynamic regime involving spatial variation of distribution function due to boundaries (walls, electrodes, electron source, etc hor-ellipsis) by using direct Boltzmann equation always constitute a challenge if the main collisional processes occurring in non thermal plasmas are to be considered (elastic, inelastic and super-elastic collisions, Penning ionisation, Coulomb interactions, etc hor-ellipsis). In the non-thermal discharge modelling, the inhomogeneous electron Boltzmann equation is needed in order to be coupled for example to a fluid model to take into account the electron non-hydrodynamic effects. This is for example the case of filamentary discharge, in which the space charge electric field due to streamer propagation has a very sharp spatial profile thus leading to important space non-hydrodynamic effects. It is also the case of the cathodic zone of glow discharge where electric field has a rapid spatial decrease until the negative glow. In the present work, a new numerical scheme is proposed to solve the inhomogeneous Boltzmann equation for electrons in the framework of two-term approximation (TTA) taking into account elastic and inelastic processes. Such a method has the usual drawbacks associated with the TTA i.e. not an accurate enough at high E/N values or in presence of high inelastic processes. But the accuracy of this method is considered sufficient because in a next step it is destinated to be coupled to fluid model for charged particles and a chemical kinetic model where the accuracy is of the same order of magnitude or worse. However there are numerous advantages of this method concerning time computing, treatment of non-linear collision processes (Coulomb, Penning, etc hor-ellipsis)

  2. The integral first collision kernel method for gamma-ray skyshine analysis[Skyshine; Gamma-ray; First collision kernel; Monte Carlo calculation

    Energy Technology Data Exchange (ETDEWEB)

    Sheu, R.-D.; Chui, C.-S.; Jiang, S.-H. E-mail: shjiang@mx.nthu.edu.tw

    2003-12-01

    A simplified method, based on the integral of the first collision kernel, is presented for performing gamma-ray skyshine calculations for the collimated sources. The first collision kernels were calculated in air for a reference air density by use of the EGS4 Monte Carlo code. These kernels can be applied to other air densities by applying density corrections. The integral first collision kernel (IFCK) method has been used to calculate two of the ANSI/ANS skyshine benchmark problems and the results were compared with a number of other commonly used codes. Our results were generally in good agreement with others but only spend a small fraction of the computation time required by the Monte Carlo calculations. The scheme of the IFCK method for dealing with lots of source collimation geometry is also presented in this study.

  3. Boltzmann, Einstein, Natural Law and Evolution

    International Nuclear Information System (INIS)

    Broda, E.

    1980-01-01

    Like Boltzmann, Einstein was a protagonist of atomistics. As a physicist, he has been called Boltzmann's true successor. Also in epistemology, after overcoming the positivist influence of Mach, Einstein approached Boltzmann. Any difference between Boltzmann's realism, or even materialism, and Einstein's pantheism may be merely a matter of emphasis. Yet a real difference exists in another respect. Boltzmann explained man's power of thinking and feeling, his morality and his esthetic sense, on an evolutionary, Darwinian, basis. In contrast, evolution had no role in Einstein's thought, though Darwin was accepted by him. This lack of appreciation of the importance of evolution is now attributed to socio-political factors. (author)

  4. The Boltzmann-Langevin Equation derived from the real-time path formalism

    International Nuclear Information System (INIS)

    Suraud, E.; Reinhard, P.G.

    1991-01-01

    We derive the Boltzmann-Langevin equation using Green's functions techniques in the real-time path formalism. We start from the Martin-Schwinger hierarchy and close it approximately at the two-body level. A careful discussion of the initial conditions for the free two-body Green's function provides the flexibility to recover the discarded correlations as fluctuations leading to the Langevin force. The derivation is generalized to the T-matrix approach which allows to prove that one can use the same effective interaction in the mean-field as well as in the collision term and Langevin force

  5. Dynamical scenario of intermediary mass fragments formation in heavy ion collisions

    International Nuclear Information System (INIS)

    Ayik, S.; Belkacem, M.; Gregoire, C.; Stryjewski, J.; Suraud, E.

    1989-01-01

    We briefly remind the possible dynamical scenario of fragments formation in heavy-ion collisions at some tens fo MeV/A. We discuss how present day dynamical models can describe fragment formation. We next turn to the Boltzmann-Langevin formalism which provides a well defined theoretical framework for the understanding of the growing of the dynamical instabilities leading to multifragmentation. We present a first numerical solution of the Boltzmann-Langevin equation and we apply the formalism to the onset of multifragmentation of the 40 Ca + 40 Ca system between 20 and 60 MeV/A beam energy [fr

  6. Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

    KAUST Repository

    Neumann, Philipp

    2012-01-01

    We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to fur-ther reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

  7. Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

    Science.gov (United States)

    Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

    2018-04-01

    The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

  8. Direct integration multiple collision integral transport analysis method for high energy fusion neutronics

    International Nuclear Information System (INIS)

    Koch, K.R.

    1985-01-01

    A new analysis method specially suited for the inherent difficulties of fusion neutronics was developed to provide detailed studies of the fusion neutron transport physics. These studies should provide a better understanding of the limitations and accuracies of typical fusion neutronics calculations. The new analysis method is based on the direct integration of the integral form of the neutron transport equation and employs a continuous energy formulation with the exact treatment of the energy angle kinematics of the scattering process. In addition, the overall solution is analyzed in terms of uncollided, once-collided, and multi-collided solution components based on a multiple collision treatment. Furthermore, the numerical evaluations of integrals use quadrature schemes that are based on the actual dependencies exhibited in the integrands. The new DITRAN computer code was developed on the Cyber 205 vector supercomputer to implement this direct integration multiple-collision fusion neutronics analysis. Three representative fusion reactor models were devised and the solutions to these problems were studied to provide suitable choices for the numerical quadrature orders as well as the discretized solution grid and to understand the limitations of the new analysis method. As further verification and as a first step in assessing the accuracy of existing fusion-neutronics calculations, solutions obtained using the new analysis method were compared to typical multigroup discrete ordinates calculations

  9. Determination of a basic set of Eigen-functions and of the corresponding norm in the case of the one-velocity integral differential Boltzmann equation in spherical geometry

    International Nuclear Information System (INIS)

    Lafore, P.

    1965-01-01

    The object of the present work is to draw up a basic set of orthogonal eigenfunctions; resolution of the one-velocity integral-differential Boltzmann equation; this in the case of a spherical geometry system. (author) [fr

  10. Limitations of Boltzmann's principle

    International Nuclear Information System (INIS)

    Lavenda, B.H.

    1995-01-01

    The usual form of Boltzmann's principle assures that maximum entropy, or entropy reduction, occurs with maximum probability, implying a unimodal distribution. Boltzmann's principle cannot be applied to nonunimodal distributions, like the arcsine law, because the entropy may be concave only over a limited portion of the interval. The method of subordination shows that the arcsine distribution corresponds to a process with a single degree of freedom, thereby confirming the invalidation of Boltzmann's principle. The fractalization of time leads to a new distribution in which arcsine and Cauchy distributions can coexist simultaneously for nonintegral degrees of freedom between √2 and 2

  11. Ludwig Boltzmann: Atomic genius

    Energy Technology Data Exchange (ETDEWEB)

    Cercignani, C. [Department of Mathematics, Politecnico di Milano (Italy)]. E-mail: carcer@mate.polimi.it

    2006-09-15

    On the centenary of the death of Ludwig Boltzmann, Carlo Cercignani examines the immense contributions of the man who pioneered our understanding of the atomic nature of matter. The man who first gave a convincing explanation of the irreversibility of the macroscopic world and the symmetry of the laws of physics was the Austrian physicist Ludwig Boltzmann, who tragically committed suicide 100 years ago this month. One of the key figures in the development of the atomic theory of matter, Boltzmann's fame will be forever linked to two fundamental contributions to science. The first was his interpretation of 'entropy' as a mathematically well-defined measure of the disorder of atoms. The second was his derivation of what is now known as the Boltzmann equation, which describes the statistical properties of a gas as made up of molecules. The equation, which described for the first time how a probability can evolve with time, allowed Boltzmann to explain why macroscopic phenomena are irreversible. The key point is that while microscopic objects like atoms can behave reversibly, we never see broken coffee cups reforming because it would involve a long series of highly improbable interactions - and not because it is forbidden by the laws of physics. (U.K.)

  12. Thermal, chemical and spectral equilibration in heavy-ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Almási, Gábor András, E-mail: g.almasi@gsi.de [Gesellschaft für Schwerionenforschung, GSI, D-64291 Darmstadt (Germany); Wolf, György, E-mail: wolf.gyorgy@wigner.mta.hu [Wigner RCP, Budapest (Hungary)

    2015-11-15

    We have considered the equilibration in relativistic heavy ion collisions at energies 1–7 A GeV using our transport model. We applied periodic boundary conditions to close the system in a box. We found that the thermal equilibration takes place in the first 20–40 fm/c whose time is comparable to the duration of a heavy ion collision. The chemical equilibration is a much slower process and the system does not equilibrate in a heavy ion collision. We have shown that in the testparticle simulation of the Boltzmann equation the mass spectra of broad resonances follow instantaneously their in-medium spectral functions as expected from the Markovian approximation to the Kadanoff–Baym equations employed via the (local) gradient expansion.

  13. Modification of reconstructed gamma-jets in heavy-ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Tan; He, Yayun; Wang, Enke [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Wang, Xin-Nian [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Nuclear Science Division Mailstop 70R0319, Lawrence Berkeley National Laboratory, Berkeley, CA 94740 (United States)

    2016-12-15

    We use the Linear Boltzmann Transport model to study gamma-triggered jets in high-energy heavy-ion collisions. Since both recoiled partons from elastic scattering and radiated gluons from inelastic processes and their further propagation are considered, the model can provide a description of not only the medium modification of reconstructed jets but also the energy flow in the underlying hydrodynamic background. In this study, we discuss the modification of jet shape and jet fragmentation function of γ-jet in central Pb+Pb collisions and in particular the energy flow induced by the jet-medium interaction.

  14. Accurate collision integrals for the attractive static screened Coulomb potential with application to electrical conductivity

    International Nuclear Information System (INIS)

    Macdonald, J.

    1991-01-01

    The results of accurate calculations of collision integrals for the attractive static screened Coulomb potential are presented. To obtain high accuracy with minimal computational cost, the integrals are evaluated by a quadrature method based on the Whittaker cardinal function. The collision integrals for the attractive potential are needed for calculation of the electrical conductivity of a dense fully or partially ionized plasma, and the results presented here are appropriate for the conditions in the nondegenerate envelopes of white dwarf stars. 25 refs

  15. Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

    Science.gov (United States)

    Servan-Camas, Borja; Tsai, Frank T.-C.

    2010-02-01

    This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

  16. Gli atomi di Boltzmann

    CERN Document Server

    Lindley, David

    2002-01-01

    Ludwig Boltzmann (1844-1906) è il fisico e matematico austriaco che negli ultimi decenni dell'Ottocento e ancora ai primi del Novecento lottò contro l'opinione dominante tra gli scienziati dell'epoca per affermare la teoria atomica della materia. È noto come con Albert Einstein e fino a oggi la fisica si sia sviluppata e abbia celebrato i propri trionfi lungo le linee anticipate da Boltzmann. La controversia con Mach non riguardava soltanto l'esistenza degli atomi, ma l'intero modo di fare fisica che Boltzmann non riteneva di dover limitare allo studio di quantità misurabili, introducendo invece spiegazioni più elaborate basate su ipotesi più ampie.

  17. Study of flow over object problems by a nodal discontinuous Galerkin-lattice Boltzmann method

    Science.gov (United States)

    Wu, Jie; Shen, Meng; Liu, Chen

    2018-04-01

    The flow over object problems are studied by a nodal discontinuous Galerkin-lattice Boltzmann method (NDG-LBM) in this work. Different from the standard lattice Boltzmann method, the current method applies the nodal discontinuous Galerkin method into the streaming process in LBM to solve the resultant pure convection equation, in which the spatial discretization is completed on unstructured grids and the low-storage explicit Runge-Kutta scheme is used for time marching. The present method then overcomes the disadvantage of standard LBM for depending on the uniform meshes. Moreover, the collision process in the LBM is completed by using the multiple-relaxation-time scheme. After the validation of the NDG-LBM by simulating the lid-driven cavity flow, the simulations of flows over a fixed circular cylinder, a stationary airfoil and rotating-stationary cylinders are performed. Good agreement of present results with previous results is achieved, which indicates that the current NDG-LBM is accurate and effective for flow over object problems.

  18. Lattice Boltzmann modeling an introduction for geoscientists and engineers

    CERN Document Server

    Sukop, Michael C

    2005-01-01

    Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.

  19. Nonaligned shocks for discrete velocity models of the Boltzmann equation

    Directory of Open Access Journals (Sweden)

    J. M. Greenberg

    1991-05-01

    Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

  20. Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows

    Energy Technology Data Exchange (ETDEWEB)

    Roohi, Ehsan, E-mail: e.roohi@ferdowsi.um.ac.ir; Stefanov, Stefan

    2016-10-25

    The motivation of this review paper is to present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method. The emphasis is put on a newly developed collision model, i.e., the Simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows. The paper starts with a brief review of the governing equations of the rarefied gas dynamics including Boltzmann and Kac master equations and reiterates that the linear Kac equation reduces to a non-linear Boltzmann equation under the assumption of molecular chaos. An introduction to the DSMC method is provided, and principles of collision algorithms in the DSMC are discussed. A distinction is made between those collision models that are based on classical kinetic theory (time counter, no time counter (NTC), and nearest neighbor (NN)) and the other class that could be derived mathematically from the Kac master equation (pseudo-Poisson process, ballot box, majorant frequency, null collision, Bernoulli trials scheme and its variants). To provide a deeper insight, the derivation of both collision models, either from the principles of the kinetic theory or the Kac master equation, is provided with sufficient details. Some discussions on the importance of subcells in the DSMC collision procedure are also provided and different types of subcells are presented. The paper then focuses on the simplified version of the Bernoulli trials algorithm (SBT) and presents a detailed summary of validation of the SBT family collision schemes (SBT on transient adaptive subcells: SBT-TAS, and intelligent SBT: ISBT) in a broad spectrum of rarefied gas-flow test cases, ranging from low speed, internal micro and nano flows to external hypersonic flow, emphasizing first the accuracy of these new collision models and second, demonstrating that the SBT family scheme, if compared to other conventional and recent collision models, requires smaller

  1. Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows

    International Nuclear Information System (INIS)

    Roohi, Ehsan; Stefanov, Stefan

    2016-01-01

    The motivation of this review paper is to present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method. The emphasis is put on a newly developed collision model, i.e., the Simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows. The paper starts with a brief review of the governing equations of the rarefied gas dynamics including Boltzmann and Kac master equations and reiterates that the linear Kac equation reduces to a non-linear Boltzmann equation under the assumption of molecular chaos. An introduction to the DSMC method is provided, and principles of collision algorithms in the DSMC are discussed. A distinction is made between those collision models that are based on classical kinetic theory (time counter, no time counter (NTC), and nearest neighbor (NN)) and the other class that could be derived mathematically from the Kac master equation (pseudo-Poisson process, ballot box, majorant frequency, null collision, Bernoulli trials scheme and its variants). To provide a deeper insight, the derivation of both collision models, either from the principles of the kinetic theory or the Kac master equation, is provided with sufficient details. Some discussions on the importance of subcells in the DSMC collision procedure are also provided and different types of subcells are presented. The paper then focuses on the simplified version of the Bernoulli trials algorithm (SBT) and presents a detailed summary of validation of the SBT family collision schemes (SBT on transient adaptive subcells: SBT-TAS, and intelligent SBT: ISBT) in a broad spectrum of rarefied gas-flow test cases, ranging from low speed, internal micro and nano flows to external hypersonic flow, emphasizing first the accuracy of these new collision models and second, demonstrating that the SBT family scheme, if compared to other conventional and recent collision models, requires smaller

  2. The Boltzmann project

    Science.gov (United States)

    Fischer, J.; Fellmuth, B.; Gaiser, C.; Zandt, T.; Pitre, L.; Sparasci, F.; Plimmer, M. D.; de Podesta, M.; Underwood, R.; Sutton, G.; Machin, G.; Gavioso, R. M.; Madonna Ripa, D.; Steur, P. P. M.; Qu, J.; Feng, X. J.; Zhang, J.; Moldover, M. R.; Benz, S. P.; White, D. R.; Gianfrani, L.; Castrillo, A.; Moretti, L.; Darquié, B.; Moufarej, E.; Daussy, C.; Briaudeau, S.; Kozlova, O.; Risegari, L.; Segovia, J. J.; Martín, M. C.; del Campo, D.

    2018-04-01

    The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649  ×  10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7  ×  10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

  3. Simulation of bubble motion under gravity by lattice Boltzmann method

    International Nuclear Information System (INIS)

    Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo

    2001-01-01

    We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method (LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single-and two-bubble motions, setting flow conditions according to the Eoetvoes and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two-bubble interaction of their approach and coalescence in circular tube. There results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity. (author)

  4. Multispeed models in off-lattice Boltzmann simulations

    NARCIS (Netherlands)

    Bardow, A.; Karlin, I.V.; Gusev, A.A.

    2008-01-01

    The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

  5. Unified solution of the Boltzmann equation for electron and ion velocity distribution functions and transport coefficients in weakly ionized plasmas

    Science.gov (United States)

    Konovalov, Dmitry A.; Cocks, Daniel G.; White, Ronald D.

    2017-10-01

    The velocity distribution function and transport coefficients for charged particles in weakly ionized plasmas are calculated via a multi-term solution of Boltzmann's equation and benchmarked using a Monte-Carlo simulation. A unified framework for the solution of the original full Boltzmann's equation is presented which is valid for ions and electrons, avoiding any recourse to approximate forms of the collision operator in various limiting mass ratio cases. This direct method using Lebedev quadratures over the velocity and scattering angles avoids the need to represent the ion mass dependence in the collision operator through an expansion in terms of the charged particle to neutral mass ratio. For the two-temperature Burnett function method considered in this study, this amounts to avoiding the need for the complex Talmi-transformation methods and associated mass-ratio expansions. More generally, we highlight the deficiencies in the two-temperature Burnett function method for heavy ions at high electric fields to calculate the ion velocity distribution function, even though the transport coefficients have converged. Contribution to the Topical Issue "Physics of Ionized Gases (SPIG 2016)", edited by Goran Poparic, Bratislav Obradovic, Dragana Maric and Aleksandar Milosavljevic.

  6. Lattice Boltzmann model for simulating immiscible two-phase flows

    International Nuclear Information System (INIS)

    Reis, T; Phillips, T N

    2007-01-01

    The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

  7. Determination of kinetic coefficients for proton-nucleus collisions at high energy

    International Nuclear Information System (INIS)

    Rizzato, C.M.

    1987-01-01

    From the effective proton dynamics, the approximations in the context of high energy collisions which lead to the Boltzmann equation, are established. From this equation, general expressions for the kinetic coefficients are deduced. Using a simple model, analytical expressions for kinetic coefficients are obtained. The importance of the effect of Pauli blocking is also shown. (author) [pt

  8. Lattice Boltzmann methods for global linear instability analysis

    Science.gov (United States)

    Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

    2017-12-01

    Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

  9. Collision integral and equilibrium distributions for a bounded plasma

    International Nuclear Information System (INIS)

    Zagorodnij, A.G.; Usenko, A.S.; Yakimenko, I.P.

    1985-01-01

    A kinetic equation of Balesku-Lennard type for multicomponent system of charged particle limited by two flat-parallel surfaces is derived on the basis of the general theory of electromagnetic fluctuations in plasma. Equilibrium values of collision integral for a plasma with arbitrary configuration boundaries are calculated and general ratios describing charged particles density profiles in such systems are obtained

  10. Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

    International Nuclear Information System (INIS)

    Hendriks, E.M.

    1983-01-01

    Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

  11. New analytical treatment for a kind of two dimensional integrals in ion-atom collisions

    International Nuclear Information System (INIS)

    Yang Qifeng; Kuang Yurang

    1994-01-01

    A kind of two-dimensional integrals, separated from two-center matrix elements in ion-atom collisions, is analytically integrated by introducing the Laplace transform into the integrals and expressed by the modified Bessel functions. The traditional Feynman transform is very complicated for this kind of more general integrals related to the excited state capture

  12. Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

    Directory of Open Access Journals (Sweden)

    Y. Peng

    2017-01-01

    Full Text Available Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

  13. Differential and integral cross sections in OH(X) + Xe collisions

    Energy Technology Data Exchange (ETDEWEB)

    Sarma, Gautam; Saha, Ashim Kumar; Meulen, J. J. ter; Parker, David H., E-mail: parker@science.ru.nl [Institute for Molecules and Materials, Radboud University Nijmegen, Heijendaalseweg 135, 6525 ED Nijmegen (Netherlands); Marinakis, Sarantos, E-mail: s.marinakis@qmul.ac.uk [School of Biological and Chemical Sciences, Queen Mary University of London, Joseph Priestley Building, Mile End Road, London E1 4NS (United Kingdom)

    2015-01-21

    Differential cross sections (DCSs) for inelastic collisions of OH(X) with Xe have been measured at a collision energy of 483 cm{sup −1}. The hydroxyl (OH) radicals were initially prepared in the X{sup 2}Π{sub 3/2} (v = 0, j = 1.5, f) level using the hexapole electric field selection method. Products were detected state-selectively by [2 + 1] resonance-enhanced multiphoton ionization of OH, combined with velocity-map imaging. Integral cross sections in OH(X) + Xe at a collision energy of 490 cm{sup −1} were also measured by laser-induced fluorescence. The results are compared with exact close-coupling quantum mechanical scattering calculations on the only available ab initio potential energy surface (PES). The agreement between experimental and theoretical results is generally very satisfactory. This highlights the ability of such measurements to test the available PES for such a benchmark open-shell system. The agreement between experiment and theory for DCSs is less satisfactory at low scattering angles, and possible reasons for this disagreement are discussed. Finally, theoretical calculations of OH(X) + He DCSs have been obtained at various collision energies and are compared with those of OH(X) + Xe. The role of the reduced mass in the DCSs and partial cross sections is also examined.

  14. Differential and integral cross sections in OH(X) + Xe collisions

    International Nuclear Information System (INIS)

    Sarma, Gautam; Saha, Ashim Kumar; Meulen, J. J. ter; Parker, David H.; Marinakis, Sarantos

    2015-01-01

    Differential cross sections (DCSs) for inelastic collisions of OH(X) with Xe have been measured at a collision energy of 483 cm −1 . The hydroxyl (OH) radicals were initially prepared in the X 2 Π 3/2 (v = 0, j = 1.5, f) level using the hexapole electric field selection method. Products were detected state-selectively by [2 + 1] resonance-enhanced multiphoton ionization of OH, combined with velocity-map imaging. Integral cross sections in OH(X) + Xe at a collision energy of 490 cm −1 were also measured by laser-induced fluorescence. The results are compared with exact close-coupling quantum mechanical scattering calculations on the only available ab initio potential energy surface (PES). The agreement between experimental and theoretical results is generally very satisfactory. This highlights the ability of such measurements to test the available PES for such a benchmark open-shell system. The agreement between experiment and theory for DCSs is less satisfactory at low scattering angles, and possible reasons for this disagreement are discussed. Finally, theoretical calculations of OH(X) + He DCSs have been obtained at various collision energies and are compared with those of OH(X) + Xe. The role of the reduced mass in the DCSs and partial cross sections is also examined

  15. Novel diagrammatic method for computing transport coefficients - beyond the Boltzmann approximation

    International Nuclear Information System (INIS)

    Hidaka, Y.; Kunihiro, T.

    2010-01-01

    We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. Our method is based on a reformulation and extension of the diagrammatic method by Eliashberg given in the imaginary-time formalism to the relativistic quantum field theory in the real-time formalism, in which the cumbersome analytical continuation problem can be avoided. The transport coefficients are obtained from a two-point function via Kubo formula. It is know that naive perturbation theory breaks down owing to a so called pinch singularity, and hence a resummation is required for getting a finite and sensible result. As a novel resummation method, we first decompose the two point function into the singular part and the regular part, and then reconstruct the diagrams. We find that a self-consistent equation for the two-point function has the same structure as the linearized Boltzmann equation. It is known that the two-point function at the leading order is equivalent to the linearized Boltzmann equation. We find the higher order corrections are nicely summarized as a renormalization of the vertex function, spectral function, and collision term. We also discuss the critical behavior of the transport coefficients near a phase transition, applying our method. (author)

  16. An introduction to the theory of the Boltzmann equation

    CERN Document Server

    Harris, Stewart

    2011-01-01

    Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes

  17. Kinetic theory of cross-modulation in a weakly ionized plasma

    International Nuclear Information System (INIS)

    Garrett, A.J.M.

    1991-01-01

    Cross-modulation in plasma is an electromagnetic wave interaction in which the modulation of one 'disturbing' wave is imposed nonlinearly on the transport properties of the medium, and thence onto a second, 'wanted' wave propagating linearly through it. This analysis is restricted to weakly ionized plasma with allowance for ambient magnetic field, as in the lower ionosphere. A kinetic description is used, based on the Boltzmann equation for the electrons, with electron-molecule collisions described by Boltzmann's collision integral. Because of the small mass ratio this simplifies to a differential form. There is no cross-modulation if the collision frequency is independent of collision speed, when contributions from all parts of velocity space cancel. (author)

  18. Soft-Deep Boltzmann Machines

    OpenAIRE

    Kiwaki, Taichi

    2015-01-01

    We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs over RBMs has not ever been validated in a theoretical fashion. In this paper, we provide both theoretical and empirical evidences that the representational power of DBMs can be a...

  19. Topology optimization and lattice Boltzmann methods

    DEFF Research Database (Denmark)

    Nørgaard, Sebastian Arlund

    This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

  20. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

    Science.gov (United States)

    Li, Weidong

    2017-09-01

    This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

  1. Joint Training of Deep Boltzmann Machines

    OpenAIRE

    Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua

    2012-01-01

    We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.

  2. Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function

    International Nuclear Information System (INIS)

    Mao, G.; Li, Z.; Zhuo, Y.

    1996-01-01

    We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society

  3. Combinatorial optimization on a Boltzmann machine

    NARCIS (Netherlands)

    Korst, J.H.M.; Aarts, E.H.L.

    1989-01-01

    We discuss the problem of solving (approximately) combinatorial optimization problems on a Boltzmann machine. It is shown for a number of combinatorial optimization problems how they can be mapped directly onto a Boltzmann machine by choosing appropriate connection patterns and connection strengths.

  4. On Descriptions of Particle Transverse Momentum Spectra in High Energy Collisions

    Directory of Open Access Journals (Sweden)

    Fu-Hu Liu

    2014-01-01

    is obtained that, at a given set of parameters, the standard distributions show a narrower shape than their Tsallis forms which result in wide and/or multicomponent spectra with the Tsallis distribution in between. A comparison among the temperatures obtained from the distributions is made with a possible relation to the Boltzmann temperature. An example of the angular distributions of projectile fragments in nuclear collisions is given.

  5. Theory of conductivity of chiral particles

    International Nuclear Information System (INIS)

    Kailasvuori, Janik; Šopík, Břetislav; Trushin, Maxim

    2013-01-01

    In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with an N-fold chiral twist that arises in a low-energy description of charge carriers in rhombohedrally stacked multilayer graphene. To understand the role of chirality in the conductivity of such particles we also consider the artificial model with the chiral winding number decoupled from the power of the dispersion. We first utilize the approximate but analytically solvable band-coherent Boltzmann approach including the ill-understood principal value terms that are a byproduct of several quantum many-body theory derivations of Boltzmann collision integrals. Further on, we employ the finite-size Kubo formula with the exact diagonalization of the total Hamiltonian perturbed by disorder. Finally, we compare several choices of Ansatz in the derivation of the Boltzmann equation according to the qualitative agreement between the Boltzmann and Kubo conductivities. We find that the best agreement can be reached in the approach where the principal value terms in the collision integral are absent. (paper)

  6. THREE-DIMENSIONAL BOLTZMANN HYDRO CODE FOR CORE COLLAPSE IN MASSIVE STARS. I. SPECIAL RELATIVISTIC TREATMENTS

    International Nuclear Information System (INIS)

    Nagakura, Hiroki; Sumiyoshi, Kohsuke; Yamada, Shoichi

    2014-01-01

    We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M ☉ progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method

  7. Nuclear shape evolution starting from superdeformed state. Role of two-body collision and rotation

    International Nuclear Information System (INIS)

    Liu, Yu-xin; Sakata, Fumihiko

    1999-01-01

    With the nuclear density distribution being simulated by the Boltzmann Uehling-Uhlenbeck equation and Vlasov equation with several rotational frequencies, the time evolution of the quadrupole moment of nucleus 86 Zr starting with superdeformed shape is studied. The contribution of two-body collisions and the effects of collective rotation to the shape evolution is investigated. The numerical results indicate that the two-body collisions play a role of damping on the evolution from a superdeformed shape to a normal deformed one in a case without rotation. In a case of rotation with lower frequency, the two-body collisions accelerate the evolution process. A new role of the collective rotation to enhance the nuclear fission is proposed. (author)

  8. Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

    Science.gov (United States)

    Asinari, Pietro

    2010-10-01

    .gz Programming language: Tested with Matlab version ⩽6.5. However, in principle, any recent version of Matlab or Octave should work Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: 300 MBytes Classification: 23 Nature of problem: The problem consists in integrating the homogeneous Boltzmann equation for a generic collisional kernel in case of isotropic symmetry, by a deterministic direct method. Difficulties arise from the multi-dimensionality of the collisional operator and from satisfying the conservation of particle number and energy (momentum is trivial for this test case) as accurately as possible, in order to preserve the late dynamics. Solution method: The solution is based on the method proposed by Aristov (2001) [1], but with two substantial improvements: (a) the original problem is reformulated in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium). Both these corrections make possible to derive very accurate reference solutions for this test case. Restrictions: The nonlinear Boltzmann equation is extremely challenging from the computational point of view, in particular for deterministic methods, despite the increased computational power of recent hardware. In this work, only the homogeneous isotropic case is considered, for making possible the development of a minimal program (by a simple scripting language) and allowing the user to check the advantages of the proposed improvements beyond Aristov's (2001) method [1]. The initial conditions are supposed parameterized according to a fixed analytical expression, but this can be

  9. Closed form formula for the exchange integrals in the impact-parameter treatment of heavy-particle collisions

    International Nuclear Information System (INIS)

    Kocbach, Ladislav; Liska, Richard

    1994-01-01

    The three-dimensional exchange integrals in the impact-parameter treatment of heavy particle collisions can be transformed to one-dimensional integrals over finite range. The closed form formula for the integrands of these one-dimensional integrals is derived. (Author)

  10. The convergence of parallel Boltzmann machines

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.; Eckmiller, R.; Hartmann, G.; Hauske, G.

    1990-01-01

    We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular

  11. Parallel Boltzmann machines : a mathematical model

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.

    1991-01-01

    A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

  12. Ethic and Evolution in Boltzmann's and Einstein's Thought

    Energy Technology Data Exchange (ETDEWEB)

    Broda, E.

    1980-07-01

    In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

  13. Ethic and Evolution in Boltzmann's and Einstein's Thought

    International Nuclear Information System (INIS)

    Broda, E.

    1980-01-01

    In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

  14. Application of the non-extensive statistical approach to high energy particle collisions

    Science.gov (United States)

    Bíró, Gábor; Barnaföldi, Gergely Gábor; Biró, Tamás Sándor; Ürmössy, Károly

    2017-06-01

    In high-energy collisions the number of created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution are appreciable. As a consequence the characterization of identified hadron spectra with the Boltzmann - Gibbs thermodynamical approach is insuffcient [1]. Instead particle spectra measured in high-energy collisions can be described very well with Tsallis -Pareto distributions, derived from non-extensive thermodynamics [2, 3]. Using the Tsallis q-entropy formula, a generalization of the Boltzmann - Gibbs entropy, we interpret the microscopic physics by analysing the Tsallis q and T parameters. In this paper we give a quick overview on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species. Our findings are described well by a QCD inspired evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and barionic components found to be non-extensive (q > 1), beside the mass ordered hierarchy observed in parameter T.

  15. Celebrating Cercignani's conjecture for the Boltzmann equation

    KAUST Repository

    Villani, Cé dric; Mouhot, Clé ment; Desvillettes, Laurent

    2011-01-01

    Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.

  16. Spin effects in intermediate-energy heavy-ion collisions

    International Nuclear Information System (INIS)

    Xu Jun; Li Baoan; Xia Yin; Shen Wenqing

    2014-01-01

    In this paper, we report and extend our recent work where the nucleon spin-orbit interaction and its spin degree of freedom were introduced explicitly for the first time in the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model for heavy-ion reactions. Despite of the significant cancellation of the time-even and time-odd spin-related mean-field potentials from the spin-orbit interaction,an appreciable local spin polarization is observed in heavy-ion collisions at intermediate energies because of the dominating role of the time-odd terms. It is also found that the spin up-down differential transverse flow in heavy-ion collisions is a useful probe of the strength, density dependence, and isospin dependence of the in-medium spin-orbit interaction, and its magnitude is still considerable even at smaller systems. (authors)

  17. Exploring cluster Monte Carlo updates with Boltzmann machines.

    Science.gov (United States)

    Wang, Lei

    2017-11-01

    Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

  18. Exploring cluster Monte Carlo updates with Boltzmann machines

    Science.gov (United States)

    Wang, Lei

    2017-11-01

    Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

  19. Doubly charmed baryon production in heavy ion collisions

    Science.gov (United States)

    Yao, Xiaojun; Müller, Berndt

    2018-04-01

    We give an estimate of Ξcc ++ production rate and transverse momentum spectra in relativistic heavy ion collisions. We use Boltzmann transport equations to describe the dynamical evolution of charm quarks and diquarks inside quark-gluon plasma. In-medium formation and dissociation rates of charm diquarks are calculated from potential nonrelativistic QCD for the diquark sector. We solve the transport equations by Monte Carlo simulations. For 2.76 TeV Pb-Pb collisions with 0-10% centrality, the number of Ξcc ++ produced in the transverse momentum range 0-5 GeV and rapidity from -1 to 1 is roughly 0.02 per collision. We repeat the calculation with a melting temperature 250 MeV above which no diquarks can be formed. The number of Ξcc ++ produced in the same kinematic region is about 0.0125 per collision. We discuss how to study diquarks at finite temperature on a lattice and construct the antitriplet free energy in a gauge invariant but path dependent way. We also comment on extensions of the calculation to other doubly heavy baryons and doubly heavy tetraquarks and the feasibility of experimental measurements.

  20. Electron collision cross sections and electron swarm parameters for gas molecules

    International Nuclear Information System (INIS)

    Hayashi, Makoto

    1986-01-01

    Elastic and inelastic electron collision cross sections for molecules which interest in radiation research have been determined from available electron beam and electron swarm data by utilizing the Boltzmann equation and Monte Carlo simulation method. Electron drift velocity data which interest in radiation Pysics have been discussed and some calculated results of electron drift velocity data for CF 4 and CF 4 -inert gases mixtures will be presented. (author)

  1. Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method

    KAUST Repository

    Ibrahem, Ahmed M.

    2017-05-04

    In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatangar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103to105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

  2. A note on Boltzmann brains

    Energy Technology Data Exchange (ETDEWEB)

    Nomura, Yasunori, E-mail: ynomura@berkeley.edu

    2015-10-07

    Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except for the one imposed by the Poincaré recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.

  3. High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mozolevski, I.E.

    2001-01-01

    We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

  4. Compressible fluids with Maxwell-type equations, the minimal coupling with electromagnetic field and the Stefan–Boltzmann law

    Energy Technology Data Exchange (ETDEWEB)

    Mendes, Albert C.R., E-mail: albert@fisica.ufjf.br [Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora - MG (Brazil); Takakura, Flavio I., E-mail: takakura@fisica.ufjf.br [Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora - MG (Brazil); Abreu, Everton M.C., E-mail: evertonabreu@ufrrj.br [Grupo de Física Teórica e Matemática Física, Departamento de Física, Universidade Federal Rural do Rio de Janeiro, 23890-971, Seropédica - RJ (Brazil); Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora - MG (Brazil); Neto, Jorge Ananias, E-mail: jorge@fisica.ufjf.br [Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora - MG (Brazil)

    2017-05-15

    In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac’s constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge condition were obtained. The path integral formalism was used to obtain the partition function for the corresponding higher-derivative Hamiltonian and the Faddeev–Popov ansatz was used to construct an effective Lagrangian. Through the partition function, a Stefan–Boltzmann type law was obtained. - Highlights: • Higher-derivative Lagrangian for a charged fluid. • Electromagnetic coupling and Dirac’s constraint analysis. • Partition function through path integral formalism. • Stefan–Boltzmann-kind law through the partition function.

  5. Kinetic parameters, collision rates, energy exchanges and transport coefficients of non-thermal electrons in premixed flames at sub-breakdown electric field strengths

    KAUST Repository

    Bisetti, Fabrizio; El Morsli, Mbark

    2014-01-01

    The effects of an electric field on the collision rates, energy exchanges and transport properties of electrons in premixed flames are investigated via solutions to the Boltzmann kinetic equation. The case of high electric field strength, which

  6. Expansion, thermalization, and entropy production in high-energy nuclear collisions

    International Nuclear Information System (INIS)

    Heiselberg, H.; Wang, X.

    1996-01-01

    The thermalization process is studied in an expanding parton gas using the Boltzmann equation with two types of collision terms. In the relaxation time approximation we determine the criteria under which a time-dependent relaxation time leads to thermalization of the partons. We calculate the entropy production due to collisions for the general time-dependent relaxation time. In a perturbative QCD approach on the other hand, we can, given the initial conditions, estimate the effective relaxation time due to elastic collisions; this will be an upper limit only since radiative processes will also contribute to thermalization. We find that the parton gas does thermalize eventually but only after having undergone a phase of free streaming and gradual equilibration where considerable entropy is produced (open-quote open-quote after burning close-quote close-quote). The final entropy and thus particle density depends on the collision time as well as the initial conditions (a open-quote open-quote memory effect close-quote close-quote). Results for entropy production are presented based upon various model estimates of early parton production. copyright 1996 The American Physical Society

  7. The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1981-01-01

    These four men were influential in the transition from classical to modern physics. They interacted as scientists, often antagonistically. Thus Boltzmann was the greatest champion of the atom, while Mach remained unconvinced all his life. As a aphysicist, Einstein was greatly influenced by both Mach and Boltzmann, although Mach in the end rejected relativity as well. Because of his work on statistical mechanics, fluctuations, and quantum theory, Einstein has been called the natural successor to Boltzmann. Planck also was influenced by Mach at first. Hence he and Boltzmann were adversaries antil Planck converted to atomistics in 1900 and used the statistical interpretation of entropy to establish his radiation law. Planck accepted relativity early, but in quantum theory he was for a long time partly opposed to Einstein, and vice versa - Einstein considered Planck's derivation of his radiation law as unsound, while Planck could not accept the light quantum. In the case of all four physicists, science was interwoven with philosophy. Boltzmann consistently fought Mach's positivism, while Planck and Einstein moved from positivism to realism. All were also, though in very different ways, actively interested in public affairs. (orig.)

  8. Accurate collision integrals for the attractive static screened Coulomb potential with application to electrical conductivity. [For white dwarf stars

    Energy Technology Data Exchange (ETDEWEB)

    Macdonald, J. (Delaware, University, Newark (USA))

    1991-05-01

    The results of accurate calculations of collision integrals for the attractive static screened Coulomb potential are presented. To obtain high accuracy with minimal computational cost, the integrals are evaluated by a quadrature method based on the Whittaker cardinal function. The collision integrals for the attractive potential are needed for calculation of the electrical conductivity of a dense fully or partially ionized plasma, and the results presented here are appropriate for the conditions in the nondegenerate envelopes of white dwarf stars. 25 refs.

  9. Pruning Boltzmann networks and hidden Markov models

    DEFF Research Database (Denmark)

    Pedersen, Morten With; Stork, D.

    1996-01-01

    We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...

  10. Boltzmann equations for a binary one-dimensional ideal gas.

    Science.gov (United States)

    Boozer, A D

    2011-09-01

    We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

  11. Monte Carlo variance reduction approaches for non-Boltzmann tallies

    International Nuclear Information System (INIS)

    Booth, T.E.

    1992-12-01

    Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed

  12. A cryofuge for cold-collision experiments with slow polar molecules

    Science.gov (United States)

    Wu, Xing; Gantner, Thomas; Koller, Manuel; Zeppenfeld, Martin; Chervenkov, Sotir; Rempe, Gerhard

    2017-11-01

    Ultracold molecules represent a fascinating research frontier in physics and chemistry, but it has proven challenging to prepare dense samples at low velocities. Here, we present a solution to this goal by means of a nonconventional approach dubbed cryofuge. It uses centrifugal force to bring cryogenically cooled molecules to kinetic energies below 1 K × kB in the laboratory frame, where kB is the Boltzmann constant, with corresponding fluxes exceeding 1010 per second at velocities below 20 meters per second. By attaining densities higher than 109 per cubic centimeter and interaction times longer than 25 milliseconds in samples of fluoromethane as well as deuterated ammonia, we observed cold dipolar collisions between molecules and determined their collision cross sections.

  13. Head-on collisions of electrostatic solitons in multi-ion plasmas

    International Nuclear Information System (INIS)

    Verheest, Frank; Hellberg, Manfred A.; Hereman, Willy A.

    2012-01-01

    Head-on collisions between two electrostatic solitons are dealt with by the Poincaré-Lighthill-Kuo method of strained coordinates, for a plasma composed of a number of cold (positive and negative) ion species and Boltzmann electrons. The nonlinear evolution equations for both solitons and their phase shift due to the collision, resulting in time delays, are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is special enough to replace the quadratic by a cubic nonlinearity in the evolution equations, with concomitant repercussions on the phase shifts. Applications include different two-ion plasmas, showing positive or negative polarity solitons in the generic case. At critical composition, a combination of a positive and a negative polarity soliton is possible.

  14. Boltzmann und das Ende des mechanistischen Weltbildes

    CERN Document Server

    Renn, Jürgen

    2007-01-01

    Der Wissenschaftshistoriker und Physiker Jürgen Renn untersucht die Rolle des österreichischen Physikers und Philosophen Ludwig Boltzmann (18441906) bei der Entwicklung der modernen Physik. Boltzmann war einer der letzen Vertreter des mechanistischen Weltbildes und stand somit am Ende eines Zeitalters. Renn porträtiert den Wissenschaftler aber als einen Pionier der modernen Physik, dessen Beschäftigung mit den inneren Spannungen der klassischen Physik ihn visionär zukünftige Fragestellungen aufgreifen ließ. So befasste sich Boltzmann etwa mit den Grenzproblemen zwischen Mechanik und Thermodynamik, die ihn zur Entwicklung immer raffinierterer Instrumente der statistischen Physik antrieb, die schließlich zu Schlüsselinstrumenten der modernen Physik wurden. Boltzmanns Werk steht somit am Übergang vom mechanistischen Weltbild zur Relativitäts- und Quantentheorie. Der Aussage des viel bekannteren Physikers Albert Einstein, dass Fantasie wichtiger sei als Wissen, hält Jürgen Renn im Hinblick auf Leben ...

  15. Model of a plasma without collisions in a cylindrical geometry by the study of the motions of the particles (1960); Modele d'un plasma sans collisions dans une geometrie cylindrique par l'etude des mouvements de particules (1960)

    Energy Technology Data Exchange (ETDEWEB)

    Rebut, P H [Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee

    1960-07-01

    The Boltzmann equation for a group of particles in the absence of collisions may be written df/dt = 0, where f is the distribution function in the phase space. This equation means that f is an individual motion constant. This leads to a study, of the paths and to a research of the first integrals of the differential system related to them. This study leads also to a confinement condition on the velocities of a particle. The following step is related to the theoretical study of some distribution functions and of the resulting consequences. A differential system is obtained, giving density and magnetic and electric fields. This system has been in a number of cases solved by a digital computer. This solution allows an experimental comparison to be made. The first integrals obtained are still valid when magnetic 'screw-type' fields are concerned, which results in the obtention of a type of helicoidal deformation and of a stability criteria with respect to these deformations. (author) [French] L'equation de Boltzmann pour un groupe de particules en l'absence de collision peut s'ecrire df/dt = 0, ou f est la fonction de distribution dans l'espace des phases. Cette equation signifie que f est une constante du mouvement individuel. On est donc amene a etudier les trajectoires et a rechercher des integrales premieres du systeme differentiel qui leur est lie; cette etude conduit aussi a une condition de confinement portant sur les vitesses d'une particule. L'etape suivante se rapporte a l'etude theorique de certaines fonctions de distribution et des consequences qui en decoulent. On arrive a un systeme differentiel donnant densite, champs magnetiques et electriques, systeme qui a ete resolu dans un certain nombre de cas par une machine a calculer digitale. Cette resolution permet une confrontation experimentale. Les integrales premieres obtenues restent encore valables lors de champs magnetiques en 'vis'; il en resulte l'obtention d'un type de deformation helicoidale et d

  16. Kinetic solvers with adaptive mesh in phase space

    Science.gov (United States)

    Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.

    2013-12-01

    An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

  17. The polaron problem and the Boltzmann equation

    International Nuclear Information System (INIS)

    Devreese, J.

    1979-01-01

    A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

  18. Non-markovian boltzmann equation

    International Nuclear Information System (INIS)

    Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.

    1997-01-01

    A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc

  19. Boltzmann-Gaussian transition under specific noise effect

    International Nuclear Information System (INIS)

    Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai

    2014-01-01

    It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.

  20. Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport

    Science.gov (United States)

    Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; Hilpert, Markus

    2017-11-01

    The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.

  1. Strange hadrons and antiprotons as probes of hot and dense nuclear matter in relativistic heavy-ion collisions; Seltsame Hadronen und Antiprotonen als Proben heisser und dichter Kernmaterie in relativistischen Schwerionenkollisionen

    Energy Technology Data Exchange (ETDEWEB)

    Schade, Henry

    2010-09-15

    Strange particles play an important role as probes of relativistic heavy-ion collisions where hot and dense matter is studied. The focus of this thesis is on the production of strange particles within a transport model of Boltzmann-Uehling-Uhlenbeck (BUU) type. Current data of the HADES Collaboration concerning K{sup {+-}} and {phi} spectra provide the appropriate experimental framework. Moreover, the double-strange hyperon {xi}{sup -} is analyzed below the free NN production threshold. Hadron multiplicities, transversemomentum and rapidity spectra are compared with recent experimental data. Further important issues are in-medium mass shifts, the nuclear equation of state as well as the mean field of nucleons. Besides the study of AA collisions a comparison with recent ANKE data regarding the {phi} yield in pA collisions is done. Transparency ratios are determined and primarily investigated for absorption of {phi} mesons by means of the BUU transport code. Thereby, secondary {phi} production channels, isospin asymmetry and detector acceptance are important issues. A systematic analysis is presented for different system sizes. The momentum integrated Boltzmann equations describe dense nuclear matter on a hadronic level appearing in the Big Bang as well as in little bangs, in the context of kinetic off-equilibrium dynamics. This theory is applied to antiprotons and numerically calculated under consideration of various expansion models. Here, the evolution of proton- and antiproton densities till freeze-out is analyzed for ultra-relativistic heavy-ion collisions within a hadrochemic resonance gas model acting as a possible ansatz for solving the ''antiproton puzzle''. Furthermore, baryonic matter and antimatter is investigated in the early universe and the adiabatic path of cosmic matter is sketched in the QCD phase diagram. (orig.)

  2. Ludwig Boltzmann - The Man and His Work

    International Nuclear Information System (INIS)

    Broda, E.

    1982-01-01

    It is argued that Ludwig Boltzmann was, along with Newton and Maxwell, one of the three greatest theoretical physicists of classical times. It is less generally known that he was also a powerful realist-materialist philosopher and a keen opponent of Ernst Mach's positivism and of the philosophical idealism of Berkeley, Hegel and Schopenhauer. Boltzmann was also opposed to Kant. Moreover, he had a lively interest in biology and especially in Darwinian evolution, and he should be taken as one of the founders of biophysics. Boltzmann discussed the origin of life and of the mind. Finally, he also was a most vigorous, colourful and attractive person. (author)

  3. Comparative study on contribution of charge-transfer collision to excitations of iron ion between argon radio-frequency inductively-coupled plasma and nitrogen microwave induced plasma

    Energy Technology Data Exchange (ETDEWEB)

    Satoh, Kozue; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp

    2015-06-01

    This paper describes an ionization/excitation phenomenon of singly-ionized iron occurring in an Okamoto-cavity microwave induced plasma (MIP) as well as an argon radio-frequency inductively-coupled plasma (ICP), by comparing the Boltzmann distribution among iron ionic lines (Fe II) having a wide range of the excitation energy from 4.76 to 9.01 eV. It indicated in both the plasmas that plots of Fe II lines having lower excitation energies (4.76 to 5.88 eV) were fitted on each linear relationship, implying that their excitations were caused by a dominant thermal process such as collision with energetic electron. However, Fe II lines having higher excitation energies (more than 7.55 eV) had a different behavior from each other. In the ICP, Boltzmann plots of Fe II lines assigned to the higher excited levels also followed the normal Boltzmann relationship among the low-lying excited levels, even including a deviation from it in particular excited levels having an excitation energy of ca. 7.8 eV. This deviation can be attributed to a charge-transfer collision with argon ion, which results in the overpopulation of these excited levels, but the contribution is small. On the other hand, the distribution of the high-lying excited levels was non-thermal in the Okamoto-cavity MIP, which did not follow the normal Boltzmann relationship among the low-lying excited levels. A probable reason for the non-thermal characteristics in the MIP is that a charge-transfer collision with nitrogen molecule ion having many vibrational/rotational levels could work for populating the 3d{sup 6}4p (3d{sup 5}4s4p) excited levels of iron ion broadly over an energy range of 7.6–9.0 eV, while collisional excitation by energetic electron would occur insufficiently to excite these high-energy levels. - Highlights: • This paper describes the excitation mechanism of iron ion in Okamoto-cavity MIP in comparison with conventional ICP. • Boltzmann distribution is studied among iron ionic lines of

  4. Diffusion equations and hard collisions in multiple scattering of charged particles

    International Nuclear Information System (INIS)

    Papiez, Lech; Tulovsky, Vladimir

    1998-01-01

    The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities

  5. Diffusion equations and hard collisions in multiple scattering of charged particles

    Energy Technology Data Exchange (ETDEWEB)

    Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States); Tulovsky, Vladimir [Department of Mathematics, St. John' s College, Staten Island, New York, NY (United States)

    1998-09-01

    The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities.

  6. Central moments of ion implantation distributions derived by the backward Boltzmann transport equation compared with Monte Carlo simulations

    International Nuclear Information System (INIS)

    Bowyer, M.D.J.; Ashworth, D.G.; Oven, R.

    1992-01-01

    In this paper we study solutions to the backward Boltzmann transport equation (BBTE) specialized to equations governing moments of the distribution of ions implanted into amorphous targets. A central moment integral equation set has been derived starting from the classical plane source BBTE for non-central moments. A full generator equation is provided to allow construction of equation sets of an arbitrary size, thus allowing computation of moments of arbitrary order. A BBTE solver program has been written that uses the residual correction technique proposed by Winterbon. A simple means is presented to allow direct incorporation of Biersack's two-parameter ''magic formula'' into a BBTE solver program. Results for non-central and central moment integral equation sets are compared with Monte Carlo simulations, using three different formulae for the mean free flight path between collisions. Comparisons are performed for the ions B and As, implanted into the target a-Si, over the energy range 1 keV-1 MeV. The central moment integral equation set is found to have superior convergence properties to the non-central moment equation set. For As ions implanted into a-Si, at energies below ∼ 30 keV, significant differences are observed, for third- and fourth-order moments, when using alternative versions for the mean free flight path. Third- and fourth-order moments derived using one- and two-parameter scattering mechanisms also show significant differences over the same energy range. (Author)

  7. Semi-classical approaches to the phase space evolutions in intermediate energy heavy ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Remaud, B; Sebille, F; Raffray, Y; Gregoire, C; Vinet, L

    1986-01-06

    The properties of semi-classical phase space evolution equations - as the Vlasov/Boltzmann equations - are discussed in the context of the heavy ion reaction theory at intermediate energies (from 10 to 100 MeV per nucleon). The generalized coherent state set is shown to form a (over) complete basis for the phase space; then every solution of the Vlasov/Boltzmann equations can be defined as a convolution product of the generalized coherent state basis by an appropriate weight function w. The uniform approximation for w is shown to provide an accurate semi-classical description of fermion systems in their ground state: the examples of fermions in a harmonic well and of cold nuclei are discussed. The solution of the Vlasov equation amounts to follow the time evolution of the coherent states which play the role of a moving basis. For the Boltzmann equation, the collision term is taken into account by explicit or implicit variations of the function w. Typical applications are discussed: nuclear response to the giant monopole resonance excitation, fast nucleon emission in heavy-ion reactions. (orig.).

  8. Global existence proof for relativistic Boltzmann equation

    International Nuclear Information System (INIS)

    Dudynski, M.; Ekiel-Jezewska, M.L.

    1992-01-01

    The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions

  9. Quantum Heat Engine and Negative Boltzmann Temperature

    International Nuclear Information System (INIS)

    Xi Jing-Yi; Quan Hai-Tao

    2017-01-01

    To clarify the ambiguity on negative Boltzmann temperature in literature, we study the Carnot and the Otto cycle with one of the heat reservoirs at the negative Boltzmann temperature based on a canonical ensemble description. The work extraction, entropy production and the efficiency of these cycles are explored. Conditions for constructing and properties of these thermodynamic cycles are elucidated. We find that the apparent “violation” of the second law of thermodynamics in these cycles are due to the fact that the traditional definition of thermodynamic efficiency is inappropriate in this situation. When properly understanding the efficiency and the adiabatic processes, in which the system crosses over “absolute ZERO” in a limit sense, the Carnot cycle with one of the heat reservoirs at a negative Boltzmann temperature can be understood straightforwardly, and it contradicts neither the second nor the third law of thermodynamics. Hence, negative Boltzmann temperature is a consistent concept in thermodynamics. We use a two-level system and an Ising spin system to illustrate our central results. (paper)

  10. Boltzmann machines as a model for parallel annealing

    NARCIS (Netherlands)

    Aarts, E.H.L.; Korst, J.H.M.

    1991-01-01

    The potential of Boltzmann machines to cope with difficult combinatorial optimization problems is investigated. A discussion of various (parallel) models of Boltzmann machines is given based on the theory of Markov chains. A general strategy is presented for solving (approximately) combinatorial

  11. Polar pattern formation in driven filament systems requires non-binary particle collisions

    Science.gov (United States)

    Suzuki, Ryo; Weber, Christoph A.; Frey, Erwin; Bausch, Andreas R.

    2015-10-01

    From the self-organization of the cytoskeleton to the synchronous motion of bird flocks, living matter has the extraordinary ability to behave in a concerted manner. The Boltzmann equation for self-propelled particles is frequently used in silico to link a system’s meso- or macroscopic behaviour to the microscopic dynamics of its constituents. But so far such studies have relied on an assumption of simplified binary collisions owing to a lack of experimental data suggesting otherwise. We report here experimentally determined binary-collision statistics by studying a recently introduced molecular system, the high-density actomyosin motility assay. We demonstrate that the alignment induced by binary collisions is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, indicating that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. Our findings demonstrate that the unique properties of biological active-matter systems require a description that goes well beyond that developed in the framework of kinetic theories.

  12. A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

    Science.gov (United States)

    Luo, Li-Shi

    1998-01-01

    A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

  13. On centrality and rapidity dependences of transverse momentum spectra of negative pions in 12C + 12C collisions at 4.2 GeV/c per nucleon

    International Nuclear Information System (INIS)

    Iqbal, A.; Haseeb, M.Q.; Olimov, K.K.; Khan, Imran; Yuldashev, B.S.

    2014-01-01

    The dependences of the experimental transverse momentum spectra of the negative pions, produced in minimum bias 12 C + 12 C collisions at a momentum of 4.2A GeV/c, on the collision centrality and the pion rapidity range were studied. To analyze quantitatively the change in the p t spectra of π - mesons with the changes of collision centrality and pion rapidity range, the extracted p t spectra were fitted by Hagedorn, Boltzmann, simple exponential and Gaussian functions. The values of the extracted spectral temperatures T 1 and T 2 were consistently larger for the p t spectra of π - mesons coming from midrapidity range as compared to those of the negative pions generated in the target and projectile fragmentation regions. The spectral temperatures T 1 and T 2 extracted from fitting the p t spectra of π - mesons in range p t = 0.1–1.2 GeV/c practically coincided with each other in peripheral, semicentral and central 12 C + 12 C collision events, and thus did not show any collision centrality dependence. However, the values of T 1 and T 2 extracted from fitting in range p t = 0.1–0.7 GeV/c were consistently and noticeably larger in case of central collisions as compared to peripheral and semicentral 12 C + 12 C collisions. Hagedorn and Boltzmann functions provided significantly better fits of the transverse momentum spectra of the negative pions with the physically acceptable values of the extracted temperatures as compared to Gaussian and simple exponential functions. (author)

  14. Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas

    International Nuclear Information System (INIS)

    Drallos, P.J.; Riley, M.E.

    1995-01-01

    We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ''cited state densities in the ''GEC'' Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions

  15. Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Drallos, P.J.; Riley, M.E.

    1995-01-01

    We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ``cited state densities in the ``GEC`` Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions.

  16. Calculation of Ground State Rotational Populations for Kinetic Gas Homonuclear Diatomic Molecules including Electron-Impact Excitation and Wall Collisions

    International Nuclear Information System (INIS)

    Farley, David R.

    2010-01-01

    A model has been developed to calculate the ground-state rotational populations of homonuclear diatomic molecules in kinetic gases, including the effects of electron-impact excitation, wall collisions, and gas feed rate. The equations are exact within the accuracy of the cross sections used and of the assumed equilibrating effect of wall collisions. It is found that the inflow of feed gas and equilibrating wall collisions can significantly affect the rotational distribution in competition with non-equilibrating electron-impact effects. The resulting steady-state rotational distributions are generally Boltzmann for N (ge) 3, with a rotational temperature between the wall and feed gas temperatures. The N = 0,1,2 rotational level populations depend sensitively on the relative rates of electron-impact excitation versus wall collision and gas feed rates.

  17. Influence of second kind collisions on the electron distribution function in the positive column of low pressure nitrogen discharge

    International Nuclear Information System (INIS)

    Rohlena, K.; Ruzicka, T.

    1979-01-01

    A numerical solution of the Boltzmann equation for the electron gas in the positive column of a DC discharge in nitrogen is presented. The Boltzmann equation was solved with the inclusion of the second-kind (superelastic) collisions proceeding from the first six excited vibrational levels of molecular nitrogen. The vibrational level population is supposed to follow the Boltzmann distribution for the given vibrational temperature Tsub(v), with a possible deviation of the ground level, which can be overpopulated in the given ratio γ. Apart from the electron distribution functions, which were gained for various values of E/p 0 , Tsub(v) and γ, the values of some production frequencies and kinetic coefficients are presented in form of tables and plots. It is found that the electron distribution (and also the corresponding production rates) only above a certain energy limit depends on Tsub(v) and γ through the normalization constant. (author)

  18. Studies of Fluctuation Processes in Nuclear Collisions

    Energy Technology Data Exchange (ETDEWEB)

    Ayik, Sakir [Tennessee Technological Univ., Cookeville, TN (United States). Dept. of Physics

    2016-04-14

    The standard one-body transport approaches have been extensively applied to investigate heavy-ion collision dynamics at low and intermediate energies. At low energies the approach is the mean-field description of the time-dependent Hartree-Fock (TDHF) theory. At intermediate energies the approach is extended by including a collision term, and its application has been carried out mostly in the semi-classical framework of the Boltzmann-Uhling-Uhlenbeck (BUU) model. The standard transport models provide a good understanding of the average properties of the collision dynamics in terms of the effective interactions in both low and intermediate energies. However, the standard models are inadequate for describing the fluctuation dynamics of collective motion at low energies and disassembling of the nuclear system into fragments at intermediate energies resulting from the growth of density fluctuations in the spinodal region. Our tasks have been to improve the standard transport approaches by incorporating fluctuation mechanisms into the description. There are mainly two different mechanisms for fluctuations: (i) Collisional fluctuations generated by binary nucleon collisions, which provide the dominant mechanism at intermediate energies, and (ii) One-body mechanism or mean-field fluctuations, which is the dominant mechanism at low energies. In the first part of our project, the PI extended the standard transport model at intermediate energies by incorporating collisional mechanism according to the “Generalized Langevin Description” of Mori formalism. The PI and his collaborators carried out a number of applications for describing dynamical mechanism of nuclear multi fragmentations, and nuclear collective response in the semi-classical framework of the approach, which is known as the Boltzmann-Langevin model. In the second part of the project, we considered dynamical description at low energies. Because of the effective Pauli blocking, the collisional dissipation and

  19. Dissipative Boltzmann-Robertson-Walker cosmologies

    International Nuclear Information System (INIS)

    Hiscock, W.A.; Salmonson, J.

    1991-01-01

    The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that ''bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory

  20. Lattice Boltzmann method used to simulate particle motion in a conduit

    Directory of Open Access Journals (Sweden)

    Dolanský Jindřich

    2017-06-01

    Full Text Available A three-dimensional numerical simulation of particle motion in a pipe with a rough bed is presented. The simulation based on the Lattice Boltzmann Method (LBM employs the hybrid diffuse bounce-back approach to model moving boundaries. The bed of the pipe is formed by stationary spherical particles of the same size as the moving particles. Particle movements are induced by gravitational and hydrodynamic forces. To evaluate the hydrodynamic forces, the Momentum Exchange Algorithm is used. The LBM unified computational frame makes it possible to simulate both the particle motion and the fluid flow and to study mutual interactions of the carrier liquid flow and particles and the particle–bed and particle–particle collisions. The trajectories of simulated and experimental particles are compared. The Particle Tracking method is used to track particle motion. The correctness of the applied approach is assessed.

  1. Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

    Science.gov (United States)

    Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

    2007-03-01

    There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

  2. Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

    Science.gov (United States)

    Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

    2014-12-26

    Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

  3. PB-AM: An open-source, fully analytical linear poisson-boltzmann solver.

    Science.gov (United States)

    Felberg, Lisa E; Brookes, David H; Yap, Eng-Hui; Jurrus, Elizabeth; Baker, Nathan A; Head-Gordon, Teresa

    2017-06-05

    We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized PB equation, for molecules represented as non-overlapping spherical cavities. The PB-AM software package includes the generation of outputs files appropriate for visualization using visual molecular dynamics, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmann Solver (APBS) software package to make it more accessible to a larger group of scientists, educators, and students that are more familiar with the APBS framework. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

  4. General relativistic Boltzmann equation, II: Manifestly covariant treatment

    NARCIS (Netherlands)

    Debbasch, F.; van Leeuwen, W.A.

    2009-01-01

    In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann

  5. Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

    Directory of Open Access Journals (Sweden)

    Kosuke Hayashi

    2012-06-01

    Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

  6. Kinetic Boltzmann, Vlasov and Related Equations

    CERN Document Server

    Sinitsyn, Alexander; Vedenyapin, Victor

    2011-01-01

    Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

  7. Multiple-relaxation-time lattice Boltzmann model for compressible fluids

    International Nuclear Information System (INIS)

    Chen Feng; Xu Aiguo; Zhang Guangcai; Li Yingjun

    2011-01-01

    We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version. - Highlights: → We present an energy-conserving MRT finite-difference LB model. → The moment space is constructed according to the group representation theory. → The new model works for both low and high speeds compressible flows. → It has better numerical stability and wider applicable range than its SRT version.

  8. Internal energy relaxation in shock wave structure

    International Nuclear Information System (INIS)

    Josyula, Eswar; Suchyta, Casimir J.; Boyd, Iain D.; Vedula, Prakash

    2013-01-01

    The Wang Chang-Uhlenbeck (WCU) equation is numerically integrated to characterize the internal structure of Mach 3 and Mach 5 shock waves in a gas with excitation in the internal energy states for the treatment of inelastic collisions. Elastic collisions are modeled with the hard sphere collision model and the transition rates for the inelastic collisions modified appropriately using probabilities based on relative velocities of the colliding particles. The collision integral is evaluated by the conservative discrete ordinate method [F. Tcheremissine, “Solution of the Boltzmann kinetic equation for high-speed flows,” Comput. Math. Math. Phys. 46, 315–329 (2006); F. Cheremisin, “Solution of the Wang Chang-Uhlenbeck equation,” Dokl. Phys. 47, 487–490 (2002)] developed for the Boltzmann equation. For the treatment of the diatomic molecules, the internal energy modes in the Boltzmann equation are described quantum mechanically given by the WCU equation. As a first step in the treatment of the inelastic collisions by the WCU equation, a two- and three-quantum system is considered to study the effect of the varying of (1) the inelastic cross section and (2) the energy gap between the quantum energy states. An alternative method, the direct simulation Monte Carlo method, is used for the Mach 3 shock wave to ensure the consistency of implementation in the two methods and there is an excellent agreement between the two methods. The results from the WCU implementation showed consistent trends for the Mach 3 and Mach5 standing shock waves simulations. Inelastic contributions change the downstream equilibrium state and allow the flow to transition to the equilibrium state further upstream

  9. A new algorithm for the simulation of the Boltzmann equation using the direct simulation monte-carlo method

    International Nuclear Information System (INIS)

    Ganjaei, A. A.; Nourazar, S. S.

    2009-01-01

    A new algorithm, the modified direct simulation Monte-Carlo (MDSMC) method, for the simulation of Couette- Taylor gas flow problem is developed. The Taylor series expansion is used to obtain the modified equation of the first order time discretization of the collision equation and the new algorithm, MDSMC, is implemented to simulate the collision equation in the Boltzmann equation. In the new algorithm (MDSMC) there exists a new extra term which takes in to account the effect of the second order collision. This new extra term has the effect of enhancing the appearance of the first Taylor instabilities of vortices streamlines. In the new algorithm (MDSMC) there also exists a second order term in time step in the probabilistic coefficients which has the effect of simulation with higher accuracy than the previous DSMC algorithm. The appearance of the first Taylor instabilities of vortices streamlines using the MDSMC algorithm at different ratios of ω/ν (experimental data of Taylor) occurred at less time-step than using the DSMC algorithm. The results of the torque developed on the stationary cylinder using the MDSMC algorithm show better agreement in comparison with the experimental data of Kuhlthau than the results of the torque developed on the stationary cylinder using the DSMC algorithm

  10. Transverse Momentum Spectra of KS0 and K*0 at Midrapidity in d + Au, Cu + Cu, and p+p Collisions at √(sNN)=200 GeV

    International Nuclear Information System (INIS)

    Zhang, Guo-Xing; Li, Bao-Chun; Guo, Yuan-Yuan

    2015-01-01

    We analyze transverse momentum spectra of K S 0 and K *0 at midrapidity in d + Au, Cu + Cu, and p+p collisions at √(s NN )=200 GeV in the formworks of Tsallis statistics and Boltzmann statistics, respectively. Both of them can describe the transverse momentum spectra and extract the thermodynamics parameters of matter evolution in the collisions. The parameters are helpful for us to understand the thermodynamics factors of the particle production

  11. On some asymptotic relations in the Boltzmann-Enskog model

    International Nuclear Information System (INIS)

    Sadovnikov, B.I.; Inozemtseva, N.G.

    1977-04-01

    The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

  12. Description of the approach to equilibrium in the Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

    1985-06-01

    An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

  13. Hot electrons in superlattices: quantum transport versus Boltzmann equation

    DEFF Research Database (Denmark)

    Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

    1999-01-01

    A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

  14. Navier-Stokes Dynamics by a Discrete Boltzmann Model

    Science.gov (United States)

    Rubinstein, Robet

    2010-01-01

    This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

  15. Azimuthal anisotropy in heavy-ion collisions using non-extensive statistics in Boltzmann transport equation

    International Nuclear Information System (INIS)

    Tripathy, S.; Tiwari, S.K.; Younus, M.; Sahoo, R.

    2017-01-01

    One of the major goals in heavy-ion physics is to understand the properties of Quark Gluon Plasma (QGP), a deconfined hot and dense state of quarks and gluons existed shortly after the Big Bang. In the present scenario, the high-energy particle accelerators are able to reach energies where this extremely dense nuclear matter can be probed for a short time. Here, we follow our earlier works which use non-extensive statistics in Boltzmann Transport Equation (BTE). We represent the initial distribution of particles with the help of Tsallis power law distribution parameterized by the nonextensive parameter q and the Tsallis temperature T, remembering the fact that their origin is due to hard scatterings. We use the initial distribution (f in ) with Relaxation Time Approximation (RTA) of the BTE and calculate the final distribution (f fin ). Then we calculate ν 2 of the system using the final distribution in the definition of ν2

  16. Non-Maxwellian electron velocity distribution as a result of electron-attachment collisions in ionized gases

    International Nuclear Information System (INIS)

    Schmidt, R.; Stiller, W.

    1981-01-01

    The effects of electron-attachment collisions on the velocity distribution of electrons is studied on the basis of Boltzmann kinetic equations governing the energetic balance of electrons (e), atoms of a carrier gas (c), and SF 6 -molecules (m) capturing electrons. Under the assumption that 1) the densities of the particles fulfill the conditions nsub(e) << nsub(c), nsub(m), nsub(m) << nsub(c), and that 2) only the electron-attachment process is in competition with the elastic collision process between electrons and the atoms of the carrier gas, the time behaviour of the energetic balance of the electrons is investigated. The calculations lead to non-Maxwellian forms of the electron velocity distribution changing the mean electron energy. (author)

  17. Thermal equation of state for lattice Boltzmann gases

    International Nuclear Information System (INIS)

    Zheng, Ran

    2009-01-01

    The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar–Gross–Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar–Gross–Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics

  18. Polar Pattern Formation in Driven Filament Systems Require Non-Binary Particle Collisions.

    Science.gov (United States)

    Suzuki, Ryo; Weber, Christoph A; Frey, Erwin; Bausch, Andreas R

    2015-10-01

    Living matter has the extraordinary ability to behave in a concerted manner, which is exemplified throughout nature ranging from the self-organisation of the cytoskeleton to flocks of animals [1-4]. The microscopic dynamics of constituents have been linked to the system's meso- or macroscopic behaviour in silico via the Boltzmann equation for propelled particles [5-10]. Thereby, simplified binary collision rules between the constituents had to be assumed due to the lack of experimental data. We report here experimentally determined binary collision statistics by studying the recently introduced molecular system, the high density actomyosin motility assay [11-13]. We demonstrate that the alignment effect of the binary collision statistics is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, which indicates that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. The presented findings demonstrate that the unique properties of biological active matter systems require a description that goes well beyond a gas-like picture developed in the framework of kinetic theories.

  19. Open heavy flavor and other hard probes in ultra-relativistic heavy-ion collisions

    International Nuclear Information System (INIS)

    Uphoff, Jan

    2013-01-01

    In this thesis hard probes are studied in the partonic transport model BAMPS (Boltzmann Approach to MultiParton Scatterings). Employing Monte Carlo techniques, this model describes the 3+1 dimensional evolution of the quark gluon plasma phase in ultra-relativistic heavy-ion collisions by propagating all particles in space and time and carrying out their collisions according to the Boltzmann equation. Since hard probes are produced in hard processes with a large momentum transfer, the value of the running coupling is small and their interactions should be describable within perturbative QCD (pQCD). This work focuses on open heavy flavor, but also addresses the suppression of light parton jets, in particular to highlight differences due to the mass. For light partons, radiative processes are the dominant contribution to their energy loss. For heavy quarks, we show that also binary interactions with a running coupling and an improved Debye screening matched to hard-thermal-loop calculations play an important role. Furthermore, the impact of the mass in radiative interactions, prominently named the dead cone effect, and the interplay with the Landau-Pomeranchuk-Migdal (LPM) effect are studied in great detail. Since the transport model BAMPS has access to all medium properties and the space time information of heavy quarks, it is the ideal tool to study the dissociation and regeneration of J/ψ mesons, which is also investigated in this thesis.

  20. Ion trapping in one-minimum potentials via charge-exchange collisions

    International Nuclear Information System (INIS)

    Maier, H.; Kuhn, S.

    1994-01-01

    A (1 d, 2 v), electrostatic, kinetics model for time-independent single-ended Q-machine states with a positively biased cold plate and a single internal minimum near the hot plate is presented. While the electrons are treated as collisionless, charge-exchange collisions between the ions and the neutral background gas atoms are taken into account by means of a linearized Boltzmann collision operator. The self-consistent plasma states are found by using an iterative analytic-numerical trajectory-simulation method in which the charge-density and potential distributions are alternately determined numerical results clearly demonstrate the sensitive role that trapped ions play in shaping the microscopic and macroscopic properties of the dc states under study. The trapped-ion distributions themselves are shown to be controlled critically by the detailed scattering conditions, which in turn are determined by the choice of the background properties. (author). 10 refs, 3 figs

  1. Lattice Boltzmann approach for complex nonequilibrium flows.

    Science.gov (United States)

    Montessori, A; Prestininzi, P; La Rocca, M; Succi, S

    2015-10-01

    We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

  2. L2-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians

    International Nuclear Information System (INIS)

    Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang

    2013-01-01

    We present a L 2 -stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L 2 -distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L 2 -stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L 2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L 2 -stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L 2 -stability estimate. This is the first result on the L 2 -stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

  3. Precritical increase of particle collision rates

    International Nuclear Information System (INIS)

    Muenchow, L.

    1990-01-01

    In quantum kinetics the collision integral follows from the imaginary part of the mass operator. Using this connection it is shown that the coupling of single particle motion to precritical density fluctuations causes a strong increase of the collision integral near the point of phase instability. 13 refs

  4. Predicting drug-target interactions using restricted Boltzmann machines.

    Science.gov (United States)

    Wang, Yuhao; Zeng, Jianyang

    2013-07-01

    In silico prediction of drug-target interactions plays an important role toward identifying and developing new uses of existing or abandoned drugs. Network-based approaches have recently become a popular tool for discovering new drug-target interactions (DTIs). Unfortunately, most of these network-based approaches can only predict binary interactions between drugs and targets, and information about different types of interactions has not been well exploited for DTI prediction in previous studies. On the other hand, incorporating additional information about drug-target relationships or drug modes of action can improve prediction of DTIs. Furthermore, the predicted types of DTIs can broaden our understanding about the molecular basis of drug action. We propose a first machine learning approach to integrate multiple types of DTIs and predict unknown drug-target relationships or drug modes of action. We cast the new DTI prediction problem into a two-layer graphical model, called restricted Boltzmann machine, and apply a practical learning algorithm to train our model and make predictions. Tests on two public databases show that our restricted Boltzmann machine model can effectively capture the latent features of a DTI network and achieve excellent performance on predicting different types of DTIs, with the area under precision-recall curve up to 89.6. In addition, we demonstrate that integrating multiple types of DTIs can significantly outperform other predictions either by simply mixing multiple types of interactions without distinction or using only a single interaction type. Further tests show that our approach can infer a high fraction of novel DTIs that has been validated by known experiments in the literature or other databases. These results indicate that our approach can have highly practical relevance to DTI prediction and drug repositioning, and hence advance the drug discovery process. Software and datasets are available on request. Supplementary data are

  5. Studies of fluctuation processes in nuclear collisions

    International Nuclear Information System (INIS)

    Ayik, S.

    1991-02-01

    This report summarizes the progress on grant No. DE-FG05-89ER40530 during the period April 15, 1990 to February 15, 1991. Our studies of heavy-ion collisions in the framework of ''a stochastic one-body transport model'' has progress in several directions. We developed a method for obtaining approximate numerical solutions of the transport-equation in semi-classical limit, i.e., Boltzmann-Langevin equation, and tested the method in realistic cases of heavy-ion collisions at energies below 100 MeV per nucleon. Some results of the numerical simulations for a head-on collision of 12 C + 12 C system is included in this report. Work has also continued on studying the stochastic one-body transport model in a quantal representation, which provides a microscopic basis for a consistent description of dissipation and fluctuation properties of large amplitude collective nuclear motion. The previous derivation of the stochastic one-body transport model was presented within the density matrix formalisam. We generalized this treatment and proposed an alternative derivation of the model by employing the Green's function approach within the real-time path formalism of Keldish. One manuscript has been submitted to Nucl. Phys. A for publication. Two other manuscripts are in preparation for publication. Several seminars and contributed talks were presented at various meeting

  6. Boltzmann and Einstein: Statistics and dynamics –An unsolved ...

    Indian Academy of Sciences (India)

    The struggle of Boltzmann with the proper description of the behavior of classical macroscopic bodies in equilibrium in terms of the properties of the particles out of which they consist will be sketched. He used both a dynamical and a statistical method. However, Einstein strongly disagreed with Boltzmann's statistical method ...

  7. Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

    Science.gov (United States)

    Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

    2018-01-01

    In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

  8. Integral transport multiregion geometrical shadowing factor for the approximate collision probability matrix calculation of infinite closely packed lattices

    International Nuclear Information System (INIS)

    Jowzani-Moghaddam, A.

    1981-01-01

    An integral transport method of calculating the geometrical shadowing factor in multiregion annular cells for infinite closely packed lattices in cylindrical geometry is developed. This analytical method has been programmed in the TPGS code. This method is based upon a consideration of the properties of the integral transport method for a nonuniform body, which together with Bonalumi's approximations allows the determination of the approximate multiregion collision probability matrix for infinite closely packed lattices with sufficient accuracy. The multiregion geometrical shadowing factors have been calculated for variations in fuel pin annular segment rings in a geometry of annular cells. These shadowing factors can then be used in the calculation of neutron transport from one annulus to another in an infinite lattice. The result of this new geometrical shadowing and collision probability matrix are compared with the Dancoff-Ginsburg correction and the probability matrix using constant shadowing on Yankee fuel elements in an infinite lattice. In these cases the Dancoff-Ginsburg correction factor and collision probability matrix using constant shadowing are in difference by at most 6.2% and 6%, respectively

  9. Tomography and generative training with quantum Boltzmann machines

    Science.gov (United States)

    Kieferová, Mária; Wiebe, Nathan

    2017-12-01

    The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP , provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

  10. Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

    Science.gov (United States)

    Boozer, A. D.

    2011-01-01

    We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

  11. The influence of isotope substitution of neon atom on the integral cross sections of rotational excitation in Ne—Na2 collisions

    International Nuclear Information System (INIS)

    Zang Hua-Ping; Li Wen-Feng; Linghu Rong-Feng; Cheng Xin-Lu; Yang Xiang-Dong

    2011-01-01

    This paper applies the multiple ellipsoid model to the 16 Ne ( 20 Ne, 28 Ne, 34 Ne)-Na 2 collision systems, and calculates integral cross sections for rotational excitation at the incident energy of 190 meV. It can be seen that the accuracy of the integral cross sections can be improved by increasing the number of equipotential ellipsoid surfaces. Moreover, by analysing the differences of these integral cross sections, it obtains the change rules of the integral cross sections with the increase of rotational angular quantum number J', and with the change of the mass of isotope substitution neon atom. Finally, the contribution of different regions of the potential to inelastic cross sections for 20 Ne-Na 2 collision system is investigated at relative incident energy of 190 meV. (general)

  12. Entropy à la Boltzmann

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...

  13. Axisymmetric multiphase lattice Boltzmann method for generic equations of state

    NARCIS (Netherlands)

    Reijers, S.A.; Gelderblom, H.; Toschi, F.

    2016-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

  14. Riemann-Theta Boltzmann Machine arXiv

    CERN Document Server

    Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

    A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

  15. Deviation from normal Boltzmann distribution of high-lying energy levels of iron atom excited by Okamoto-cavity microwave-induced plasmas using pure nitrogen and nitrogen–oxygen gases

    International Nuclear Information System (INIS)

    Wagatsuma, Kazuaki

    2015-01-01

    This paper describes several interesting excitation phenomena occurring in a microwave-induced plasma (MIP) excited with Okamoto-cavity, especially when a small amount of oxygen was mixed with nitrogen matrix in the composition of the plasma gas. An ion-to-atom ratio of iron, which was estimated from the intensity ratio of ion to atomic lines having almost the same excitation energy, was reduced by adding oxygen gas to the nitrogen MIP, eventually contributing to an enhancement in the emission intensities of the atomic lines. Furthermore, Boltzmann plots for iron atomic lines were observed in a wide range of the excitation energy from 3.4 to 6.9 eV, indicating that plots of the atomic lines having lower excitation energies (3.4 to 4.8 eV) were well fitted on a straight line while those having more than 5.5 eV deviated upwards from the linear relationship. This overpopulation would result from any other excitation process in addition to the thermal excitation that principally determines the Boltzmann distribution. A Penning-type collision with excited species of nitrogen molecules probably explains this additional excitation mechanism, in which the resulting iron ions recombine with captured electrons, followed by cascade de-excitations between closely-spaced excited levels just below the ionization limit. As a result, these high-lying levels might be more populated than the low-lying levels of iron atom. The ionization of iron would be caused less actively in the nitrogen–oxygen plasma than in a pure nitrogen plasma, because excited species of nitrogen molecule, which can provide the ionization energy in a collision with iron atom, are consumed through collisions with oxygen molecules to cause their dissociation. It was also observed that the overpopulation occurred to a lesser extent when oxygen gas was added to the nitrogen plasma. The reason for this was also attributed to decreased number density of the excited nitrogen species due to collisions with oxygen

  16. Progress in lattice Boltzmann methods for magnetohydrodynamic flows relevant to fusion applications

    International Nuclear Information System (INIS)

    Pattison, M.J.; Premnath, K.N.; Morley, N.B.; Abdou, M.A.

    2008-01-01

    In this paper, an approach to simulating magnetohydrodynamic (MHD) flows based on the lattice Boltzmann method (LBM) is presented. The dynamics of the flow are simulated using a so-called multiple relaxation time (MRT) lattice Boltzmann equation (LBE), in which a source term is included for the Lorentz force. The evolution of the magnetic induction is represented by introducing a vector distribution function and then solving an appropriate lattice kinetic equation for this function. The solution of both distribution functions are obtained through a simple, explicit, and computationally efficient stream-and-collide procedure. The use of the MRT collision term enhances the numerical stability over that of a single relaxation time approach. To apply the methodology to solving practical problems, a new extrapolation-based method for imposing magnetic boundary conditions is introduced and a technique for simulating steady-state flows with low magnetic Prandtl number is developed. In order to resolve thin layers near the walls arising in the presence of high magnetic fields, a non-uniform gridding strategy is introduced through an interpolated-streaming step applied to both distribution functions. These advances are particularly important for applications in fusion engineering where liquid metal flows with low magnetic Prandtl numbers and high Hartmann numbers are introduced. A number of MHD benchmark problems, under various physical and geometrical conditions are presented, including 3-D MHD lid driven cavity flow, high Hartmann number flows and turbulent MHD flows, with good agreement with prior data. Due to the local nature of the method, the LBM also demonstrated excellent performance on parallel machines, with almost linear scaling up to 128 processors for a MHD flow problem

  17. Nuclear de-excitation processes following medium energy heavy ion collisions

    International Nuclear Information System (INIS)

    Blann, M.

    1986-09-01

    As heavy ion reaction studies have progressed from beam energies below 10 MeV/nucleon to higher energies, many non-equilibrium reaction phenomena have been observed. Among these are nucleon emission with velocities in excess of the beam velocity, incomplete momentum transfer to evaporation residue and fission-like fragments, γ-rays with energies in excess of 100 MeV, and π 0 production when beam energies are below the threshold for production by the nucleon-nucleon collision mechanism. Additionally, prefission neutrons have been observed in excess of numbers expected from equilibrium models. A few of the approaches which have been applied to these phenomena are as follows: Intranuclear cascade: two body collisions are assumed to mediate the equilibration. The geometry and momentum space is followed semiclassically. The approach has many successes though it may suffer in a few applications is not following holes; TDHF considers one body processes only; in the energy regime of interest, two body processes are important so that this may not be a viable approach; Boltzmann-Uehling-Uhlenbeck or Vlasov-Uehling-Uhlenbeck (BUU/VUU) equations combine both one body and two body dynamics. The spatial and momentum evolution of the reactions are followed in a mean field. These should be the Cadillacs of the models. They are computationally tedious, and sometimes significant approximations are made in order to achieve computational tract ability; models of collective deceleration. A very simple model approach is discussed to interpret these phenomena, the Boltzmann master equation (BME). The hybrid model was the first to be applied to the question of heavy ion precompound decay, and the BME second. 26 refs., 5 figs., 2 tabs

  18. Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

    International Nuclear Information System (INIS)

    Velarde, G.

    1976-01-01

    Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

  19. On a Boltzmann-type price formation model

    KAUST Repository

    Burger, Martin; Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie Therese

    2013-01-01

    In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann-type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore, we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

  20. On a Boltzmann-type price formation model

    KAUST Repository

    Burger, Martin

    2013-06-26

    In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann-type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore, we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

  1. A lattice Boltzmann model for solute transport in open channel flow

    Science.gov (United States)

    Wang, Hongda; Cater, John; Liu, Haifei; Ding, Xiangyi; Huang, Wei

    2018-01-01

    A lattice Boltzmann model of advection-dispersion problems in one-dimensional (1D) open channel flows is developed for simulation of solute transport and pollutant concentration. The hydrodynamics are calculated based on a previous lattice Boltzmann approach to solving the 1D Saint-Venant equations (LABSVE). The advection-dispersion model is coupled with the LABSVE using the lattice Boltzmann method. Our research recovers the advection-dispersion equations through the Chapman-Enskog expansion of the lattice Boltzmann equation. The model differs from the existing schemes in two points: (1) the lattice Boltzmann numerical method is adopted to solve the advection-dispersion problem by meso-scopic particle distribution; (2) and the model describes the relation between discharge, cross section area and solute concentration, which increases the applicability of the water quality model in practical engineering. The model is verified using three benchmark tests: (1) instantaneous solute transport within a short distance; (2) 1D point source pollution with constant velocity; (3) 1D point source pollution in a dam break flow. The model is then applied to a 50-year flood point source pollution accident on the Yongding River, which showed good agreement with a MIKE 11 solution and gauging data.

  2. Studying the collision energy dependence of elliptic and triangular flow with a hybrid model

    Energy Technology Data Exchange (ETDEWEB)

    Auvinen, Jussi [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Petersen, Hannah [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany)

    2014-07-01

    Elliptic flow has been one of the key observables for establishing the finding of the quark-gluon plasma (QGP) at the highest energies of Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). As a sign of collectively behaving matter, the elliptic flow is expected to decrease at lower beam energies, where the QGP is not produced. However, in the recent RHIC beam energy scan, it has been found that the inclusive charged hadron elliptic flow changes relatively little in magnitude within the energy range 7.7-39 GeV per nucleon-nucleon collision. We study the collision energy dependence of the elliptic and triangular flow utilizing a Boltzmann+hydrodynamics hybrid model. Such a hybrid model provides a natural framework for the transition from high collision energies, where the hydrodynamical description is essential, to smaller energies, where the hadron transport dominates. This approach is thus suitable for investigating the relative importance of these two mechanisms for the production of the collective flow at different beam energies.

  3. Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

    Science.gov (United States)

    Chen, Z.; Shu, C.; Tan, D.

    2018-05-01

    An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

  4. Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases

    OpenAIRE

    Cates, M. E.; Henrich, O.; Marenduzzo, D.; Stratford, K.

    2010-01-01

    Lattice Boltzmann simulations have become a method of choice to solve the hydrodynamic equations of motion of a number of complex fluids. Here we review some recent applications of lattice Boltzmann to study the hydrodynamics of liquid crystalline materials. In particular, we focus on the study of (a) the exotic blue phases of cholesteric liquid crystals, and (b) active gels - a model system for actin plus myosin solutions or bacterial suspensions. In both cases lattice Boltzmann studies have...

  5. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo; Vella, Dominic; Yeomans, Julia M.

    2014-01-01

    © the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

  6. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo

    2014-09-04

    © the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

  7. Lattice Boltzmann method for weakly ionized isothermal plasmas

    International Nuclear Information System (INIS)

    Li Huayu; Ki, Hyungson

    2007-01-01

    In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values

  8. The Interaction of Boltzmann with Mach, Ostwald and Planck, and his influence on Nernst and Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1981-01-01

    Boltzmann esteemed both Mach and Ostwald personally and as experimentalists, but consistently fought them in epistemology. He represented atomism and realism against energism and positivism. In the early period Boltzmann also had to struggle against Planck as a phenomenologist, but he welcomed his quantum hypothesis. As a scientist Nernst was also under Boltzmann's influence. Einstein learned atomism from (Maxwell and) Boltzmann. After Einstein had overcome Mach's positivist influence, he unknowingly approached Boltzmann's philosophical views. Some sociopolitlcal aspects of the lives of the great physicists will be discussed. It will be shown how they all, and many of Boltzmann's most eminent students, in one way or other conflicted with evil tendencies and developments in existing society. (author)

  9. Reducing the risk of rear-end collisions with infrastructure-to-vehicle (I2V) integration of variable speed limit control and adaptive cruise control system.

    Science.gov (United States)

    Li, Ye; Wang, Hao; Wang, Wei; Liu, Shanwen; Xiang, Yun

    2016-08-17

    Adaptive cruise control (ACC) has been investigated recently to explore ways to increase traffic capacity, stabilize traffic flow, and improve traffic safety. However, researchers seldom have studied the integration of ACC and roadside control methods such as the variable speed limit (VSL) to improve safety. The primary objective of this study was to develop an infrastructure-to-vehicle (I2V) integrated system that incorporated both ACC and VSL to reduce rear-end collision risks on freeways. The intelligent driver model was firstly modified to simulate ACC behavior and then the VSL strategy used in this article was introduced. Next, the I2V system was proposed to integrate the 2 advanced techniques, ACC and VSL. Four scenarios of no control, VSL only, ACC only, and the I2V system were tested in simulation experiments. Time exposed time to collision (TET) and time integrated time to collision (TIT), 2 surrogate safety measures derived from time to collision (TTC), were used to evaluate safety issues associated with rear-end collisions. The total travel times of each scenario were also compared. The simulation results indicated that both the VSL-only and ACC-only methods had a positive impact on reducing the TET and TIT values (reduced by 53.0 and 58.6% and 59.0 and 65.3%, respectively). The I2V system combined the advantages of both ACC and VSL to achieve the most safety benefits (reduced by 71.5 and 77.3%, respectively). Sensitivity analysis of the TTC threshold also showed that the I2V system obtained the largest safety benefits with all of the TTC threshold values. The impact of different market penetration rates of ACC vehicles in I2V system indicated that safety benefits increase with an increase in ACC proportions. Compared to VSL-only and ACC-only scenarios, this integrated I2V system is more effective in reducing rear-end collision risks. The findings of this study provide useful information for traffic agencies to implement novel techniques to improve

  10. Towards a dynamical description of intermediate mass fragment formation in heavy-ion collisions at some tens of MeV/A

    International Nuclear Information System (INIS)

    Suraud, E.

    1990-01-01

    We briefly remind the possible dynamical scenario of fragments formation in central heavy-ion collisions at some tens of MeV/A. We discuss how present day dynamical models can describe fragment formation. We show that particle methods provide a reasonable solution of Boltzman-like equations. We next turn to the Boltzmann-Langevin formalism which gives a well defined framework for the understanding of Intermediate Mass Fragments formation. We present a first numerical solution of this equation and show the importance of fluctuations in the dynamics of the collision. We finally apply the formalism to the onset of multifragmentation in the 40 Ca + 40 Ca system between 20 and 60 MeV/A beam energy

  11. Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

    KAUST Repository

    Reis, Tim

    2012-01-01

    We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.

  12. Boltzmann's dynamic on the primitive earth about 3.9 billion years ago

    International Nuclear Information System (INIS)

    Matsuno, Koichiro

    1995-01-01

    An evolutionary significant event that could have happened on the primitive earth would be a process of enhancing energy concentrations locally. Once the concentrated energy be released, it could drive various molecular association and dissociation. We have examined, both theoretically and experimentally, a possibility of forming such microscopic heat engines feeding upon the then available thermal environment. Theoretically, Boltzmann's dynamics of molecules that would lose their memory of pas collisions with others is found to uphold those molecules that could feed upon thermal energy if the thermal environment would fluctuate through, for instance, a diurnal cycle. Experimentally, thermal heterocomplex molecules from amino acids, that could have been ubiquitous on the primitive earth, are shown to carry with themselves a wide variety of quasi-stable states such that they could remain in excited states for a considerable period of time even if the temperature of the thermal environment is lowered. The stored energy in these excited states, once released, can be utilized as a factor for driving various molecular association and dissociation. (author). Abstract only

  13. Lattice Boltzmann model for free-surface flow and its application to filling process in casting

    CERN Document Server

    Ginzburg, I

    2003-01-01

    A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities at the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial ...

  14. Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

    Science.gov (United States)

    Badino, M.

    2011-11-01

    An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

  15. Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

    International Nuclear Information System (INIS)

    Niven, Robert K.

    2005-01-01

    The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

  16. Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes

    International Nuclear Information System (INIS)

    Morel, J.E.

    1987-01-01

    The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

  17. Transverse and radial flow in intermediate energy nucleus-nucleus collisions

    International Nuclear Information System (INIS)

    Vestfall, D. Gary

    1997-01-01

    We have studied transverse and radial flow in nucleus-nucleus collisions ranging in energy from 15 to 155 MeV/nucleon. We have measured the impact parameter dependence of the balance energy for Ar + Sc and compared the results with Quantum Molecular Dynamics calculations with and without momentum dependence. We have shown that transverse flow and the balance energy dependence on the isospin of the system using the systems 58 Fe + 58 Fe, 58 Ni + 58 Ni, and 58 Mn + 58 Fe. These results are compared with Boltzmann-Uehling-Uehlenbeck calculations incorporating isospin-dependence. We have measured radial flow for Ar + Sc and find that about 50% of the observed energy is related to radial flow. (author)

  18. Binary collision rates of relativistic thermal plasmas. I Theoretical framework

    Science.gov (United States)

    Dermer, C. D.

    1985-01-01

    Binary collision rates for arbitrary scattering cross sections are derived in the case of a beam of particles interacting with a Maxwell-Boltzmann (MB) plasma, or in the case of two MB plasmas interacting at generally different temperatures. The expressions are valid for all beam energies and plasma temperatures, from the nonrelativistic to the extreme relativistic limits. The calculated quantities include the reaction rate, the energy exchange rate, and the average rate of change of the squared transverse momentum component of a monoenergetic particle beam as a result of scatterings with particles of a MB plasma. Results are specialized to elastic scattering processes, two-temperature reaction rates, or the cold plasma limit, reproducing previous work.

  19. Concerning the theory of radiation cascades of atomic collisions in a solid with an arbitrary interatomic interaction potential

    International Nuclear Information System (INIS)

    Ryazanov, A.I.; Metelkin, E.V.

    1980-01-01

    Cascades of atomic collisions created by high energy particles as a result of irradiation of solids by them are considered. The solution of the problem is based on the investigation of the Boltzmann stationary kinetic equation for moving atoms. For this equation a model scattering indicatrix is constructed with an arbitrary form of the potential of interaction of moving atoms with lattice atoms. The choice of the model scattering indicatrix of atoms is determined by the normalization, the average energy loss in a single collision and by the deviation of the energy losses really occurring in the collision from the mean value, as well as by the initial kinetic equation for moving atoms. The energy distribution of moving atoms for arbitrary interatomic interaction potentials has been obtained using the constructed model scattering indicatrix. On the basis of the theory constructed a cascade is calculated with an interatomic interaction potential in the form of the Thomas-Fermi potential and the power potential. (author)

  20. Non-Boltzmann Ensembles and Monte Carlo Simulations

    International Nuclear Information System (INIS)

    Murthy, K. P. N.

    2016-01-01

    Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble and for calculating macroscopic properties of a closed system at desired temperatures. An estimate of a mechanical property, like energy, of an equilibrium system, is made by averaging over a large number microstates generated by Boltzmann Monte Carlo methods. This is possible because we can assign a numerical value for energy to each microstate. However, a thermal property like entropy, is not easily accessible to these methods. The reason is simple. We can not assign a numerical value for entropy, to a microstate. Entropy is not a property associated with any single microstate. It is a collective property of all the microstates. Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo technique called Umbrella sampling was proposed some forty years ago. Umbrella sampling has since undergone several metamorphoses and we have now, multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc . This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated as follows. First un-weight a microstates of the entropic ensemble; then re-weight it to the desired physical ensemble. Carry out weighted average over the entropic ensemble to estimate physical quantities. In this talk I shall tell you of the most recent non- Boltzmann Monte Carlo method and show how to calculate free energy for a few systems. We first consider estimation of free energy as a function of energy at different temperatures to characterize phase transition in an hairpin DNA in the presence of an unzipping force. Next we consider free energy as a function of order parameter and to this end we estimate density of states g ( E , M ), as a function of both energy E , and order parameter M . This is carried out in two stages. We estimate g ( E ) in the first stage

  1. Maxwell iteration for the lattice Boltzmann method with diffusive scaling

    Science.gov (United States)

    Zhao, Weifeng; Yong, Wen-An

    2017-03-01

    In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

  2. On thermalization of electron-positron-photon plasma

    Energy Technology Data Exchange (ETDEWEB)

    Siutsou, I. A., E-mail: siutsou@icranet.org [CAPES–ICRANet program, ICRANet–Rio, CBPF 22290-180, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ (Brazil); Aksenov, A. G. [Institute for Computer-Aided Design, Russian Academy of Sciences 123056, 2nd Brestskaya st., 19/18, Moscow (Russian Federation); Vereshchagin, G. V. [ICRANet 65122, p.le della Republica, 10, Pescara (Italy)

    2015-12-17

    Recently a progress has been made in understanding thermalization mechanism of relativistic plasma starting from a non-equilibrium state. Relativistic Boltzmann equations were solved numerically for homogeneous isotropic plasma with collision integrals for two- and three-particle interactions calculated from the first principles by means of QED matrix elements. All particles were assumed to fulfill Boltzmann statistics. In this work we follow plasma thermalization by accounting for Bose enhancement and Pauli blocking in particle interactions. Our results show that particle in equilibrium reach Bose-Einstein distribution for photons, and Fermi-Dirac one for electrons, respectively.

  3. On thermalization of electron-positron-photon plasma

    Science.gov (United States)

    Siutsou, I. A.; Aksenov, A. G.; Vereshchagin, G. V.

    2015-12-01

    Recently a progress has been made in understanding thermalization mechanism of relativistic plasma starting from a non-equilibrium state. Relativistic Boltzmann equations were solved numerically for homogeneous isotropic plasma with collision integrals for two- and three-particle interactions calculated from the first principles by means of QED matrix elements. All particles were assumed to fulfill Boltzmann statistics. In this work we follow plasma thermalization by accounting for Bose enhancement and Pauli blocking in particle interactions. Our results show that particle in equilibrium reach Bose-Einstein distribution for photons, and Fermi-Dirac one for electrons, respectively.

  4. Chemical Potentials of Quarks Extracted from Particle Transverse Momentum Distributions in Heavy Ion Collisions at RHIC Energies

    International Nuclear Information System (INIS)

    Zhao, Hong; Liu, Fu-Hu

    2014-01-01

    In the framework of a multisource thermal model, the transverse momentum distributions of charged particles produced in nucleus-nucleus (A-A) and deuteron-nucleus (d-A) collisions at relativistic heavy ion collider (RHIC) energies are investigated by a two-component revised Boltzmann distribution. The calculated results are in agreement with the PHENIX experimental data. It is found that the source temperature increases obviously with increase of the particle mass and incident energy, but it does not show an obvious change with the collision centrality. Then, the values of chemical potentials for up, down, and strange quarks can be obtained from the antiparticle to particle yield ratios in a wide transverse momentum range. The relationship between the chemical potentials of quarks and the transverse momentum with different centralities is investigated, too

  5. Stabilization of the Lattice Boltzmann Method Using Information Theory

    OpenAIRE

    Wilson, Tyler L; Pugh, Mary; Dawson, Francis

    2018-01-01

    A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time...

  6. Simplified simulation of Boltzmann-Langevin equation

    International Nuclear Information System (INIS)

    Ayik, S.; Randrup, J.

    1994-01-01

    We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density. (orig.)

  7. Mathematical modeling and numerical study of a spray in a rarefied gas. Application to the simulation of dust particle transport in ITER in case of vacuum loss accident

    International Nuclear Information System (INIS)

    Charles, F.

    2009-11-01

    The thesis deals with kinetic models describing a rarefied spray. These models rely on coupling two Partial Differential Equations which describe the spatio-temporal evolution of the distribution of molecules and dust particles. The model presented in the first part is described by two Boltzmann-type equations where collisions between molecules and particles are modeled by two collision operators. We suggest two models of this collision operators. In the first one, collisions between dust particles and molecules are supposed to be elastic. In the second one, we assume those collisions are inelastic and given by a diffuse reflexion mechanism on the surface of dust specks. This leads to establish non classical collision operators. We prove that in the case of elastic collisions, the spatially homogeneous system has weak solutions which preserve mass and energy, and which satisfy an entropy inequality. We then describe the numerical simulation of the inelastic model, which is based on a Direct Simulation Method. This brings to light that the numerical simulation of the system becomes too expensive because the typical size of a dust particle is too large. We therefore introduce in the second part of this work a model constituted of a coupling (by a drag force term) between a Boltzmann equation and a Vlasov equation. To this end, we perform a scaling of the Boltzmann/Boltzmann system and an asymptotic expansion of one of the dimensionless collision operators with respect to the ratio of mass between a molecule of gas and a particle. A rigorous proof of the passage to the limit is given in the spatially homogeneous setting, for the elastic model of collision operators. It includes a new variant of Povzner's inequality in which the vanishing mass ratio is taken into account. Moreover, we numerically compare the Boltzmann/Boltzmann and Vlasov/Boltzmann systems with the inelastic collision operators. The simulation of the Vlasov equation is performed with a Particle

  8. Boltzmann brains and the scale-factor cutoff measure of the multiverse

    International Nuclear Information System (INIS)

    De Simone, Andrea; Guth, Alan H.; Linde, Andrei; Noorbala, Mahdiyar; Salem, Michael P.; Vilenkin, Alexander

    2010-01-01

    To make predictions for an eternally inflating 'multiverse', one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by 'Boltzmann brains' - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.

  9. The lattice Boltzmann model for the second-order Benjamin–Ono equations

    International Nuclear Information System (INIS)

    Lai, Huilin; Ma, Changfeng

    2010-01-01

    In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

  10. Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

    International Nuclear Information System (INIS)

    Henn, Johannes M.; Melnikov, Kirill; Smirnov, Vladimir A.

    2014-01-01

    We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in ref. http://dx.doi.org/10.1007/JHEP08(2013)070, appears as a particular case of our general solution

  11. Revisiting Boltzmann learning: parameter estimation in Markov random fields

    DEFF Research Database (Denmark)

    Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik

    1996-01-01

    This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...

  12. Classical trajectory methods in molecular collisions

    International Nuclear Information System (INIS)

    Porter, R.N.; Raff, L.M.

    1976-01-01

    The discussion of classical trajectory methods in molecular collisions includes classical dynamics, Hamiltonian mechanics, classical scattering cross sections and rate coefficients, statistical averaging, the selection of initial states, integration of equations of motion, analysis of final states, consecutive collisions, and the prognosis for classical molecular scattering calculations. 61 references

  13. Boltzmann Oracle for Combinatorial Systems

    OpenAIRE

    Pivoteau , Carine; Salvy , Bruno; Soria , Michèle

    2008-01-01

    International audience; Boltzmann random generation applies to well-defined systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.

  14. The Lattice Boltzmann method principles and practice

    CERN Document Server

    Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus

    2017-01-01

    This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...

  15. Entropic multirelaxation lattice Boltzmann models for turbulent flows

    Science.gov (United States)

    Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.

    2015-10-01

    We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

  16. Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

    Science.gov (United States)

    Pradipto; Purqon, Acep

    2017-07-01

    Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

  17. Collision Probabilities for Finite Cylinders and Cuboids

    Energy Technology Data Exchange (ETDEWEB)

    Carlvik, I

    1967-05-15

    Analytical formulae have been derived for the collision probabilities of homogeneous finite cylinders and cuboids. The formula for the finite cylinder contains double integrals, and the formula for the cuboid only single integrals. Collision probabilities have been calculated by means of the formulae and compared with values obtained by other authors. It was found that the calculations using the analytical formulae are much quicker and give higher accuracy than Monte Carlo calculations.

  18. Boltzmann machines for travelling salesman problems

    NARCIS (Netherlands)

    Aarts, E.H.L.; Korst, J.H.M.

    1989-01-01

    Boltzmann machines are proposed as a massively parallel alternative to the (sequential) simulated annealing algorithm. Our approach is tailored to the travelling salesman problem, but it can also be applied to a more general class of combinatorial optimization problems. For two distinct 0–1

  19. The adaptive collision source method for discrete ordinates radiation transport

    International Nuclear Information System (INIS)

    Walters, William J.; Haghighat, Alireza

    2017-01-01

    Highlights: • A new adaptive quadrature method to solve the discrete ordinates transport equation. • The adaptive collision source (ACS) method splits the flux into n’th collided components. • Uncollided flux requires high quadrature; this is lowered with number of collisions. • ACS automatically applies appropriate quadrature order each collided component. • The adaptive quadrature is 1.5–4 times more efficient than uniform quadrature. - Abstract: A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.

  20. Large Time Behavior of the Vlasov-Poisson-Boltzmann System

    Directory of Open Access Journals (Sweden)

    Li Li

    2013-01-01

    Full Text Available The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005. The improvement of the present paper is the removal of condition on parameter λ as in the work of Li (2008.

  1. Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Tharkabhushanam, Sri Harsha

    2009-01-01

    We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S d-1 . The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ( )]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously

  2. Nonequilibrium thermodynamics of restricted Boltzmann machines

    Science.gov (United States)

    Salazar, Domingos S. P.

    2017-08-01

    In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

  3. Nonequilibrium thermodynamics of restricted Boltzmann machines.

    Science.gov (United States)

    Salazar, Domingos S P

    2017-08-01

    In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

  4. Recursive regularization step for high-order lattice Boltzmann methods

    Science.gov (United States)

    Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

    2017-09-01

    A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

  5. Mass shift of charmonium states in p bar A collision

    Science.gov (United States)

    Wolf, György; Balassa, Gábor; Kovács, Péter; Zétényi, Miklós; Lee, Su Houng

    2018-05-01

    The masses of the low lying charmonium states, namely, the J / Ψ, Ψ (3686), and Ψ (3770) are shifted downwards due to the second order Stark effect. In p bar +Au collisions at 6-10 GeV we study their in-medium propagation. The time evolution of the spectral functions of these charmonium states is studied with a Boltzmann-Uehling-Uhlenbeck (BUU) type transport model. We show that their in-medium mass shift can be observed in the dilepton spectrum. Therefore, by observing the dileptonic decay channel of these low lying charmonium states, especially for Ψ (3686), we can gain information about the magnitude of the gluon condensate in nuclear matter. This measurement could be performed at the upcoming PANDA experiment at FAIR.

  6. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Zhen Chen

    2017-03-01

    Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

  7. Tsallis-Pareto like distributions in hadron-hadron collisions

    International Nuclear Information System (INIS)

    Barnafoeldi, G G; Uermoessy, K; Biro, T S

    2011-01-01

    Non-extensive thermodynamics is a novel approach in high energy physics. In high-energy heavy-ion, and especially in proton-proton collisions we are far from a canonical thermal state, described by the Boltzmann-Gibbs statistic. In these reactions low and intermediate transverse momentum spectra are extremely well reproduced by the Tsallis-Pareto distribution, but the physical origin of Tsallis parameters is still an unsettled question. Here, we analyze whether Tsallis-Pareto energy distribution do overlap with hadron spectra at high-pT. We fitted data, measured in proton-proton (proton-antiproton) collisions in wide center of mass energy range from 200 GeV RHIC up to 7 TeV LHC energies. Furthermore, our test is extended to an investigation of a possible √s-dependence of the power in the Tsallis-Pareto distribution, motivated by QCD evolution equations. We found that Tsallis-Pareto distributions fit well high-pT data, in the wide center of mass energy range. Deviance from the fits appears at p T > 20-30 GeV/c, especially on CDF data. Introducing a pT-scaling ansatz, the fits at low and intermediate transverse momenta still remain good, and the deviations tend to disappear at the highest-pT data.

  8. From hard thermal loops to Langevin dynamics

    International Nuclear Information System (INIS)

    Boedeker, Dietrich

    1999-01-01

    In hot non-Abelian gauge theories, processes characterized by the momentum scale g 2 T (such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft (vertical bar p vertical bar ∼ g 2 T) field modes is obtained by integrating out momenta larger than than g 2 T. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale T, it is shown how to integrate out the scale gT in an expansion in the gauge coupling g. At leading order in g, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as Γ = κg 10 log(1/g)gT 4 , and it allows for a calculation for κ on the lattice

  9. Elementary Statistical Models for Vector Collision-Sequence Interference Effects with Poisson-Distributed Collision Times

    International Nuclear Information System (INIS)

    Lewis, J.C.

    2011-01-01

    In a recent paper (Lewis, 2008) a class of models suitable for application to collision-sequence interference was introduced. In these models velocities are assumed to be completely randomized in each collision. The distribution of velocities was assumed to be Gaussian. The integrated induced dipole moment μk, for vector interference, or the scalar modulation μk, for scalar interference, was assumed to be a function of the impulse (integrated force) fk, or its magnitude fk, experienced by the molecule in a collision. For most of (Lewis, 2008) it was assumed that μk fk and μk fk, but it proved to be possible to extend the models, so that the magnitude of the induced dipole moment is equal to an arbitrary power or sum of powers of the intermolecular force. This allows estimates of the in filling of the interference dip by the dis proportionality of the induced dipole moment and force. One particular such model, using data from (Herman and Lewis, 2006), leads to the most realistic estimate for the in filling of the vector interference dip yet obtained. In (Lewis, 2008) the drastic assumption was made that collision times occurred at equal intervals. In the present paper that assumption is removed: the collision times are taken to form a Poisson process. This is much more realistic than the equal-intervals assumption. The interference dip is found to be a Lorentzian in this model

  10. A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

    Science.gov (United States)

    Fakhari, Abbas; Bolster, Diogo; Luo, Li-Shi

    2017-07-01

    We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT-LBM-AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid-liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

  11. Adaptive Non-Boltzmann Monte Carlo

    International Nuclear Information System (INIS)

    Fitzgerald, M.; Picard, R.R.; Silver, R.N.

    1998-01-01

    This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods

  12. Adaptive Non-Boltzmann Monte Carlo

    Energy Technology Data Exchange (ETDEWEB)

    Fitzgerald, M.; Picard, R.R.; Silver, R.N.

    1998-06-01

    This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods.

  13. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

    International Nuclear Information System (INIS)

    Ayissi, Raoul Domingo; Noutchegueme, Norbert

    2015-01-01

    Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

  14. Hermite regularization of the lattice Boltzmann method for open source computational aeroacoustics.

    Science.gov (United States)

    Brogi, F; Malaspinas, O; Chopard, B; Bonadonna, C

    2017-10-01

    The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, which is of interest for aeroacoustic applications. Several solutions have been proposed but are often too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. An original regularized collision operator is proposed, based on the expansion of Hermite polynomials, that greatly improves the accuracy and stability of the LBM without significantly altering its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between this approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial software, while here the entire theoretical framework is implemented using an open source library (palabos).

  15. A topological insight into restricted Boltzmann machines

    NARCIS (Netherlands)

    Mocanu, D.C.; Mocanu, E.; Nguyen, H.P.; Gibescu, M.; Liotta, A.

    Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as density estimators. Thus, their generative and discriminative

  16. Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism

    Science.gov (United States)

    Wu, Bin; Kovchegov, Yuri V.

    2018-03-01

    We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function G 22 aμ, bν due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to G 22 aμ, bν coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τ Z gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τ Z ≫ 1 /Q s and τ - τ Z ≫ 1 /Q s (with Q s the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ - τ Z ≫ τ Z ≫ 1 /Q s we end up with a result very different from kinetic theory and consistent with a picture of "free-streaming" particles. Due to the approximations made, our calculation is too coarse to indicate whether the region (i) or (ii) is the correct one: to resolve this controversy, we shall present a detailed diagrammatic calculation of the rescattering correction in the φ 4 theory in the second paper of this duplex.

  17. Gravitational waves from cosmic bubble collisions

    International Nuclear Information System (INIS)

    Kim, Dong-Hoon; Lee, Bum-Hoon; Lee, Wonwoo; Yang, Jongmann; Yeom, Dong-han

    2015-01-01

    Cosmic bubbles are nucleated through the quantum tunneling process. After nucleation they would expand and undergo collisions with each other. In this paper, we focus in particular on collisions of two equal-sized bubbles and compute gravitational waves emitted from the collisions. First, we study the mechanism of the collisions by means of a real scalar field and its quartic potential. Then, using this model, we compute gravitational waves from the collisions in a straightforward manner. In the quadrupole approximation, time-domain gravitational waveforms are directly obtained by integrating the energy-momentum tensors over the volume of the wave sources, where the energy-momentum tensors are expressed in terms of the scalar field, the local geometry and the potential. We present gravitational waveforms emitted during (i) the initial-to-intermediate stage of strong collisions and (ii) the final stage of weak collisions: the former is obtained numerically, in full General Relativity and the latter analytically, in the flat spacetime approximation. We gain qualitative insights into the time-domain gravitational waveforms from bubble collisions: during (i), the waveforms show the non-linearity of the collisions, characterized by a modulating frequency and cusp-like bumps, whereas during (ii), the waveforms exhibit the linearity of the collisions, featured by smooth monochromatic oscillations. (orig.)

  18. Measurement of the centrality and pseudorapidity dependence of the integrated elliptic flow in lead-lead collisions at $\\sqrt{s_{\\mathrm{NN}}}=2.76$ TeV with the ATLAS detector.

    CERN Document Server

    Aad, Georges; Abdallah, Jalal; Abdel Khalek, Samah; Abdinov, Ovsat; Aben, Rosemarie; Abi, Babak; Abolins, Maris; AbouZeid, Ossama; Abramowicz, Halina; Abreu, Henso; Abreu, Ricardo; Abulaiti, Yiming; Acharya, Bobby Samir; Adamczyk, Leszek; Adams, David; Adelman, Jahred; Adomeit, Stefanie; Adye, Tim; Agatonovic-Jovin, Tatjana; Aguilar-Saavedra, Juan Antonio; Agustoni, Marco; Ahlen, Steven; Ahmadov, Faig; Aielli, Giulio; Åkesson, Torsten Paul Ake; Akimoto, Ginga; Akimov, Andrei; Alberghi, Gian Luigi; Albert, Justin; Albrand, Solveig; Alconada Verzini, Maria Josefina; Aleksa, Martin; Aleksandrov, Igor; Alexa, Calin; Alexander, Gideon; Alexandre, Gauthier; Alexopoulos, Theodoros; Alhroob, Muhammad; Alimonti, Gianluca; Alio, Lion; Alison, John; Allbrooke, Benedict; Allison, Lee John; Allport, Phillip; Allwood-Spiers, Sarah; Almond, John; Aloisio, Alberto; Alonso, Alejandro; Alonso, Francisco; Alpigiani, Cristiano; Altheimer, Andrew David; Alvarez Gonzalez, Barbara; Alviggi, Mariagrazia; Amako, Katsuya; Amaral Coutinho, Yara; Amelung, Christoph; Amidei, Dante; Amor Dos Santos, Susana Patricia; Amorim, Antonio; Amoroso, Simone; Amram, Nir; Amundsen, Glenn; Anastopoulos, Christos; Ancu, Lucian Stefan; Andari, Nansi; Andeen, Timothy; Anders, Christoph Falk; Anders, Gabriel; Anderson, Kelby; Andreazza, Attilio; Andrei, George Victor; Anduaga, Xabier; Angelidakis, Stylianos; Angelozzi, Ivan; Anger, Philipp; Angerami, Aaron; Anghinolfi, Francis; Anisenkov, Alexey; Anjos, Nuno; Annovi, Alberto; Antonaki, Ariadni; Antonelli, Mario; Antonov, Alexey; Antos, Jaroslav; Anulli, Fabio; Aoki, Masato; Aperio Bella, Ludovica; Apolle, Rudi; Arabidze, Giorgi; Aracena, Ignacio; Arai, Yasuo; Araque, Juan Pedro; Arce, Ayana; Arguin, Jean-Francois; Argyropoulos, Spyridon; Arik, Metin; Armbruster, Aaron James; Arnaez, Olivier; Arnal, Vanessa; Arnold, Hannah; Arslan, Ozan; Artamonov, Andrei; Artoni, Giacomo; Asai, Shoji; Asbah, Nedaa; Ashkenazi, Adi; Ask, Stefan; Åsman, Barbro; Asquith, Lily; Assamagan, Ketevi; Astalos, Robert; Atkinson, Markus; Atlay, Naim Bora; Auerbach, Benjamin; Augsten, Kamil; Aurousseau, Mathieu; Avolio, Giuseppe; Azuelos, Georges; Azuma, Yuya; Baak, Max; Bacci, Cesare; Bachacou, Henri; Bachas, Konstantinos; Backes, Moritz; Backhaus, Malte; Backus Mayes, John; Badescu, Elisabeta; Bagiacchi, Paolo; Bagnaia, Paolo; Bai, Yu; Bain, Travis; Baines, John; Baker, Oliver Keith; Baker, Sarah; Balek, Petr; Balli, Fabrice; Banas, Elzbieta; Banerjee, Swagato; Bangert, Andrea Michelle; Bannoura, Arwa A E; Bansal, Vikas; Bansil, Hardeep Singh; Barak, Liron; Baranov, Sergei; Barberio, Elisabetta Luigia; Barberis, Dario; Barbero, Marlon; Barillari, Teresa; Barisonzi, Marcello; Barklow, Timothy; Barlow, Nick; Barnett, Bruce; Barnett, Michael; Barnovska, Zuzana; Baroncelli, Antonio; Barone, Gaetano; Barr, Alan; Barreiro, Fernando; Barreiro Guimarães da Costa, João; Bartoldus, Rainer; Barton, Adam Edward; Bartos, Pavol; Bartsch, Valeria; Bassalat, Ahmed; Basye, Austin; Bates, Richard; Batkova, Lucia; Batley, Richard; Battistin, Michele; Bauer, Florian; Bawa, Harinder Singh; Beau, Tristan; Beauchemin, Pierre-Hugues; Beccherle, Roberto; Bechtle, Philip; Beck, Hans Peter; Becker, Anne Kathrin; Becker, Sebastian; Beckingham, Matthew; Becot, Cyril; Beddall, Andrew; Beddall, Ayda; Bedikian, Sourpouhi; Bednyakov, Vadim; Bee, Christopher; Beemster, Lars; Beermann, Thomas; Begel, Michael; Behr, Katharina; Belanger-Champagne, Camille; Bell, Paul; Bell, William; Bella, Gideon; Bellagamba, Lorenzo; Bellerive, Alain; Bellomo, Massimiliano; Belloni, Alberto; Belotskiy, Konstantin; Beltramello, Olga; Benary, Odette; Benchekroun, Driss; Bendtz, Katarina; Benekos, Nektarios; Benhammou, Yan; Benhar Noccioli, Eleonora; Benitez Garcia, Jorge-Armando; Benjamin, Douglas; Bensinger, James; Benslama, Kamal; Bentvelsen, Stan; Berge, David; Bergeaas Kuutmann, Elin; Berger, Nicolas; Berghaus, Frank; Berglund, Elina; Beringer, Jürg; Bernard, Clare; Bernat, Pauline; Bernius, Catrin; Bernlochner, Florian Urs; Berry, Tracey; Berta, Peter; Bertella, Claudia; Bertolucci, Federico; Besana, Maria Ilaria; Besjes, Geert-Jan; Bessidskaia, Olga; Besson, Nathalie; Betancourt, Christopher; Bethke, Siegfried; Bhimji, Wahid; Bianchi, Riccardo-Maria; Bianchini, Louis; Bianco, Michele; Biebel, Otmar; Bieniek, Stephen Paul; Bierwagen, Katharina; Biesiada, Jed; Biglietti, Michela; Bilbao De Mendizabal, Javier; Bilokon, Halina; Bindi, Marcello; Binet, Sebastien; Bingul, Ahmet; Bini, Cesare; Black, Curtis; Black, James; Black, Kevin; Blackburn, Daniel; Blair, Robert; Blanchard, Jean-Baptiste; Blazek, Tomas; Bloch, Ingo; Blocker, Craig; Blum, Walter; Blumenschein, Ulrike; Bobbink, Gerjan; Bobrovnikov, Victor; Bocchetta, Simona Serena; Bocci, Andrea; Boddy, Christopher Richard; Boehler, Michael; Boek, Jennifer; Boek, Thorsten Tobias; Bogaerts, Joannes Andreas; Bogdanchikov, Alexander; Bogouch, Andrei; Bohm, Christian; Bohm, Jan; Boisvert, Veronique; Bold, Tomasz; Boldea, Venera; Boldyrev, Alexey; Bomben, Marco; Bona, Marcella; Boonekamp, Maarten; Borisov, Anatoly; Borissov, Guennadi; Borri, Marcello; Borroni, Sara; Bortfeldt, Jonathan; Bortolotto, Valerio; Bos, Kors; Boscherini, Davide; Bosman, Martine; Boterenbrood, Hendrik; Boudreau, Joseph; Bouffard, Julian; Bouhova-Thacker, Evelina Vassileva; Boumediene, Djamel Eddine; Bourdarios, Claire; Bousson, Nicolas; Boutouil, Sara; Boveia, Antonio; Boyd, James; Boyko, Igor; Bozovic-Jelisavcic, Ivanka; Bracinik, Juraj; Branchini, Paolo; Brandt, Andrew; Brandt, Gerhard; Brandt, Oleg; Bratzler, Uwe; Brau, Benjamin; Brau, James; Braun, Helmut; Brazzale, Simone Federico; Brelier, Bertrand; Brendlinger, Kurt; Brennan, Amelia Jean; Brenner, Richard; Bressler, Shikma; Bristow, Kieran; Bristow, Timothy Michael; Britton, Dave; Brochu, Frederic; Brock, Ian; Brock, Raymond; Bromberg, Carl; Bronner, Johanna; Brooijmans, Gustaaf; Brooks, Timothy; Brooks, William; Brosamer, Jacquelyn; Brost, Elizabeth; Brown, Gareth; Brown, Jonathan; Bruckman de Renstrom, Pawel; Bruncko, Dusan; Bruneliere, Renaud; Brunet, Sylvie; Bruni, Alessia; Bruni, Graziano; Bruschi, Marco; Bryngemark, Lene; Buanes, Trygve; Buat, Quentin; Bucci, Francesca; Buchholz, Peter; Buckingham, Ryan; Buckley, Andrew; Buda, Stelian Ioan; Budagov, Ioulian; Buehrer, Felix; Bugge, Lars; Bugge, Magnar Kopangen; Bulekov, Oleg; Bundock, Aaron Colin; Burckhart, Helfried; Burdin, Sergey; Burghgrave, Blake; Burke, Stephen; Burmeister, Ingo; Busato, Emmanuel; Büscher, Daniel; Büscher, Volker; Bussey, Peter; Buszello, Claus-Peter; Butler, Bart; Butler, John; Butt, Aatif Imtiaz; Buttar, Craig; Butterworth, Jonathan; Butti, Pierfrancesco; Buttinger, William; Buzatu, Adrian; Byszewski, Marcin; Cabrera Urbán, Susana; Caforio, Davide; Cakir, Orhan; Calafiura, Paolo; Calandri, Alessandro; Calderini, Giovanni; Calfayan, Philippe; Calkins, Robert; Caloba, Luiz; Calvet, David; Calvet, Samuel; Camacho Toro, Reina; Camarda, Stefano; Cameron, David; Caminada, Lea Michaela; Caminal Armadans, Roger; Campana, Simone; Campanelli, Mario; Campoverde, Angel; Canale, Vincenzo; Canepa, Anadi; Cantero, Josu; Cantrill, Robert; Cao, Tingting; Capeans Garrido, Maria Del Mar; Caprini, Irinel; Caprini, Mihai; Capua, Marcella; Caputo, Regina; Cardarelli, Roberto; Carli, Tancredi; Carlino, Gianpaolo; Carminati, Leonardo; Caron, Sascha; Carquin, Edson; Carrillo-Montoya, German D; Carter, Janet; Carvalho, João; Casadei, Diego; Casado, Maria Pilar; Casolino, Mirkoantonio; Castaneda-Miranda, Elizabeth; Castelli, Angelantonio; Castillo Gimenez, Victoria; Castro, Nuno Filipe; Catastini, Pierluigi; Catinaccio, Andrea; Catmore, James; Cattai, Ariella; Cattani, Giordano; Caughron, Seth; Cavaliere, Viviana; Cavalli, Donatella; Cavalli-Sforza, Matteo; Cavasinni, Vincenzo; Ceradini, Filippo; Cerio, Benjamin; Cerny, Karel; Santiago Cerqueira, Augusto; Cerri, Alessandro; Cerrito, Lucio; Cerutti, Fabio; Cerv, Matevz; Cervelli, Alberto; Cetin, Serkant Ali; Chafaq, Aziz; Chakraborty, Dhiman; Chalupkova, Ina; Chan, Kevin; Chang, Philip; Chapleau, Bertrand; Chapman, John Derek; Charfeddine, Driss; Charlton, Dave; Chau, Chav Chhiv; Chavez Barajas, Carlos Alberto; Cheatham, Susan; Chegwidden, Andrew; Chekanov, Sergei; Chekulaev, Sergey; Chelkov, Gueorgui; Chelstowska, Magda Anna; Chen, Chunhui; Chen, Hucheng; Chen, Karen; Chen, Liming; Chen, Shenjian; Chen, Xin; Chen, Yujiao; Cheng, Hok Chuen; Cheng, Yangyang; Cheplakov, Alexander; Cherkaoui El Moursli, Rajaa; Chernyatin, Valeriy; Cheu, Elliott; Chevalier, Laurent; Chiarella, Vitaliano; Chiefari, Giovanni; Childers, John Taylor; Chilingarov, Alexandre; Chiodini, Gabriele; Chisholm, Andrew; Chislett, Rebecca Thalatta; Chitan, Adrian; Chizhov, Mihail; Chouridou, Sofia; Chow, Bonnie Kar Bo; Christidi, Ilektra-Athanasia; Chromek-Burckhart, Doris; Chu, Ming-Lee; Chudoba, Jiri; Chwastowski, Janusz; Chytka, Ladislav; Ciapetti, Guido; Ciftci, Abbas Kenan; Ciftci, Rena; Cinca, Diane; Cindro, Vladimir; Ciocio, Alessandra; Cirkovic, Predrag; Citron, Zvi Hirsh; Citterio, Mauro; Ciubancan, Mihai; Clark, Allan G; Clark, Philip James; Clarke, Robert; Cleland, Bill; Clemens, Jean-Claude; Clement, Christophe; Coadou, Yann; Cobal, Marina; Coccaro, Andrea; Cochran, James H; Coffey, Laurel; Cogan, Joshua Godfrey; Coggeshall, James; Cole, Brian; Cole, Stephen; Colijn, Auke-Pieter; Collins-Tooth, Christopher; Collot, Johann; Colombo, Tommaso; Colon, German; Compostella, Gabriele; Conde Muiño, Patricia; Coniavitis, Elias; Conidi, Maria Chiara; Connell, Simon Henry; Connelly, Ian; Consonni, Sofia Maria; Consorti, Valerio; Constantinescu, Serban; Conta, Claudio; Conti, Geraldine; Conventi, Francesco; Cooke, Mark; Cooper, Ben; Cooper-Sarkar, Amanda; Cooper-Smith, Neil; Copic, Katherine; Cornelissen, Thijs; Corradi, Massimo; Corriveau, Francois; Corso-Radu, Alina; Cortes-Gonzalez, Arely; Cortiana, Giorgio; Costa, Giuseppe; Costa, María José; Costanzo, Davide; Côté, David; Cottin, Giovanna; Cowan, Glen; Cox, Brian; Cranmer, Kyle; Cree, Graham; Crépé-Renaudin, Sabine; Crescioli, Francesco; Crispin Ortuzar, Mireia; Cristinziani, Markus; Croft, Vince; Crosetti, Giovanni; Cuciuc, Constantin-Mihai; Cuhadar Donszelmann, Tulay; Cummings, Jane; Curatolo, Maria; Cuthbert, Cameron; Czirr, Hendrik; Czodrowski, Patrick; Czyczula, Zofia; D'Auria, Saverio; D'Onofrio, Monica; Da Cunha Sargedas De Sousa, Mario Jose; Da Via, Cinzia; Dabrowski, Wladyslaw; Dafinca, Alexandru; Dai, Tiesheng; Dale, Orjan; Dallaire, Frederick; Dallapiccola, Carlo; Dam, Mogens; Daniells, Andrew Christopher; Dano Hoffmann, Maria; Dao, Valerio; Darbo, Giovanni; Darlea, Georgiana Lavinia; Darmora, Smita; Dassoulas, James; Dattagupta, Aparajita; Davey, Will; David, Claire; Davidek, Tomas; Davies, Eleanor; Davies, Merlin; Davignon, Olivier; Davison, Adam; Davison, Peter; Davygora, Yuriy; Dawe, Edmund; Dawson, Ian; Daya-Ishmukhametova, Rozmin; De, Kaushik; de Asmundis, Riccardo; De Castro, Stefano; De Cecco, Sandro; de Graat, Julien; De Groot, Nicolo; de Jong, Paul; De la Torre, Hector; De Lorenzi, Francesco; De Nooij, Lucie; De Pedis, Daniele; De Salvo, Alessandro; De Sanctis, Umberto; De Santo, Antonella; De Vivie De Regie, Jean-Baptiste; De Zorzi, Guido; Dearnaley, William James; Debbe, Ramiro; Debenedetti, Chiara; Dechenaux, Benjamin; Dedovich, Dmitri; Degenhardt, James; Deigaard, Ingrid; Del Peso, Jose; Del Prete, Tarcisio; Deliot, Frederic; Delitzsch, Chris Malena; Deliyergiyev, Maksym; Dell'Acqua, Andrea; Dell'Asta, Lidia; Dell'Orso, Mauro; Della Pietra, Massimo; della Volpe, Domenico; Delmastro, Marco; Delsart, Pierre-Antoine; Deluca, Carolina; Demers, Sarah; Demichev, Mikhail; Demilly, Aurelien; Denisov, Sergey; Derendarz, Dominik; Derkaoui, Jamal Eddine; Derue, Frederic; Dervan, Paul; Desch, Klaus Kurt; Deterre, Cecile; Deviveiros, Pier-Olivier; Dewhurst, Alastair; Dhaliwal, Saminder; Di Ciaccio, Anna; Di Ciaccio, Lucia; Di Domenico, Antonio; Di Donato, Camilla; Di Girolamo, Alessandro; Di Girolamo, Beniamino; Di Mattia, Alessandro; Di Micco, Biagio; Di Nardo, Roberto; Di Simone, Andrea; Di Sipio, Riccardo; Di Valentino, David; Diaz, Marco Aurelio; Diehl, Edward; Dietrich, Janet; Dietzsch, Thorsten; Diglio, Sara; Dimitrievska, Aleksandra; Dingfelder, Jochen; Dionisi, Carlo; Dita, Petre; Dita, Sanda; Dittus, Fridolin; Djama, Fares; Djobava, Tamar; Barros do Vale, Maria Aline; Do Valle Wemans, André; Doan, Thi Kieu Oanh; Dobos, Daniel; Dobson, Ellie; Doglioni, Caterina; Doherty, Tom; Dohmae, Takeshi; Dolejsi, Jiri; Dolezal, Zdenek; Dolgoshein, Boris; Donadelli, Marisilvia; Donati, Simone; Dondero, Paolo; Donini, Julien; Dopke, Jens; Doria, Alessandra; Dova, Maria-Teresa; Doyle, Tony; Dris, Manolis; Dubbert, Jörg; Dube, Sourabh; Dubreuil, Emmanuelle; Duchovni, Ehud; Duckeck, Guenter; Ducu, Otilia Anamaria; Duda, Dominik; Dudarev, Alexey; Dudziak, Fanny; Duflot, Laurent; Duguid, Liam; Dührssen, Michael; Dunford, Monica; Duran Yildiz, Hatice; Düren, Michael; Durglishvili, Archil; Dwuznik, Michal; Dyndal, Mateusz; Ebke, Johannes; Edson, William; Edwards, Nicholas Charles; Ehrenfeld, Wolfgang; Eifert, Till; Eigen, Gerald; Einsweiler, Kevin; Ekelof, Tord; El Kacimi, Mohamed; Ellert, Mattias; Elles, Sabine; Ellinghaus, Frank; Ellis, Nicolas; Elmsheuser, Johannes; Elsing, Markus; Emeliyanov, Dmitry; Enari, Yuji; Endner, Oliver Chris; Endo, Masaki; Engelmann, Roderich; Erdmann, Johannes; Ereditato, Antonio; Eriksson, Daniel; Ernis, Gunar; Ernst, Jesse; Ernst, Michael; Ernwein, Jean; Errede, Deborah; Errede, Steven; Ertel, Eugen; Escalier, Marc; Esch, Hendrik; Escobar, Carlos; Esposito, Bellisario; Etienvre, Anne-Isabelle; Etzion, Erez; Evans, Hal; Fabbri, Laura; Facini, Gabriel; Fakhrutdinov, Rinat; Falciano, Speranza; Faltova, Jana; Fang, Yaquan; Fanti, Marcello; Farbin, Amir; Farilla, Addolorata; Farooque, Trisha; Farrell, Steven; Farrington, Sinead; Farthouat, Philippe; Fassi, Farida; Fassnacht, Patrick; Fassouliotis, Dimitrios; Favareto, Andrea; Fayard, Louis; Federic, Pavol; Fedin, Oleg; Fedorko, Wojciech; Fehling-Kaschek, Mirjam; Feigl, Simon; Feligioni, Lorenzo; Feng, Cunfeng; Feng, Eric; Feng, Haolu; Fenyuk, Alexander; Fernandez Perez, Sonia; Ferrag, Samir; Ferrando, James; Ferrari, Arnaud; Ferrari, Pamela; Ferrari, Roberto; Ferreira de Lima, Danilo Enoque; Ferrer, Antonio; Ferrere, Didier; Ferretti, Claudio; Ferretto Parodi, Andrea; Fiascaris, Maria; Fiedler, Frank; Filipčič, Andrej; Filipuzzi, Marco; Filthaut, Frank; Fincke-Keeler, Margret; Finelli, Kevin Daniel; Fiolhais, Miguel; Fiorini, Luca; Firan, Ana; Fischer, Julia; Fisher, Wade Cameron; Fitzgerald, Eric Andrew; Flechl, Martin; Fleck, Ivor; Fleischmann, Philipp; Fleischmann, Sebastian; Fletcher, Gareth Thomas; Fletcher, Gregory; Flick, Tobias; Floderus, Anders; Flores Castillo, Luis; Florez Bustos, Andres Carlos; Flowerdew, Michael; Formica, Andrea; Forti, Alessandra; Fortin, Dominique; Fournier, Daniel; Fox, Harald; Fracchia, Silvia; Francavilla, Paolo; Franchini, Matteo; Franchino, Silvia; Francis, David; Franklin, Melissa; Franz, Sebastien; Fraternali, Marco; French, Sky; Friedrich, Conrad; Friedrich, Felix; Froidevaux, Daniel; Frost, James; Fukunaga, Chikara; Fullana Torregrosa, Esteban; Fulsom, Bryan Gregory; Fuster, Juan; Gabaldon, Carolina; Gabizon, Ofir; Gabrielli, Alessandro; Gabrielli, Andrea; Gadatsch, Stefan; Gadomski, Szymon; Gagliardi, Guido; Gagnon, Pauline; Galea, Cristina; Galhardo, Bruno; Gallas, Elizabeth; Gallo, Valentina Santina; Gallop, Bruce; Gallus, Petr; Galster, Gorm Aske Gram Krohn; Gan, KK; Gandrajula, Reddy Pratap; Gao, Jun; Gao, Yongsheng; Garay Walls, Francisca; Garberson, Ford; García, Carmen; García Navarro, José Enrique; Garcia-Sciveres, Maurice; Gardner, Robert; Garelli, Nicoletta; Garonne, Vincent; Gatti, Claudio; Gaudio, Gabriella; Gaur, Bakul; Gauthier, Lea; Gauzzi, Paolo; Gavrilenko, Igor; Gay, Colin; Gaycken, Goetz; Gazis, Evangelos; Ge, Peng; Gecse, Zoltan; Gee, Norman; Geerts, Daniël Alphonsus Adrianus; Geich-Gimbel, Christoph; Gellerstedt, Karl; Gemme, Claudia; Gemmell, Alistair; Genest, Marie-Hélène; Gentile, Simonetta; George, Matthias; George, Simon; Gerbaudo, Davide; Gershon, Avi; Ghazlane, Hamid; Ghodbane, Nabil; Giacobbe, Benedetto; Giagu, Stefano; Giangiobbe, Vincent; Giannetti, Paola; Gianotti, Fabiola; Gibbard, Bruce; Gibson, Stephen; Gilchriese, Murdock; Gillam, Thomas; Gillberg, Dag; Gilles, Geoffrey; Gingrich, Douglas; Giokaris, Nikos; Giordani, MarioPaolo; Giordano, Raffaele; Giorgi, Francesco Michelangelo; Giraud, Pierre-Francois; Giugni, Danilo; Giuliani, Claudia; Giulini, Maddalena; Gjelsten, Børge Kile; Gkialas, Ioannis; Gladilin, Leonid; Glasman, Claudia; Glatzer, Julian; Glaysher, Paul; Glazov, Alexandre; Glonti, George; Goblirsch-Kolb, Maximilian; Goddard, Jack Robert; Godfrey, Jennifer; Godlewski, Jan; Goeringer, Christian; Goldfarb, Steven; Golling, Tobias; Golubkov, Dmitry; Gomes, Agostinho; Gomez Fajardo, Luz Stella; Gonçalo, Ricardo; Goncalves Pinto Firmino Da Costa, Joao; Gonella, Laura; González de la Hoz, Santiago; Gonzalez Parra, Garoe; Gonzalez Silva, Laura; Gonzalez-Sevilla, Sergio; Goossens, Luc; Gorbounov, Petr Andreevich; Gordon, Howard; Gorelov, Igor; Gorini, Benedetto; Gorini, Edoardo; Gorišek, Andrej; Gornicki, Edward; Goshaw, Alfred; Gössling, Claus; Gostkin, Mikhail Ivanovitch; Gouighri, Mohamed; Goujdami, Driss; Goulette, Marc Phillippe; Goussiou, Anna; Goy, Corinne; Gozpinar, Serdar; Grabas, Herve Marie Xavier; Graber, Lars; Grabowska-Bold, Iwona; Grafström, Per; Grahn, Karl-Johan; Gramling, Johanna; Gramstad, Eirik; Grancagnolo, Sergio; Grassi, Valerio; Gratchev, Vadim; Gray, Heather; Graziani, Enrico; Grebenyuk, Oleg; Greenwood, Zeno Dixon; Gregersen, Kristian; Gregor, Ingrid-Maria; Grenier, Philippe; Griffiths, Justin; Grillo, Alexander; Grimm, Kathryn; Grinstein, Sebastian; Gris, Philippe Luc Yves; Grishkevich, Yaroslav; Grivaz, Jean-Francois; Grohs, Johannes Philipp; Grohsjean, Alexander; Gross, Eilam; Grosse-Knetter, Joern; Grossi, Giulio Cornelio; Groth-Jensen, Jacob; Grout, Zara Jane; Grybel, Kai; Guan, Liang; Guescini, Francesco; Guest, Daniel; Gueta, Orel; Guicheney, Christophe; Guido, Elisa; Guillemin, Thibault; Guindon, Stefan; Gul, Umar; Gumpert, Christian; Gunther, Jaroslav; Guo, Jun; Gupta, Shaun; Gutierrez, Phillip; Gutierrez Ortiz, Nicolas Gilberto; Gutschow, Christian; Guttman, Nir; Guyot, Claude; Gwenlan, Claire; Gwilliam, Carl; Haas, Andy; Haber, Carl; Hadavand, Haleh Khani; Haddad, Nacim; Haefner, Petra; Hageboeck, Stephan; Hajduk, Zbigniew; Hakobyan, Hrachya; Haleem, Mahsana; Hall, David; Halladjian, Garabed; Hamacher, Klaus; Hamal, Petr; Hamano, Kenji; Hamer, Matthias; Hamilton, Andrew; Hamilton, Samuel; Hamnett, Phillip George; Han, Liang; Hanagaki, Kazunori; Hanawa, Keita; Hance, Michael; Hanke, Paul; Hansen, Jørgen Beck; Hansen, Jorn Dines; Hansen, Peter Henrik; Hara, Kazuhiko; Hard, Andrew; Harenberg, Torsten; Harkusha, Siarhei; Harper, Devin; Harrington, Robert; Harris, Orin; Harrison, Paul Fraser; Hartjes, Fred; Hasegawa, Satoshi; Hasegawa, Yoji; Hasib, A; Hassani, Samira; Haug, Sigve; Hauschild, Michael; Hauser, Reiner; Havranek, Miroslav; Hawkes, Christopher; Hawkings, Richard John; Hawkins, Anthony David; Hayashi, Takayasu; Hayden, Daniel; Hays, Chris; Hayward, Helen; Haywood, Stephen; Head, Simon; Heck, Tobias; Hedberg, Vincent; Heelan, Louise; Heim, Sarah; Heim, Timon; Heinemann, Beate; Heinrich, Lukas; Heisterkamp, Simon; Hejbal, Jiri; Helary, Louis; Heller, Claudio; Heller, Matthieu; Hellman, Sten; Hellmich, Dennis; Helsens, Clement; Henderson, James; Henderson, Robert; Hengler, Christopher; Henrichs, Anna; Henriques Correia, Ana Maria; Henrot-Versille, Sophie; Hensel, Carsten; Herbert, Geoffrey Henry; Hernández Jiménez, Yesenia; Herrberg-Schubert, Ruth; Herten, Gregor; Hertenberger, Ralf; Hervas, Luis; Hesketh, Gavin Grant; Hessey, Nigel; Hickling, Robert; Higón-Rodriguez, Emilio; Hill, Ewan; Hill, John; Hiller, Karl Heinz; Hillert, Sonja; Hillier, Stephen; Hinchliffe, Ian; Hines, Elizabeth; Hirose, Minoru; Hirschbuehl, Dominic; Hobbs, John; Hod, Noam; Hodgkinson, Mark; Hodgson, Paul; Hoecker, Andreas; Hoeferkamp, Martin; Hoffman, Julia; Hoffmann, Dirk; Hofmann, Julia Isabell; Hohlfeld, Marc; Holmes, Tova Ray; Hong, Tae Min; Hooft van Huysduynen, Loek; Hostachy, Jean-Yves; Hou, Suen; Hoummada, Abdeslam; Howard, Jacob; Howarth, James; Hrabovsky, Miroslav; Hristova, Ivana; Hrivnac, Julius; Hryn'ova, Tetiana; Hsu, Pai-hsien Jennifer; Hsu, Shih-Chieh; Hu, Diedi; Hu, Xueye; Huang, Yanping; Hubacek, Zdenek; Hubaut, Fabrice; Huegging, Fabian; Huffman, Todd Brian; Hughes, Emlyn; Hughes, Gareth; Huhtinen, Mika; Hülsing, Tobias Alexander; Hurwitz, Martina; Huseynov, Nazim; Huston, Joey; Huth, John; Iacobucci, Giuseppe; Iakovidis, Georgios; Ibragimov, Iskander; Iconomidou-Fayard, Lydia; Ideal, Emma; Iengo, Paolo; Igonkina, Olga; Iizawa, Tomoya; Ikegami, Yoichi; Ikematsu, Katsumasa; Ikeno, Masahiro; Iliadis, Dimitrios; Ilic, Nikolina; Inamaru, Yuki; Ince, Tayfun; Ioannou, Pavlos; Iodice, Mauro; Iordanidou, Kalliopi; Ippolito, Valerio; Irles Quiles, Adrian; Isaksson, Charlie; Ishino, Masaya; Ishitsuka, Masaki; Ishmukhametov, Renat; Issever, Cigdem; Istin, Serhat; Iturbe Ponce, Julia Mariana; Ivarsson, Jenny; Ivashin, Anton; Iwanski, Wieslaw; Iwasaki, Hiroyuki; Izen, Joseph; Izzo, Vincenzo; Jackson, Brett; Jackson, Matthew; Jackson, Paul; Jaekel, Martin; Jain, Vivek; Jakobs, Karl; Jakobsen, Sune; Jakoubek, Tomas; Jakubek, Jan; Jamin, David Olivier; Jana, Dilip; Jansen, Eric; Jansen, Hendrik; Janssen, Jens; Janus, Michel; Jarlskog, Göran; Javadov, Namig; Javůrek, Tomáš; Jeanty, Laura; Jeng, Geng-yuan; Jennens, David; Jenni, Peter; Jentzsch, Jennifer; Jeske, Carl; Jézéquel, Stéphane; Ji, Haoshuang; Ji, Weina; Jia, Jiangyong; Jiang, Yi; Jimenez Belenguer, Marcos; Jin, Shan; Jinaru, Adam; Jinnouchi, Osamu; Joergensen, Morten Dam; Johansson, Erik; Johansson, Per; Johns, Kenneth; Jon-And, Kerstin; Jones, Graham; Jones, Roger; Jones, Tim; Jongmanns, Jan; Jorge, Pedro; Joshi, Kiran Daniel; Jovicevic, Jelena; Ju, Xiangyang; Jung, Christian; Jungst, Ralph Markus; Jussel, Patrick; Juste Rozas, Aurelio; Kaci, Mohammed; Kaczmarska, Anna; Kado, Marumi; Kagan, Harris; Kagan, Michael; Kajomovitz, Enrique; Kama, Sami; Kanaya, Naoko; Kaneda, Michiru; Kaneti, Steven; Kanno, Takayuki; Kantserov, Vadim; Kanzaki, Junichi; Kaplan, Benjamin; Kapliy, Anton; Kar, Deepak; Karakostas, Konstantinos; Karastathis, Nikolaos; Karnevskiy, Mikhail; Karpov, Sergey; Karthik, Krishnaiyengar; Kartvelishvili, Vakhtang; Karyukhin, Andrey; Kashif, Lashkar; Kasieczka, Gregor; Kass, Richard; Kastanas, Alex; Kataoka, Yousuke; Katre, Akshay; Katzy, Judith; Kaushik, Venkatesh; Kawagoe, Kiyotomo; Kawamoto, Tatsuo; Kawamura, Gen; Kazama, Shingo; Kazanin, Vassili; Kazarinov, Makhail; Keeler, Richard; Kehoe, Robert; Keil, Markus; Keller, John; Keoshkerian, Houry; Kepka, Oldrich; Kerševan, Borut Paul; Kersten, Susanne; Kessoku, Kohei; Keung, Justin; Khalil-zada, Farkhad; Khandanyan, Hovhannes; Khanov, Alexander; Khodinov, Alexander; Khomich, Andrei; Khoo, Teng Jian; Khoriauli, Gia; Khoroshilov, Andrey; Khovanskiy, Valery; Khramov, Evgeniy; Khubua, Jemal; Kim, Hee Yeun; Kim, Hyeon Jin; Kim, Shinhong; Kimura, Naoki; Kind, Oliver; King, Barry; King, Matthew; King, Robert Steven Beaufoy; King, Samuel Burton; Kirk, Julie; Kiryunin, Andrey; Kishimoto, Tomoe; Kisielewska, Danuta; Kiss, Florian; Kitamura, Takumi; Kittelmann, Thomas; Kiuchi, Kenji; Kladiva, Eduard; Klein, Max; Klein, Uta; Kleinknecht, Konrad; Klimek, Pawel; Klimentov, Alexei; Klingenberg, Reiner; Klinger, Joel Alexander; Klioutchnikova, Tatiana; Klok, Peter; Kluge, Eike-Erik; Kluit, Peter; Kluth, Stefan; Kneringer, Emmerich; Knoops, Edith; Knue, Andrea; Kobayashi, Tomio; Kobel, Michael; Kocian, Martin; Kodys, Peter; Koevesarki, Peter; Koffas, Thomas; Koffeman, Els; Kogan, Lucy Anne; Kohlmann, Simon; Kohout, Zdenek; Kohriki, Takashi; Koi, Tatsumi; Kolanoski, Hermann; Koletsou, Iro; Koll, James; Komar, Aston; Komori, Yuto; Kondo, Takahiko; Kondrashova, Nataliia; Köneke, Karsten; König, Adriaan; König, Sebastian; Kono, Takanori; Konoplich, Rostislav; Konstantinidis, Nikolaos; Kopeliansky, Revital; Koperny, Stefan; Köpke, Lutz; Kopp, Anna Katharina; Korcyl, Krzysztof; Kordas, Kostantinos; Korn, Andreas; Korol, Aleksandr; Korolkov, Ilya; Korolkova, Elena; Korotkov, Vladislav; Kortner, Oliver; Kortner, Sandra; Kostyukhin, Vadim; Kotov, Vladislav; Kotwal, Ashutosh; Kourkoumelis, Christine; Kouskoura, Vasiliki; Koutsman, Alex; Kowalewski, Robert Victor; Kowalski, Tadeusz; Kozanecki, Witold; Kozhin, Anatoly; Kral, Vlastimil; Kramarenko, Viktor; Kramberger, Gregor; Krasnopevtsev, Dimitriy; Krasny, Mieczyslaw Witold; Krasznahorkay, Attila; Kraus, Jana; Kravchenko, Anton; Kreiss, Sven; Kretz, Moritz; Kretzschmar, Jan; Kreutzfeldt, Kristof; Krieger, Peter; Kroeninger, Kevin; Kroha, Hubert; Kroll, Joe; Kroseberg, Juergen; Krstic, Jelena; Kruchonak, Uladzimir; Krüger, Hans; Kruker, Tobias; Krumnack, Nils; Krumshteyn, Zinovii; Kruse, Amanda; Kruse, Mark; Kruskal, Michael; Kubota, Takashi; Kuday, Sinan; Kuehn, Susanne; Kugel, Andreas; Kuhl, Andrew; Kuhl, Thorsten; Kukhtin, Victor; Kulchitsky, Yuri; Kuleshov, Sergey; Kuna, Marine; Kunkle, Joshua; Kupco, Alexander; Kurashige, Hisaya; Kurochkin, Yurii; Kurumida, Rie; Kus, Vlastimil; Kuwertz, Emma Sian; Kuze, Masahiro; Kvita, Jiri; La Rosa, Alessandro; La Rotonda, Laura; Lacasta, Carlos; Lacava, Francesco; Lacey, James; Lacker, Heiko; Lacour, Didier; Lacuesta, Vicente Ramón; Ladygin, Evgueni; Lafaye, Remi; Laforge, Bertrand; Lagouri, Theodota; Lai, Stanley; Laier, Heiko; Lambourne, Luke; Lammers, Sabine; Lampen, Caleb; Lampl, Walter; Lançon, Eric; Landgraf, Ulrich; Landon, Murrough; Lang, Valerie Susanne; Lange, Clemens; Lankford, Andrew; Lanni, Francesco; Lantzsch, Kerstin; Laplace, Sandrine; Lapoire, Cecile; Laporte, Jean-Francois; Lari, Tommaso; Lassnig, Mario; Laurelli, Paolo; Lavrijsen, Wim; Law, Alexander; Laycock, Paul; Le, Bao Tran; Le Dortz, Olivier; Le Guirriec, Emmanuel; Le Menedeu, Eve; LeCompte, Thomas; Ledroit-Guillon, Fabienne Agnes Marie; Lee, Claire Alexandra; Lee, Hurng-Chun; Lee, Jason; Lee, Shih-Chang; Lee, Lawrence; Lefebvre, Guillaume; Lefebvre, Michel; Legger, Federica; Leggett, Charles; Lehan, Allan; Lehmacher, Marc; Lehmann Miotto, Giovanna; Lei, Xiaowen; Leister, Andrew Gerard; Leite, Marco Aurelio Lisboa; Leitner, Rupert; Lellouch, Daniel; Lemmer, Boris; Leney, Katharine; Lenz, Tatjana; Lenzen, Georg; Lenzi, Bruno; Leone, Robert; Leonhardt, Kathrin; Leontsinis, Stefanos; Leroy, Claude; Lester, Christopher; Lester, Christopher Michael; Levchenko, Mikhail; Levêque, Jessica; Levin, Daniel; Levinson, Lorne; Levy, Mark; Lewis, Adrian; Lewis, George; Leyko, Agnieszka; Leyton, Michael; Li, Bing; Li, Bo; Li, Haifeng; Li, Ho Ling; Li, Liang; Li, Shu; Li, Yichen; Liang, Zhijun; Liao, Hongbo; Liberti, Barbara; Lichard, Peter; Lie, Ki; Liebal, Jessica; Liebig, Wolfgang; Limbach, Christian; Limosani, Antonio; Limper, Maaike; Lin, Simon; Linde, Frank; Lindquist, Brian Edward; Linnemann, James; Lipeles, Elliot; Lipniacka, Anna; Lisovyi, Mykhailo; Liss, Tony; Lissauer, David; Lister, Alison; Litke, Alan; Liu, Bo; Liu, Dong; Liu, Jianbei; Liu, Kun; Liu, Lulu; Liu, Miaoyuan; Liu, Minghui; Liu, Yanwen; Livan, Michele; Livermore, Sarah; Lleres, Annick; Llorente Merino, Javier; Lloyd, Stephen; Lo Sterzo, Francesco; Lobodzinska, Ewelina; Loch, Peter; Lockman, William; Loddenkoetter, Thomas; Loebinger, Fred; Loevschall-Jensen, Ask Emil; Loginov, Andrey; Loh, Chang Wei; Lohse, Thomas; Lohwasser, Kristin; Lokajicek, Milos; Lombardo, Vincenzo Paolo; Long, Brian Alexander; Long, Jonathan; Long, Robin Eamonn; Lopes, Lourenco; Lopez Mateos, David; Lopez Paredes, Brais; Lorenz, Jeanette; Lorenzo Martinez, Narei; Losada, Marta; Loscutoff, Peter; Lou, XinChou; Lounis, Abdenour; Love, Jeremy; Love, Peter; Lowe, Andrew; Lu, Feng; Lubatti, Henry; Luci, Claudio; Lucotte, Arnaud; Luehring, Frederick; Lukas, Wolfgang; Luminari, Lamberto; Lundberg, Olof; Lund-Jensen, Bengt; Lungwitz, Matthias; Lynn, David; Lysak, Roman; Lytken, Else; Ma, Hong; Ma, Lian Liang; Maccarrone, Giovanni; Macchiolo, Anna; Machado Miguens, Joana; Macina, Daniela; Madaffari, Daniele; Madar, Romain; Maddocks, Harvey Jonathan; Mader, Wolfgang; Madsen, Alexander; Maeno, Mayuko; Maeno, Tadashi; Magradze, Erekle; Mahboubi, Kambiz; Mahlstedt, Joern; Mahmoud, Sara; Maiani, Camilla; Maidantchik, Carmen; Maio, Amélia; Majewski, Stephanie; Makida, Yasuhiro; Makovec, Nikola; Mal, Prolay; Malaescu, Bogdan; Malecki, Pawel; Maleev, Victor; Malek, Fairouz; Mallik, Usha; Malon, David; Malone, Caitlin; Maltezos, Stavros; Malyshev, Vladimir; Malyukov, Sergei; Mamuzic, Judita; Mandelli, Beatrice; Mandelli, Luciano; Mandić, Igor; Mandrysch, Rocco; Maneira, José; Manfredini, Alessandro; Manhaes de Andrade Filho, Luciano; Manjarres Ramos, Joany Andreina; Mann, Alexander; Manning, Peter; Manousakis-Katsikakis, Arkadios; Mansoulie, Bruno; Mantifel, Rodger; Mapelli, Livio; March, Luis; Marchand, Jean-Francois; Marchiori, Giovanni; Marcisovsky, Michal; Marino, Christopher; Marques, Carlos; Marroquim, Fernando; Marsden, Stephen Philip; Marshall, Zach; Marti, Lukas Fritz; Marti-Garcia, Salvador; Martin, Brian; Martin, Brian Thomas; Martin, Tim; Martin, Victoria Jane; Martin dit Latour, Bertrand; Martinez, Homero; Martinez, Mario; Martin-Haugh, Stewart; Martyniuk, Alex; Marx, Marilyn; Marzano, Francesco; Marzin, Antoine; Masetti, Lucia; Mashimo, Tetsuro; Mashinistov, Ruslan; Masik, Jiri; Maslennikov, Alexey; Massa, Ignazio; Massol, Nicolas; Mastrandrea, Paolo; Mastroberardino, Anna; Masubuchi, Tatsuya; Matsunaga, Hiroyuki; Matsushita, Takashi; Mättig, Peter; Mättig, Stefan; Mattmann, Johannes; Maurer, Julien; Maxfield, Stephen; Maximov, Dmitriy; Mazini, Rachid; Mazzaferro, Luca; Mc Goldrick, Garrin; Mc Kee, Shawn Patrick; McCarn, Allison; McCarthy, Robert; McCarthy, Tom; McCubbin, Norman; McFarlane, Kenneth; Mcfayden, Josh; Mchedlidze, Gvantsa; Mclaughlan, Tom; McMahon, Steve; McPherson, Robert; Meade, Andrew; Mechnich, Joerg; Medinnis, Michael; Meehan, Samuel; Mehlhase, Sascha; Mehta, Andrew; Meier, Karlheinz; Meineck, Christian; Meirose, Bernhard; Melachrinos, Constantinos; Mellado Garcia, Bruce Rafael; Meloni, Federico; Mengarelli, Alberto; Menke, Sven; Meoni, Evelin; Mercurio, Kevin Michael; Mergelmeyer, Sebastian; Meric, Nicolas; Mermod, Philippe; Merola, Leonardo; Meroni, Chiara; Merritt, Frank; Merritt, Hayes; Messina, Andrea; Metcalfe, Jessica; Mete, Alaettin Serhan; Meyer, Carsten; Meyer, Christopher; Meyer, Jean-Pierre; Meyer, Jochen; Middleton, Robin; Migas, Sylwia; Mijović, Liza; Mikenberg, Giora; Mikestikova, Marcela; Mikuž, Marko; Miller, David; Mills, Corrinne; Milov, Alexander; Milstead, David; Milstein, Dmitry; Minaenko, Andrey; Minashvili, Irakli; Mincer, Allen; Mindur, Bartosz; Mineev, Mikhail; Ming, Yao; Mir, Lluisa-Maria; Mirabelli, Giovanni; Mitani, Takashi; Mitrevski, Jovan; Mitsou, Vasiliki A; Mitsui, Shingo; Miucci, Antonio; Miyagawa, Paul; Mjörnmark, Jan-Ulf; Moa, Torbjoern; Mochizuki, Kazuya; Moeller, Victoria; Mohapatra, Soumya; Mohr, Wolfgang; Molander, Simon; Moles-Valls, Regina; Mönig, Klaus; Monini, Caterina; Monk, James; Monnier, Emmanuel; Montejo Berlingen, Javier; Monticelli, Fernando; Monzani, Simone; Moore, Roger; Moraes, Arthur; Morange, Nicolas; Morel, Julien; Moreno, Deywis; Moreno Llácer, María; Morettini, Paolo; Morgenstern, Marcus; Morii, Masahiro; Moritz, Sebastian; Morley, Anthony Keith; Mornacchi, Giuseppe; Morris, John; Morvaj, Ljiljana; Moser, Hans-Guenther; Mosidze, Maia; Moss, Josh; Mount, Richard; Mountricha, Eleni; Mouraviev, Sergei; Moyse, Edward; Muanza, Steve; Mudd, Richard; Mueller, Felix; Mueller, James; Mueller, Klemens; Mueller, Thibaut; Mueller, Timo; Muenstermann, Daniel; Munwes, Yonathan; Murillo Quijada, Javier Alberto; Murray, Bill; Musheghyan, Haykuhi; Musto, Elisa; Myagkov, Alexey; Myska, Miroslav; Nackenhorst, Olaf; Nadal, Jordi; Nagai, Koichi; Nagai, Ryo; Nagai, Yoshikazu; Nagano, Kunihiro; Nagarkar, Advait; Nagasaka, Yasushi; Nagel, Martin; Nairz, Armin Michael; Nakahama, Yu; Nakamura, Koji; Nakamura, Tomoaki; Nakano, Itsuo; Namasivayam, Harisankar; Nanava, Gizo; Narayan, Rohin; Nattermann, Till; Naumann, Thomas; Navarro, Gabriela; Nayyar, Ruchika; Neal, Homer; Nechaeva, Polina; Neep, Thomas James; Negri, Andrea; Negri, Guido; Negrini, Matteo; Nektarijevic, Snezana; Nelson, Andrew; Nelson, Timothy Knight; Nemecek, Stanislav; Nemethy, Peter; Nepomuceno, Andre Asevedo; Nessi, Marzio; Neubauer, Mark; Neumann, Manuel; Neves, Ricardo; Nevski, Pavel; Newman, Paul; Nguyen, Duong Hai; Nickerson, Richard; Nicolaidou, Rosy; Nicquevert, Bertrand; Nielsen, Jason; Nikiforou, Nikiforos; Nikiforov, Andriy; Nikolaenko, Vladimir; Nikolic-Audit, Irena; Nikolics, Katalin; Nikolopoulos, Konstantinos; Nilsson, Paul; Ninomiya, Yoichi; Nisati, Aleandro; Nisius, Richard; Nobe, Takuya; Nodulman, Lawrence; Nomachi, Masaharu; Nomidis, Ioannis; Norberg, Scarlet; Nordberg, Markus; Nowak, Sebastian; Nozaki, Mitsuaki; Nozka, Libor; Ntekas, Konstantinos; Nunes Hanninger, Guilherme; Nunnemann, Thomas; Nurse, Emily; Nuti, Francesco; O'Brien, Brendan Joseph; O'grady, Fionnbarr; O'Neil, Dugan; O'Shea, Val; Oakham, Gerald; Oberlack, Horst; Obermann, Theresa; Ocariz, Jose; Ochi, Atsuhiko; Ochoa, Ines; Oda, Susumu; Odaka, Shigeru; Ogren, Harold; Oh, Alexander; Oh, Seog; Ohm, Christian; Ohman, Henrik; Ohshima, Takayoshi; Okamura, Wataru; Okawa, Hideki; Okumura, Yasuyuki; Okuyama, Toyonobu; Olariu, Albert; Olchevski, Alexander; Olivares Pino, Sebastian Andres; Oliveira Damazio, Denis; Oliver Garcia, Elena; Olszewski, Andrzej; Olszowska, Jolanta; Onofre, António; Onyisi, Peter; Oram, Christopher; Oreglia, Mark; Oren, Yona; Orestano, Domizia; Orlando, Nicola; Oropeza Barrera, Cristina; Orr, Robert; Osculati, Bianca; Ospanov, Rustem; Otero y Garzon, Gustavo; Otono, Hidetoshi; Ouchrif, Mohamed; Ouellette, Eric; Ould-Saada, Farid; Ouraou, Ahmimed; Oussoren, Koen Pieter; Ouyang, Qun; Ovcharova, Ana; Owen, Mark; Ozcan, Veysi Erkcan; Ozturk, Nurcan; Pachal, Katherine; Pacheco Pages, Andres; Padilla Aranda, Cristobal; Pagáčová, Martina; Pagan Griso, Simone; Paganis, Efstathios; Pahl, Christoph; Paige, Frank; Pais, Preema; Pajchel, Katarina; Palacino, Gabriel; Palestini, Sandro; Pallin, Dominique; Palma, Alberto; Palmer, Jody; Pan, Yibin; Panagiotopoulou, Evgenia; Panduro Vazquez, William; Pani, Priscilla; Panikashvili, Natalia; Panitkin, Sergey; Pantea, Dan; Paolozzi, Lorenzo; Papadopoulou, Theodora; Papageorgiou, Konstantinos; Paramonov, Alexander; Paredes Hernandez, Daniela; Parker, Michael Andrew; Parodi, Fabrizio; Parsons, John; Parzefall, Ulrich; Pasqualucci, Enrico; Passaggio, Stefano; Passeri, Antonio; Pastore, Fernanda; Pastore, Francesca; Pásztor, Gabriella; Pataraia, Sophio; Patel, Nikhul; Pater, Joleen; Patricelli, Sergio; Pauly, Thilo; Pearce, James; Pedersen, Maiken; Pedraza Lopez, Sebastian; Pedro, Rute; Peleganchuk, Sergey; Pelikan, Daniel; Peng, Haiping; Penning, Bjoern; Penwell, John; Perepelitsa, Dennis; Perez Codina, Estel; Pérez García-Estañ, María Teresa; Perez Reale, Valeria; Perini, Laura; Pernegger, Heinz; Perrino, Roberto; Peschke, Richard; Peshekhonov, Vladimir; Peters, Krisztian; Peters, Yvonne; Petersen, Brian; Petersen, Jorgen; Petersen, Troels; Petit, Elisabeth; Petridis, Andreas; Petridou, Chariclia; Petrolo, Emilio; Petrucci, Fabrizio; Petteni, Michele; Pettersson, Nora Emilia; Pezoa, Raquel; Phillips, Peter William; Piacquadio, Giacinto; Pianori, Elisabetta; Picazio, Attilio; Piccaro, Elisa; Piccinini, Maurizio; Piegaia, Ricardo; Pignotti, David; Pilcher, James; Pilkington, Andrew; Pina, João Antonio; Pinamonti, Michele; Pinder, Alex; Pinfold, James; Pingel, Almut; Pinto, Belmiro; Pires, Sylvestre; Pitt, Michael; Pizio, Caterina; Pleier, Marc-Andre; Pleskot, Vojtech; Plotnikova, Elena; Plucinski, Pawel; Poddar, Sahill; Podlyski, Fabrice; Poettgen, Ruth; Poggioli, Luc; Pohl, David-leon; Pohl, Martin; Polesello, Giacomo; Policicchio, Antonio; Polifka, Richard; Polini, Alessandro; Pollard, Christopher Samuel; Polychronakos, Venetios; Pommès, Kathy; Pontecorvo, Ludovico; Pope, Bernard; Popeneciu, Gabriel Alexandru; Popovic, Dragan; Poppleton, Alan; Portell Bueso, Xavier; Pospelov, Guennady; Pospisil, Stanislav; Potamianos, Karolos; Potrap, Igor; Potter, Christina; Potter, Christopher; Poulard, Gilbert; Poveda, Joaquin; Pozdnyakov, Valery; Pralavorio, Pascal; Pranko, Aliaksandr; Prasad, Srivas; Pravahan, Rishiraj; Prell, Soeren; Price, Darren; Price, Joe; Price, Lawrence; Prieur, Damien; Primavera, Margherita; Proissl, Manuel; Prokofiev, Kirill; Prokoshin, Fedor; Protopapadaki, Eftychia-sofia; Protopopescu, Serban; Proudfoot, James; Przybycien, Mariusz; Przysiezniak, Helenka; Ptacek, Elizabeth; Pueschel, Elisa; Puldon, David; Purohit, Milind; Puzo, Patrick; Qian, Jianming; Qin, Gang; Qin, Yang; Quadt, Arnulf; Quarrie, David; Quayle, William; Quilty, Donnchadha; Qureshi, Anum; Radeka, Veljko; Radescu, Voica; Radhakrishnan, Sooraj Krishnan; Radloff, Peter; Rados, Pere; Ragusa, Francesco; Rahal, Ghita; Rajagopalan, Srinivasan; Rammensee, Michael; Randle-Conde, Aidan Sean; Rangel-Smith, Camila; Rao, Kanury; Rauscher, Felix; Rave, Tobias Christian; Ravenscroft, Thomas; Raymond, Michel; Read, Alexander Lincoln; Rebuzzi, Daniela; Redelbach, Andreas; Redlinger, George; Reece, Ryan; Reeves, Kendall; Rehnisch, Laura; Reinsch, Andreas; Reisin, Hernan; Relich, Matthew; Rembser, Christoph; Ren, Zhongliang; Renaud, Adrien; Rescigno, Marco; Resconi, Silvia; Rezanova, Olga; Reznicek, Pavel; Rezvani, Reyhaneh; Richter, Robert; Ridel, Melissa; Rieck, Patrick; Rijssenbeek, Michael; Rimoldi, Adele; Rinaldi, Lorenzo; Ritsch, Elmar; Riu, Imma; Rizatdinova, Flera; Rizvi, Eram; Robertson, Steven; Robichaud-Veronneau, Andree; Robinson, Dave; Robinson, James; Robson, Aidan; Roda, Chiara; Rodrigues, Luis; Roe, Shaun; Røhne, Ole; Rolli, Simona; Romaniouk, Anatoli; Romano, Marino; Romeo, Gaston; Romero Adam, Elena; Rompotis, Nikolaos; Roos, Lydia; Ros, Eduardo; Rosati, Stefano; Rosbach, Kilian; Rose, Matthew; Rosendahl, Peter Lundgaard; Rosenthal, Oliver; Rossetti, Valerio; Rossi, Elvira; Rossi, Leonardo Paolo; Rosten, Rachel; Rotaru, Marina; Roth, Itamar; Rothberg, Joseph; Rousseau, David; Royon, Christophe; Rozanov, Alexandre; Rozen, Yoram; Ruan, Xifeng; Rubbo, Francesco; Rubinskiy, Igor; Rud, Viacheslav; Rudolph, Christian; Rudolph, Matthew Scott; Rühr, Frederik; Ruiz-Martinez, Aranzazu; Rurikova, Zuzana; Rusakovich, Nikolai; Ruschke, Alexander; Rutherfoord, John; Ruthmann, Nils; Ryabov, Yury; Rybar, Martin; Rybkin, Grigori; Ryder, Nick; Saavedra, Aldo; Sacerdoti, Sabrina; Saddique, Asif; Sadeh, Iftach; Sadrozinski, Hartmut; Sadykov, Renat; Safai Tehrani, Francesco; Sakamoto, Hiroshi; Sakurai, Yuki; Salamanna, Giuseppe; Salamon, Andrea; Saleem, Muhammad; Salek, David; Sales De Bruin, Pedro Henrique; Salihagic, Denis; Salnikov, Andrei; Salt, José; Salvachua Ferrando, Belén; Salvatore, Daniela; Salvatore, Pasquale Fabrizio; Salvucci, Antonio; Salzburger, Andreas; Sampsonidis, Dimitrios; Sanchez, Arturo; Sánchez, Javier; Sanchez Martinez, Victoria; Sandaker, Heidi; Sandbach, Ruth Laura; Sander, Heinz Georg; Sanders, Michiel; Sandhoff, Marisa; Sandoval, Tanya; Sandoval, Carlos; Sandstroem, Rikard; Sankey, Dave; Sansoni, Andrea; Santoni, Claudio; Santonico, Rinaldo; Santos, Helena; Santoyo Castillo, Itzebelt; Sapp, Kevin; Sapronov, Andrey; Saraiva, João; Sarrazin, Bjorn; Sartisohn, Georg; Sasaki, Osamu; Sasaki, Yuichi; Sauvage, Gilles; Sauvan, Emmanuel; Savard, Pierre; Savu, Dan Octavian; Sawyer, Craig; Sawyer, Lee; Saxon, David; Saxon, James; Sbarra, Carla; Sbrizzi, Antonio; Scanlon, Tim; Scannicchio, Diana; Scarcella, Mark; Schaarschmidt, Jana; Schacht, Peter; Schaefer, Douglas; Schaefer, Ralph; Schaepe, Steffen; Schaetzel, Sebastian; Schäfer, Uli; Schaffer, Arthur; Schaile, Dorothee; Schamberger, R. Dean; Scharf, Veit; Schegelsky, Valery; Scheirich, Daniel; Schernau, Michael; Scherzer, Max; Schiavi, Carlo; Schieck, Jochen; Schillo, Christian; Schioppa, Marco; Schlenker, Stefan; Schmidt, Evelyn; Schmieden, Kristof; Schmitt, Christian; Schmitt, Christopher; Schmitt, Sebastian; Schneider, Basil; Schnellbach, Yan Jie; Schnoor, Ulrike; Schoeffel, Laurent; Schoening, Andre; Schoenrock, Bradley Daniel; Schorlemmer, Andre Lukas; Schott, Matthias; Schouten, Doug; Schovancova, Jaroslava; Schramm, Steven; Schreyer, Manuel; Schroeder, Christian; Schuh, Natascha; Schultens, Martin Johannes; Schultz-Coulon, Hans-Christian; Schulz, Holger; Schumacher, Markus; Schumm, Bruce; Schune, Philippe; Schwartzman, Ariel; Schwegler, Philipp; Schwemling, Philippe; Schwienhorst, Reinhard; Schwindling, Jerome; Schwindt, Thomas; Schwoerer, Maud; Sciacca, Gianfranco; Scifo, Estelle; Sciolla, Gabriella; Scott, Bill; Scuri, Fabrizio; Scutti, Federico; Searcy, Jacob; Sedov, George; Sedykh, Evgeny; Seidel, Sally; Seiden, Abraham; Seifert, Frank; Seixas, José; Sekhniaidze, Givi; Sekula, Stephen; Selbach, Karoline Elfriede; Seliverstov, Dmitry; Sellers, Graham; Semprini-Cesari, Nicola; Serfon, Cedric; Serin, Laurent; Serkin, Leonid; Serre, Thomas; Seuster, Rolf; Severini, Horst; Sforza, Federico; Sfyrla, Anna; Shabalina, Elizaveta; Shamim, Mansoora; Shan, Lianyou; Shank, James; Shao, Qi Tao; Shapiro, Marjorie; Shatalov, Pavel; Shaw, Kate; Sherwood, Peter; Shimizu, Shima; Shimmin, Chase Owen; Shimojima, Makoto; Shiyakova, Mariya; Shmeleva, Alevtina; Shochet, Mel; Short, Daniel; Shrestha, Suyog; Shulga, Evgeny; Shupe, Michael; Shushkevich, Stanislav; Sicho, Petr; Sidorov, Dmitri; Sidoti, Antonio; Siegert, Frank; Sijacki, Djordje; Silbert, Ohad; Silva, José; Silver, Yiftah; Silverstein, Daniel; Silverstein, Samuel; Simak, Vladislav; Simard, Olivier; Simic, Ljiljana; Simion, Stefan; Simioni, Eduard; Simmons, Brinick; Simoniello, Rosa; Simonyan, Margar; Sinervo, Pekka; Sinev, Nikolai; Sipica, Valentin; Siragusa, Giovanni; Sircar, Anirvan; Sisakyan, Alexei; Sivoklokov, Serguei; Sjölin, Jörgen; Sjursen, Therese; Skottowe, Hugh Philip; Skovpen, Kirill; Skubic, Patrick; Slater, Mark; Slavicek, Tomas; Sliwa, Krzysztof; Smakhtin, Vladimir; Smart, Ben; Smestad, Lillian; Smirnov, Sergei; Smirnov, Yury; Smirnova, Lidia; Smirnova, Oxana; Smith, Kenway; Smizanska, Maria; Smolek, Karel; Snesarev, Andrei; Snidero, Giacomo; Snyder, Scott; Sobie, Randall; Socher, Felix; Soffer, Abner; Soh, Dart-yin; Solans, Carlos; Solar, Michael; Solc, Jaroslav; Soldatov, Evgeny; Soldevila, Urmila; Solfaroli Camillocci, Elena; Solodkov, Alexander; Solovyanov, Oleg; Solovyev, Victor; Sommer, Philip; Song, Hong Ye; Soni, Nitesh; Sood, Alexander; Sopczak, Andre; Sopko, Vit; Sopko, Bruno; Sorin, Veronica; Sosebee, Mark; Soualah, Rachik; Soueid, Paul; Soukharev, Andrey; South, David; Spagnolo, Stefania; Spanò, Francesco; Spearman, William Robert; Spighi, Roberto; Spigo, Giancarlo; Spousta, Martin; Spreitzer, Teresa; Spurlock, Barry; St Denis, Richard Dante; Staerz, Steffen; Stahlman, Jonathan; Stamen, Rainer; Stanecka, Ewa; Stanek, Robert; Stanescu, Cristian; Stanescu-Bellu, Madalina; Stanitzki, Marcel Michael; Stapnes, Steinar; Starchenko, Evgeny; Stark, Jan; Staroba, Pavel; Starovoitov, Pavel; Staszewski, Rafal; Stavina, Pavel; Steele, Genevieve; Steinberg, Peter; Stelzer, Bernd; Stelzer, Harald Joerg; Stelzer-Chilton, Oliver; Stenzel, Hasko; Stern, Sebastian; Stewart, Graeme; Stillings, Jan Andre; Stockton, Mark; Stoebe, Michael; Stoicea, Gabriel; Stolte, Philipp; Stonjek, Stefan; Stradling, Alden; Straessner, Arno; Stramaglia, Maria Elena; Strandberg, Jonas; Strandberg, Sara; Strandlie, Are; Strauss, Emanuel; Strauss, Michael; Strizenec, Pavol; Ströhmer, Raimund; Strom, David; Stroynowski, Ryszard; Stucci, Stefania Antonia; Stugu, Bjarne; Styles, Nicholas Adam; Su, Dong; Su, Jun; Subramania, Halasya Siva; Subramaniam, Rajivalochan; Succurro, Antonella; Sugaya, Yorihito; Suhr, Chad; Suk, Michal; Sulin, Vladimir; Sultansoy, Saleh; Sumida, Toshi; Sun, Xiaohu; Sundermann, Jan Erik; Suruliz, Kerim; Susinno, Giancarlo; Sutton, Mark; Suzuki, Yu; Svatos, Michal; Swedish, Stephen; Swiatlowski, Maximilian; Sykora, Ivan; Sykora, Tomas; Ta, Duc; Tackmann, Kerstin; Taenzer, Joe; Taffard, Anyes; Tafirout, Reda; Taiblum, Nimrod; Takahashi, Yuta; Takai, Helio; Takashima, Ryuichi; Takeda, Hiroshi; Takeshita, Tohru; Takubo, Yosuke; Talby, Mossadek; Talyshev, Alexey; Tam, Jason; Tamsett, Matthew; Tan, Kong Guan; Tanaka, Junichi; Tanaka, Reisaburo; Tanaka, Satoshi; Tanaka, Shuji; Tanasijczuk, Andres Jorge; Tani, Kazutoshi; Tannoury, Nancy; Tapprogge, Stefan; Tarem, Shlomit; Tarrade, Fabien; Tartarelli, Giuseppe Francesco; Tas, Petr; Tasevsky, Marek; Tashiro, Takuya; Tassi, Enrico; Tavares Delgado, Ademar; Tayalati, Yahya; Taylor, Frank; Taylor, Geoffrey; Taylor, Wendy; Teischinger, Florian Alfred; Teixeira Dias Castanheira, Matilde; Teixeira-Dias, Pedro; Temming, Kim Katrin; Ten Kate, Herman; Teng, Ping-Kun; Terada, Susumu; Terashi, Koji; Terron, Juan; Terzo, Stefano; Testa, Marianna; Teuscher, Richard; Therhaag, Jan; Theveneaux-Pelzer, Timothée; Thoma, Sascha; Thomas, Juergen; Thomas-Wilsker, Joshuha; Thompson, Emily; Thompson, Paul; Thompson, Peter; Thompson, Stan; Thomsen, Lotte Ansgaard; Thomson, Evelyn; Thomson, Mark; Thong, Wai Meng; Thun, Rudolf; Tian, Feng; Tibbetts, Mark James; Tikhomirov, Vladimir; Tikhonov, Yury; Timoshenko, Sergey; Tiouchichine, Elodie; Tipton, Paul; Tisserant, Sylvain; Todorov, Theodore; Todorova-Nova, Sharka; Toggerson, Brokk; Tojo, Junji; Tokár, Stanislav; Tokushuku, Katsuo; Tollefson, Kirsten; Tomlinson, Lee; Tomoto, Makoto; Tompkins, Lauren; Toms, Konstantin; Topilin, Nikolai; Torrence, Eric; Torres, Heberth; Torró Pastor, Emma; Toth, Jozsef; Touchard, Francois; Tovey, Daniel; Tran, Huong Lan; Trefzger, Thomas; Tremblet, Louis; Tricoli, Alessandro; Trigger, Isabel Marian; Trincaz-Duvoid, Sophie; Tripiana, Martin; Triplett, Nathan; Trischuk, William; Trocmé, Benjamin; Troncon, Clara; Trottier-McDonald, Michel; Trovatelli, Monica; True, Patrick; Trzebinski, Maciej; Trzupek, Adam; Tsarouchas, Charilaos; Tseng, Jeffrey; Tsiareshka, Pavel; Tsionou, Dimitra; Tsipolitis, Georgios; Tsirintanis, Nikolaos; Tsiskaridze, Shota; Tsiskaridze, Vakhtang; Tskhadadze, Edisher; Tsukerman, Ilya; Tsulaia, Vakhtang; Tsuno, Soshi; Tsybychev, Dmitri; Tudorache, Alexandra; Tudorache, Valentina; Tuna, Alexander Naip; Tupputi, Salvatore; Turchikhin, Semen; Turecek, Daniel; Turk Cakir, Ilkay; Turra, Ruggero; Tuts, Michael; Tykhonov, Andrii; Tylmad, Maja; Tyndel, Mike; Uchida, Kirika; Ueda, Ikuo; Ueno, Ryuichi; Ughetto, Michael; Ugland, Maren; Uhlenbrock, Mathias; Ukegawa, Fumihiko; Unal, Guillaume; Undrus, Alexander; Unel, Gokhan; Ungaro, Francesca; Unno, Yoshinobu; Urbaniec, Dustin; Urquijo, Phillip; Usai, Giulio; Usanova, Anna; Vacavant, Laurent; Vacek, Vaclav; Vachon, Brigitte; Valencic, Nika; Valentinetti, Sara; Valero, Alberto; Valery, Loic; Valkar, Stefan; Valladolid Gallego, Eva; Vallecorsa, Sofia; Valls Ferrer, Juan Antonio; Van Der Deijl, Pieter; van der Geer, Rogier; van der Graaf, Harry; Van Der Leeuw, Robin; van der Ster, Daniel; van Eldik, Niels; van Gemmeren, Peter; Van Nieuwkoop, Jacobus; van Vulpen, Ivo; van Woerden, Marius Cornelis; Vanadia, Marco; Vandelli, Wainer; Vanguri, Rami; Vaniachine, Alexandre; Vankov, Peter; Vannucci, Francois; Vardanyan, Gagik; Vari, Riccardo; Varnes, Erich; Varol, Tulin; Varouchas, Dimitris; Vartapetian, Armen; Varvell, Kevin; Vazeille, Francois; Vazquez Schroeder, Tamara; Veatch, Jason; Veloso, Filipe; Veneziano, Stefano; Ventura, Andrea; Ventura, Daniel; Venturi, Manuela; Venturi, Nicola; Venturini, Alessio; Vercesi, Valerio; Verducci, Monica; Verkerke, Wouter; Vermeulen, Jos; Vest, Anja; Vetterli, Michel; Viazlo, Oleksandr; Vichou, Irene; Vickey, Trevor; Vickey Boeriu, Oana Elena; Viehhauser, Georg; Viel, Simon; Vigne, Ralph; Villa, Mauro; Villaplana Perez, Miguel; Vilucchi, Elisabetta; Vincter, Manuella; Vinogradov, Vladimir; Virzi, Joseph; Vivarelli, Iacopo; Vives Vaque, Francesc; Vlachos, Sotirios; Vladoiu, Dan; Vlasak, Michal; Vogel, Adrian; Vokac, Petr; Volpi, Guido; Volpi, Matteo; von der Schmitt, Hans; von Radziewski, Holger; von Toerne, Eckhard; Vorobel, Vit; Vorobev, Konstantin; Vos, Marcel; Voss, Rudiger; Vossebeld, Joost; Vranjes, Nenad; Vranjes Milosavljevic, Marija; Vrba, Vaclav; Vreeswijk, Marcel; Vu Anh, Tuan; Vuillermet, Raphael; Vukotic, Ilija; Vykydal, Zdenek; Wagner, Wolfgang; Wagner, Peter; Wahrmund, Sebastian; Wakabayashi, Jun; Walder, James; Walker, Rodney; Walkowiak, Wolfgang; Wall, Richard; Waller, Peter; Walsh, Brian; Wang, Chao; Wang, Chiho; Wang, Fuquan; Wang, Haichen; Wang, Hulin; Wang, Jike; Wang, Jin; Wang, Kuhan; Wang, Rui; Wang, Song-Ming; Wang, Tan; Wang, Xiaoxiao; Wanotayaroj, Chaowaroj; Warburton, Andreas; Ward, Patricia; Wardrope, David Robert; Warsinsky, Markus; Washbrook, Andrew; Wasicki, Christoph; Watanabe, Ippei; Watkins, Peter; Watson, Alan; Watson, Ian; Watson, Miriam; Watts, Gordon; Watts, Stephen; Waugh, Ben; Webb, Samuel; Weber, Michele; Weber, Stefan Wolf; Webster, Jordan S; Weidberg, Anthony; Weigell, Philipp; Weinert, Benjamin; Weingarten, Jens; Weiser, Christian; Weits, Hartger; Wells, Phillippa; Wenaus, Torre; Wendland, Dennis; Weng, Zhili; Wengler, Thorsten; Wenig, Siegfried; Wermes, Norbert; Werner, Matthias; Werner, Per; Wessels, Martin; Wetter, Jeffrey; Whalen, Kathleen; White, Andrew; White, Martin; White, Ryan; White, Sebastian; Whiteson, Daniel; Wicke, Daniel; Wickens, Fred; Wiedenmann, Werner; Wielers, Monika; Wienemann, Peter; Wiglesworth, Craig; Wiik-Fuchs, Liv Antje Mari; Wijeratne, Peter Alexander; Wildauer, Andreas; Wildt, Martin Andre; Wilkens, Henric George; Will, Jonas Zacharias; Williams, Hugh; Williams, Sarah; Willis, Christopher; Willocq, Stephane; Wilson, John; Wilson, Alan; Wingerter-Seez, Isabelle; Winklmeier, Frank; Wittgen, Matthias; Wittig, Tobias; Wittkowski, Josephine; Wollstadt, Simon Jakob; Wolter, Marcin Wladyslaw; Wolters, Helmut; Wosiek, Barbara; Wotschack, Jorg; Woudstra, Martin; Wozniak, Krzysztof; Wright, Michael; Wu, Mengqing; Wu, Sau Lan; Wu, Xin; Wu, Yusheng; Wulf, Evan; Wyatt, Terry Richard; Wynne, Benjamin; Xella, Stefania; Xiao, Meng; Xu, Da; Xu, Lailin; Yabsley, Bruce; Yacoob, Sahal; Yamada, Miho; Yamaguchi, Hiroshi; Yamaguchi, Yohei; Yamamoto, Akira; Yamamoto, Kyoko; Yamamoto, Shimpei; Yamamura, Taiki; Yamanaka, Takashi; Yamauchi, Katsuya; Yamazaki, Yuji; Yan, Zhen; Yang, Haijun; Yang, Hongtao; Yang, Un-Ki; Yang, Yi; Yanush, Serguei; Yao, Liwen; Yao, Weiming; Yasu, Yoshiji; Yatsenko, Elena; Yau Wong, Kaven Henry; Ye, Jingbo; Ye, Shuwei; Yen, Andy L; Yildirim, Eda; Yilmaz, Metin; Yoosoofmiya, Reza; Yorita, Kohei; Yoshida, Rikutaro; Yoshihara, Keisuke; Young, Charles; Young, Christopher John; Youssef, Saul; Yu, David Ren-Hwa; Yu, Jaehoon; Yu, Jiaming; Yu, Jie; Yuan, Li; Yurkewicz, Adam; Zabinski, Bartlomiej; Zaidan, Remi; Zaitsev, Alexander; Zaman, Aungshuman; Zambito, Stefano; Zanello, Lucia; Zanzi, Daniele; Zaytsev, Alexander; Zeitnitz, Christian; Zeman, Martin; Zemla, Andrzej; Zengel, Keith; Zenin, Oleg; Ženiš, Tibor; Zerwas, Dirk; Zevi della Porta, Giovanni; Zhang, Dongliang; Zhang, Fangzhou; Zhang, Huaqiao; Zhang, Jinlong; Zhang, Lei; Zhang, Xueyao; Zhang, Zhiqing; Zhao, Zhengguo; Zhemchugov, Alexey; Zhong, Jiahang; Zhou, Bing; Zhou, Lei; Zhou, Ning; Zhu, Cheng Guang; Zhu, Hongbo; Zhu, Junjie; Zhu, Yingchun; Zhuang, Xuai; Zibell, Andre; Zieminska, Daria; Zimine, Nikolai; Zimmermann, Christoph; Zimmermann, Robert; Zimmermann, Simone; Zimmermann, Stephanie; Zinonos, Zinonas; Ziolkowski, Michael; Zobernig, Georg; Zoccoli, Antonio; zur Nedden, Martin; Zurzolo, Giovanni; Zutshi, Vishnu; Zwalinski, Lukasz

    2014-08-13

    The integrated elliptic flow of charged particles produced in Pb+Pb collisions at $\\sqrt{s_{NN}}=2.76$ TeV has been measured with the ATLAS detector using data collected at the Large Hadron Collider. The anisotropy parameter, $v_2$, was measured in the pseudorapidity range $|\\eta|\\leq$ 2.5 with the event-plane method. In order to include tracks with very low transverse momentum $p_T$, thus reducing the uncertainty in $v_2$ integrated over $p_T$, a $1 \\mu b^{-1}$ data sample recorded without a magnetic field in the tracking detectors is used. The centrality dependence of the integrated $v_2$ is compared to other measurements obtained with higher $p_T$ thresholds. A weak pseudorapidity dependence of the integrated elliptic flow is observed for central collisions, and a small decrease when moving away from mid-rapidity is observed only in peripheral collisions. The integrated $v_2$ transformed to the rest frame of one of the colliding nuclei is compared to the lower-energy RHIC data.

  19. Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach

    Science.gov (United States)

    Gendre, Félix; Ricot, Denis; Fritz, Guillaume; Sagaut, Pierre

    2017-08-01

    This study focuses on grid refinement techniques for the direct simulation of aeroacoustics, when using weakly compressible lattice Boltzmann models, such as the D3Q19 athermal velocity set. When it comes to direct noise computation, very small errors on the density or pressure field may have great negative consequences. Even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones. This work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface, which may contaminate the resulting aeroacoustic field. We show through an extensive literature review that, within the framework described above, this issue has never been addressed before. To tackle this problem, we develop an alternative algorithm and compare its behavior to a classical one, which fits our in-house vertex-centered data structure. Our main idea relies on a directional splitting of the continuous discrete velocity Boltzmann equation, followed by an integration over specific characteristics. This method can be seen as a specific coupling between finite difference and lattice Boltzmann, locally on the interface between the two grids. The method is assessed considering two cases: an acoustic pulse and a convected vortex. We show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface. We also show that an increased free stream Mach number (but still within the weakly compressible regime) strongly deteriorates the situation, although the magnitude of the errors may remain negligible for purely aerodynamic studies. A drastically reduced level of error for the near-field spurious noise is obtained with our approach, especially for under-resolved simulations, a situation that is crucial for industrial applications. Thus, the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm.

  20. Galilean-Invariant Lattice-Boltzmann Models with H Theorem

    National Research Council Canada - National Science Library

    Boghosian, Bruce

    2003-01-01

    The authors demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations...

  1. On the quantum Landau collision operator and electron collisions in dense plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Daligault, Jérôme, E-mail: daligaul@lanl.gov [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

    2016-03-15

    The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

  2. On the quantum Landau collision operator and electron collisions in dense plasmas

    Science.gov (United States)

    Daligault, Jérôme

    2016-03-01

    The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

  3. Boltzmann, Gibbs and Darwin-Fowler approaches in parastatistics

    International Nuclear Information System (INIS)

    Ponczek, R.L.; Yan, C.C.

    1976-01-01

    Derivations of the equilibrium values of occupation numbers are made using three approaches, namely, the Boltzmann 'elementary' one, the ensemble method of Gibbs, and that of Darwin and Fowler as well [pt

  4. The effect of repetitive subconcussive collisions on brain integrity in collegiate football players over a single football season: A multi-modal neuroimaging study.

    Science.gov (United States)

    Slobounov, Semyon M; Walter, Alexa; Breiter, Hans C; Zhu, David C; Bai, Xiaoxiao; Bream, Tim; Seidenberg, Peter; Mao, Xianglun; Johnson, Brian; Talavage, Thomas M

    2017-01-01

    The cumulative effect of repetitive subconcussive collisions on the structural and functional integrity of the brain remains largely unknown. Athletes in collision sports, like football, experience a large number of impacts across a single season of play. The majority of these impacts, however, are generally overlooked, and their long-term consequences remain poorly understood. This study sought to examine the effects of repetitive collisions across a single competitive season in NCAA Football Bowl Subdivision athletes using advanced neuroimaging approaches. Players were evaluated before and after the season using multiple MRI sequences, including T 1 -weighted imaging, diffusion tensor imaging (DTI), arterial spin labeling (ASL), resting-state functional MRI (rs-fMRI), and susceptibility weighted imaging (SWI). While no significant differences were found between pre- and post-season for DTI metrics or cortical volumes, seed-based analysis of rs-fMRI revealed significant ( p  Football Bowl Subdivision, even in the absence of clinical symptoms or a diagnosis of concussion. Whether these changes reflect compensatory adaptation to cumulative head impacts or more lasting alteration of brain integrity remains to be further explored.

  5. Generalized Stefan-Boltzmann Law

    Science.gov (United States)

    Montambaux, Gilles

    2018-03-01

    We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems whose chemical potential vanishes. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.

  6. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  7. Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

    International Nuclear Information System (INIS)

    Gan Yanbiao; Li Yingjun; Xu Aiguo; Zhang Guangcai

    2011-01-01

    We further develop the lattice Boltzmann (LB) model [Physica A 382 (2007) 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar-Gross-Krook (BGK) collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference (FLFD) scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including (i) The thermal Couette flow; (ii) One- and two-dimensional Riemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  8. Measuring the usefulness of hidden units in Boltzmann machines with mutual information.

    Science.gov (United States)

    Berglund, Mathias; Raiko, Tapani; Cho, Kyunghyun

    2015-04-01

    Restricted Boltzmann machines (RBMs) and deep Boltzmann machines (DBMs) are important models in deep learning, but it is often difficult to measure their performance in general, or measure the importance of individual hidden units in specific. We propose to use mutual information to measure the usefulness of individual hidden units in Boltzmann machines. The measure is fast to compute, and serves as an upper bound for the information the neuron can pass on, enabling detection of a particular kind of poor training results. We confirm experimentally that the proposed measure indicates how much the performance of the model drops when some of the units of an RBM are pruned away. We demonstrate the usefulness of the measure for early detection of poor training in DBMs. Copyright © 2014 Elsevier Ltd. All rights reserved.

  9. Grid refinement model in lattice Boltzmann method for stream function-vorticity formulations

    Energy Technology Data Exchange (ETDEWEB)

    Shin, Myung Seob [Dept. of Mechanical Engineering, Dongyang Mirae University, Seoul (Korea, Republic of)

    2015-03-15

    In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

  10. Immiscible multicomponent lattice Boltzmann model for fluids with ...

    Indian Academy of Sciences (India)

    College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, ... was developed from a discretized fluid model known as the lattice gas automata ... of two immiscible fluids, several lattice Boltzmann (LB) models have been ...

  11. Atoms, mechanics, and probability Ludwig Boltzmann's statistico-mechanical writings : an exegesis

    CERN Document Server

    Darrigol, Olivier

    2018-01-01

    One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844-1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given to Boltzmann's theoretical tool-box and to his patient construction of lofty formal systems even before their full conceptual import could be known. This constructive tendency largely accounts for his lengthy style, for the abundance of new constructions, for the relative vagueness of their object--and for the puzzlement of commentators. This book will help the reader cross the stylistic barrier and see how ingeniously B...

  12. Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

    Science.gov (United States)

    Garcia, Alejandro L; Wagner, Wolfgang

    2003-11-01

    In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

  13. Generalized boundary conditions in an existence and uniqueness proof for the solution of the non-stationary electron Boltzmann equation by means of operator-semigroups

    International Nuclear Information System (INIS)

    Bartolomaeus, G.; Wilhelm, J.

    1983-01-01

    Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restriction which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. (author)

  14. Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

    DEFF Research Database (Denmark)

    Pingen, Georg; Evgrafov, Anton; Maute, Kurt

    2009-01-01

    We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...

  15. Lattice Boltzmann Approach to Resistive MHD

    Czech Academy of Sciences Publication Activity Database

    Macnab, A.; Vahala, G.; Vahala, L.; Pavlo, Pavol; Soe, M.

    2002-01-01

    Roč. 47, č. 9 (2002), s. 51 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/44th./. Orlando , Florida, 11.11.2001-15.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann, magnetic fields Subject RIV: BL - Plasma and Gas Discharge Physics

  16. Metamaterial characterization using Boltzmann's kinetic equation for electrons

    DEFF Research Database (Denmark)

    Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.

    2013-01-01

    Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows...

  17. Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

    The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...

  18. Lattice gas cellular automata and lattice Boltzmann models an introduction

    CERN Document Server

    Wolf-Gladrow, Dieter A

    2000-01-01

    Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

  19. Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow

    International Nuclear Information System (INIS)

    Hammond, L A; Halliday, I; Care, C M; Stevens, A

    2002-01-01

    We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow

  20. Experimental investigation of the Boltzmann relation for a bi-Maxwellian distribution in inductively coupled plasmas

    International Nuclear Information System (INIS)

    Bang, Jin Young; Chung, Chin Wook

    2009-01-01

    In plasma, the Boltzmann relation is often used to connect the electron density to the plasma potential because it is not easy to calculate electric potentials on the basis of the Poisson equation due to the quasineutrality. From the Boltzmann relation, the electric potential can be simply obtained from the electron density or vice versa. However, the Boltzmann relation assumes that electrons are in thermal equilibrium and have a Maxwellian distribution, so it cannot be applied to non-Maxwellian distributions. In this paper, the Boltzmann relation for bi-Maxwellian distributions was newly derived from fluid equations and the comparison with the experimental results was given by measuring electron energy probability functions in an inductively coupled plasma. It was found that the spatial distribution of the electron density in bulk plasma is governed by the effective electron temperature, while that of the cold and hot electrons are governed by each electron temperature.

  1. On the possibility of using model potentials for collision integral calculations of interest for planetary atmospheres

    International Nuclear Information System (INIS)

    Capitelli, M.; Cappelletti, D.; Colonna, G.; Gorse, C.; Laricchiuta, A.; Liuti, G.; Longo, S.; Pirani, F.

    2007-01-01

    The interaction energy in systems (atom-atom, atom-ion and atom-molecule) involving open-shell species, predicted by a phenomenological method, is used for collision integral calculations. The results are compared with those obtained by different authors by using the complete set of quantum mechanical interaction potentials arizing from the electronic configurations of separate partners. A satisfactory agreement is achieved, implying that the effect of deep potential wells, present in some of the chemical potentials, is cancelled by the effect of strong repulsive potentials

  2. A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

    Science.gov (United States)

    Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

    2012-12-01

    Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

  3. A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation

    NARCIS (Netherlands)

    Hoitinga, W.; Brummelen, van E.H.

    2011-01-01

    To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly

  4. Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

    Science.gov (United States)

    Sels, Dries; Brosens, Fons

    2013-10-01

    The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

  5. Characterization and visualization of RNA secondary structure Boltzmann ensemble via information theory.

    Science.gov (United States)

    Lin, Luan; McKerrow, Wilson H; Richards, Bryce; Phonsom, Chukiat; Lawrence, Charles E

    2018-03-05

    The nearest neighbor model and associated dynamic programming algorithms allow for the efficient estimation of the RNA secondary structure Boltzmann ensemble. However because a given RNA secondary structure only contains a fraction of the possible helices that could form from a given sequence, the Boltzmann ensemble is multimodal. Several methods exist for clustering structures and finding those modes. However less focus is given to exploring the underlying reasons for this multimodality: the presence of conflicting basepairs. Information theory, or more specifically mutual information, provides a method to identify those basepairs that are key to the secondary structure. To this end we find most informative basepairs and visualize the effect of these basepairs on the secondary structure. Knowing whether a most informative basepair is present tells us not only the status of the particular pair but also provides a large amount of information about which other pairs are present or not present. We find that a few basepairs account for a large amount of the structural uncertainty. The identification of these pairs indicates small changes to sequence or stability that will have a large effect on structure. We provide a novel algorithm that uses mutual information to identify the key basepairs that lead to a multimodal Boltzmann distribution. We then visualize the effect of these pairs on the overall Boltzmann ensemble.

  6. Boltzmann factor and Hawking radiation

    International Nuclear Information System (INIS)

    Ryskin, Gregory

    2014-01-01

    Hawking radiation has thermal spectrum corresponding to the temperature T H =(8πM) −1 , where M is the mass (energy) of the black hole. Corrections to the Hawking radiation spectrum were discovered by Kraus and Wilczek (1995) and Parikh and Wilczek (2000). Here I show that these corrections follow directly from the basic principles of thermodynamics and statistical mechanics. In essence, it is the Boltzmann factor that ought to be corrected; corrections to the Hawking (or any other) radiation spectrum then follow necessarily

  7. PROCOPE, Collision Probability in Pin Clusters and Infinite Rod Lattices

    International Nuclear Information System (INIS)

    Amyot, L.; Daolio, C.; Benoist, P.

    1984-01-01

    1 - Nature of physical problem solved: Calculation of directional collision probabilities in pin clusters and infinite rod lattices. 2 - Method of solution: a) Gauss integration of analytical expressions for collision probabilities. b) alternately, an approximate closed expression (not involving integrals) may be used for pin-to-pin interactions. 3 - Restrictions on the complexity of the problem: number of fuel pins must be smaller than 62; maximum number of groups of symmetry is 300

  8. Contact angle determination in multicomponent lattice Boltzmann simultations

    NARCIS (Netherlands)

    Schmieschek, S.M.P.; Harting, J.D.R.

    2011-01-01

    Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications and there exists a number of commonly used multicomponent and multiphase lattice Boltzmann schemes to study such systems. In this paper we focus on a popular implementation of a multicomponent model as introduced by Shan

  9. Boltzmann learning of parameters in cellular neural networks

    DEFF Research Database (Denmark)

    Hansen, Lars Kai

    1992-01-01

    The use of Bayesian methods to design cellular neural networks for signal processing tasks and the Boltzmann machine learning rule for parameter estimation is discussed. The learning rule can be used for models with hidden units, or for completely unsupervised learning. The latter is exemplified...

  10. Convection-diffusion lattice Boltzmann scheme for irregular lattices

    NARCIS (Netherlands)

    Sman, van der R.G.M.; Ernst, M.H.

    2000-01-01

    In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the

  11. Improved elastic collision modeling in DEGAS 2 for low-temperature plasmas

    International Nuclear Information System (INIS)

    Kanzleiter, Randall J.; Stotler, Daren P.; Karney, Charles F. F.; Steiner, Don

    2000-01-01

    Recent emphasis on low-temperature divertor operations has focused attention on proper treatment of neutral-elastic collisions in low-temperature environments. For like species collisions, as in D + +D, quantum mechanical indistinguishability precludes differentiation of small-angle elastic scattering from resonant charge exchange for collision energies + +D 2 are included for the first time. An integration technique is utilized that reduces the total collision cross section while keeping the other transport cross sections invariant. The inclusion of ion-molecular elastic collisions results in significant increases in energy exchange between background ions and neutral test species

  12. First and second sound in He films

    International Nuclear Information System (INIS)

    Oh, H.G.; Um, C.I.; Kahng, W.H.; Isihara, A.

    1986-01-01

    In consideration of a collision integral in the Boltzmann equation and with use of kinetic and hydrodynamical equations, the velocities of the first and second sound in liquid 4 He films are evaluated as functions of temperature, and the attenuation coefficients are obtained. The second sound is 2/sup -1/2/ times the first-sound velocity in the low-temperature and low-frequency limit

  13. Fragmentation, dissipative expansion, and freeze-out in medium energy heavy-ion collisions

    International Nuclear Information System (INIS)

    Gross, D.H.E.; Li Baoan; DeAngelis, A.R.

    1992-01-01

    The collision dynamics of 96 Mo + 96 Mo at 55 A MeV is simulated by solving numerically the Boltzmann-Uehling-Uhlenbeck (BUU) transport equation for the one-body phase-space distribution-function of nucleons with and without Coulomb interaction. A scatter-plot of the one-body density distribution shows an initial compression, subsequent homogeneous expansion, a breaking into ''fragments'', a very slow creeping expansion up to a freeze-out and in the case of included Coulomb-interaction a Coulomb-explosion. In the calculation which included Coulomb-interaction the overall shape of the ensemble of dense fragments is spherical. The fragments are created over the entire volume of the dense part of the source and not at the surface only. In the simulation without Coulomb interaction a doughnut-like shape may develop. (orig.)

  14. Effect of inelastic energy losses on development of atom-atom collision cascades

    International Nuclear Information System (INIS)

    Marinyuk, V.V.; Remizovich, V.S.

    2001-01-01

    The problem of influence of inelastic energy losses (ionization braking) of particles on the development of atom-atom collision cascades in infinite medium was studied theoretically. Main attention was paid to study of angular and energy distributions of primary ions and cascade atoms in the presence of braking. Analytical calculations were made in the assumption that single scattering of particles occurs by solid balls law, while the value of electron braking ability of a medium is determined by the Lindhard formula. It is shown that account of braking (directly when solving the Boltzmann transport equation) changes in principle the previously obtained angular and energy spectra of ions and cascade atoms. Moreover, it is the braking that is the determining factor responsible for anisotropy of angular distributions of low-energy primary ions and cascade atoms [ru

  15. Fluctuations in high-energy particle collisions

    International Nuclear Information System (INIS)

    Gronqvist, Hanna

    2016-01-01

    We study fluctuations that are omnipresent in high-energy particle collisions. These fluctuations can be either of either classical or quantum origin and we will study both. Firstly, we consider the type of quantum fluctuations that arise in proton-proton collisions. These are computable perturbatively in quantum field theory and we will focus on a specific class of diagrams in this set-up. Secondly, we will consider the fluctuations that are present in collisions between nuclei that can be heavier than protons. These are the quantum laws of nature that describe the positions of nucleons within a nucleus, but also the hydrodynamic fluctuations of classical, thermal origin that affect the evolution of the medium produced in heavy-ion collisions. The fluctuations arising in proton-proton collisions can be computed analytically up to a certain order in perturbative quantum field theory. We will focus on one-loop diagrams of a fixed topology. Loop diagrams give rise to integrals that typically are hard to evaluate. We show how modern mathematical methods can be used to ease their computation. We will study the relations among unitarity cuts of a diagram, the discontinuity across the corresponding branch cut and the coproduct. We show how the original integral corresponding to a given diagram can be reconstructed from the information contained in the coproduct. We expect that these methods can be applied to solve more complicated topologies and help in the computation of new amplitudes in the future. Finally, we study the two types of fluctuations arising in heavy-ion collisions. These are related either to the initial state or the intermediate state of matter produced in such collisions. The initial state fluctuations are experimentally observed to give rise to non-Gaussianities in the final-state spectra. We show how these non-Gaussianities can be explained by the random position and interaction energy of 'sources' in the colliding nuclei. Furthermore, we

  16. Deviations from the Boltzmann distribution in vibrationally excited gas flows

    International Nuclear Information System (INIS)

    Offenhaeuser, F.; Frohn, A.

    1986-01-01

    A new model for the exchange of vibrational energy in one-dimensional flows of CO 2 -H 2 O-N 2 -O 2 -He gas mixtures is presented. In contrast to previous models, the assumption of local Boltzmann distributions for the vibrational degrees of freedom is not required. This generalization was achieved by the assumption that the molecules are harmonic oscillators with one or more degrees of freedom represented by finite numbers of energy levels. The population densities of these energy levels are coupled by a set of rate equations. It is shown that in some cases of molecular gas flow the Boltzmann distribution for the vibrational degrees of freedom may be disturbed. 12 references

  17. Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

    Science.gov (United States)

    Blossey, R.; Maggs, A. C.; Podgornik, R.

    2017-06-01

    We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

  18. Collision Detection for Underwater ROV Manipulator Systems

    Directory of Open Access Journals (Sweden)

    Satja Sivčev

    2018-04-01

    Full Text Available Work-class ROVs equipped with robotic manipulators are extensively used for subsea intervention operations. Manipulators are teleoperated by human pilots relying on visual feedback from the worksite. Operating in a remote environment, with limited pilot perception and poor visibility, manipulator collisions which may cause significant damage are likely to happen. This paper presents a real-time collision detection algorithm for marine robotic manipulation. The proposed collision detection mechanism is developed, integrated into a commercial ROV manipulator control system, and successfully evaluated in simulations and experimental setup using a real industry standard underwater manipulator. The presented collision sensing solution has a potential to be a useful pilot assisting tool that can reduce the task load, operational time, and costs of subsea inspection, repair, and maintenance operations.

  19. Second order bounce back boundary condition for the lattice Boltzmann fluid simulation

    International Nuclear Information System (INIS)

    Kim, In Chan

    2000-01-01

    A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method

  20. Diffusion on unstructured triangular grids using Lattice Boltzmann

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2004-01-01

    In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at

  1. Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

    Science.gov (United States)

    Kwang-Hua, Chu Rainer

    2018-05-01

    The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

  2. Comparison of Einstein-Boltzmann solvers for testing general relativity

    Science.gov (United States)

    Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.

    2018-01-01

    We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

  3. Lattice Boltzmann model for three-phase viscoelastic fluid flow

    Science.gov (United States)

    Xie, Chiyu; Lei, Wenhai; Wang, Moran

    2018-02-01

    A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

  4. From Pore Scale to Turbulent Flow with the Unstructured Lattice Boltzmann Method

    DEFF Research Database (Denmark)

    Matin, Rastin

    Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall...... is required. The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively...

  5. Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

    Directory of Open Access Journals (Sweden)

    Florian Thüroff

    2014-11-01

    Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

  6. Collision Risk and Damage after Collision

    DEFF Research Database (Denmark)

    Pedersen, Preben Terndrup; Hansen, Peter Friis; Nielsen, Lars Peter

    1996-01-01

    The paper presents a new and complete procedure for calculation of ship-ship collision rates on specific routes and the hull damage caused by such collisions.The procedure is applied to analysis of collision risks for Ro-Ro pasenger vessels. Given a collision the spatial probability distribution ...

  7. Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...

  8. A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

    Science.gov (United States)

    Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

    2018-01-01

    In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed

  9. The peeling process of infinite Boltzmann planar maps

    DEFF Research Database (Denmark)

    Budd, Timothy George

    2016-01-01

    criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can...

  10. Lattice Boltzmann scheme for diffusion on triangular grids

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2003-01-01

    In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas

  11. Analysis of Operation Plumbbob nuclear test: BOLTZMANN radiological and meteorological data

    International Nuclear Information System (INIS)

    Steadman, C.R. Jr.; Kennedy, N.C.; Quinn, V.E.

    1983-09-01

    This report describes the Weather Service Nuclear Support Office (WSNSO) analyses of the radiological and meteorological data collected for the BOLTZMANN nuclear test of Operation PLUMBBOB. Inconsistencies in the radiological data and their resolution are discussed. The methods of converting aerial radiological data to equivalent ground-level values and of estimating fallout arrival times are presented. The meteorological situation on D-day is described. A comparison of the WSNSO fallout analyses with analyses in the late 1950's is presented. The appendices contain tabulated radiological data used in the fallout analyses, and contain discussions of the BOLTZMANN hot spot contention and of the enhanced activity at Portola, California

  12. Optimising Boltzmann codes for the PLANCK era

    International Nuclear Information System (INIS)

    Hamann, Jan; Lesgourgues, Julien; Balbi, Amedeo; Quercellini, Claudia

    2009-01-01

    High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the PLANCK satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical error in the output of the Boltzmann codes used to calculate angular power spectra. In this work, we carry out an extensive study of the numerical accuracy of the public Boltzmann code CAMB, and identify a set of parameters which determine the error of its output. We show that at the current default settings, the cosmological parameters extracted from data of future experiments like Planck can be biased by several tenths of a standard deviation for the six parameters of the standard ΛCDM model, and potentially more seriously for extended models. We perform an optimisation procedure that leads the code to achieve sufficient precision while at the same time keeping the computation time within reasonable limits. Our conclusion is that the contribution of numerical errors to the theoretical uncertainty of model predictions is well under control—the main challenges for more accurate calculations of CMB spectra will be of an astrophysical nature instead

  13. Distribution Learning in Evolutionary Strategies and Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Krause, Oswin

    The thesis is concerned with learning distributions in the two settings of Evolutionary Strategies (ESs) and Restricted Boltzmann Machines (RBMs). In both cases, the distributions are learned from samples, albeit with different goals. Evolutionary Strategies are concerned with finding an optimum ...

  14. A topological insight into restricted Boltzmann machines (extented abstract)

    NARCIS (Netherlands)

    Mocanu, D.C.; Mocanu, E.; Nguyen, H.P.; Gibescu, M.; Liotta, A.

    2016-01-01

    Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep neural networks for automatic features extraction, unsupervised weights initialization, but also as standalone models for density estimation, activity recognition and so on.

  15. Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger's equation

    Science.gov (United States)

    Velivelli, A. C.; Bryden, K. M.

    2006-03-01

    Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.

  16. Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

    Science.gov (United States)

    Meng, Xuhui; Guo, Zhaoli

    2015-10-01

    A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

  17. Elliptic flow and energy loss of heavy quarks in ultrarelativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Uphoff, Jan; Fochler, Oliver; Greiner, Carsten; Xu, Zhe

    2011-01-01

    The space-time propagation of heavy quarks in ultrarelativistic heavy ion collisions is studied within the partonic transport model Boltzmann approach of multiparton scatterings (BAMPS). In this model heavy quarks interact with the partonic medium via binary scatterings. The cross sections for these interactions are calculated with leading-order perturbative QCD, but feature a more precise Debye screening derived within the hard thermal loop approximation and obey the running of the coupling. Within this framework the elliptic flow and the nuclear modification factor of heavy quarks are computed for the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) energies and compared to available experimental data. It is found that binary scatterings alone cannot reproduce the data and therefore radiative corrections have to be taken into account.

  18. Dimensional transitions in thermodynamic properties of ideal Maxwell–Boltzmann gases

    International Nuclear Information System (INIS)

    Aydin, Alhun; Sisman, Altug

    2015-01-01

    An ideal Maxwell–Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale. (paper)

  19. Energy Dependent Streaming in Lattice Boltzmann Simulations

    Czech Academy of Sciences Publication Activity Database

    Pavlo, Pavol; Vahala, G.; Vahala, L.

    2001-01-01

    Roč. 46, č. 8 (2001), s. 241 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/43rd./. Long Beach, CA, 29.10.2001-02.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann Simulations Subject RIV: BL - Plasma and Gas Discharge Physics

  20. Multiphase lattice Boltzmann on the Cell Broadband Engine

    International Nuclear Information System (INIS)

    Belletti, F.; Mantovani, F.; Tripiccione, R.; Biferale, L.; Schifano, S.F.; Toschi, F.

    2009-01-01

    Computational experiments are one of the most used and flexible investigation tools in fluid dynamics. The Lattice Boltzmann Equation is a well established computational method particularly promising for multi-phase flows at micro and macro scales. Here we present preliminary results on performances of the Lbe method on the Cell Broadband Engine platform.

  1. Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

    International Nuclear Information System (INIS)

    Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai

    2014-01-01

    A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  2. Lattice Boltzmann simulation for temperature-sensitive magnetic fluids in a porous square cavity

    International Nuclear Information System (INIS)

    Jin Licong; Zhang Xinrong; Niu Xiaodong

    2012-01-01

    A lattice Boltzmann method is developed to simulate temperature-sensitive magnetic fluids in a porous cavity. In the simulation, the magnetic force, efficient gravity, viscous loss term and geometric loss term in porous medium are imported to the momentum equation. To test the reliability of the method, a validation with water in porous cavity is carried out. Good agreements with the previous results verify that the present lattice Boltzmann method is promising for simulation of magnetic fluids in porous medium. In this study, we investigate the change of magnetization with external magnetic field, and we present numerical results for the streamlines, isotherms, and magnetization at vertical or horizontal mid-profiles for different values of Ram. In addition, Nusselt numbers changing with magnetic Rayleigh numbers are also investigated. - Highlights: → Developed a lattice Boltzmann method for magnetic nano-fluids in porous cavity. → Clarified flow and heat transfer for different values of (magnetic) Rayleigh numbers. → Heat transfer enhancement for magnetic fluid in porous cavity.

  3. Impact parameter and energy dependence of the dynamics of nucleus-nucleus collisions below 100 MeV/u

    International Nuclear Information System (INIS)

    Peter, J.

    1990-10-01

    The multidetector array Mur + Tonneau has been used to perform a 4π detection of charged particles and fragments emitted in reactions between 40 Ar, at energies ranging from 25 to 85 MeV/u, and 27 Al or 58 Ni target. The events have been sorted as a function of the impact parameter value, using a new global variable, the average parallel velocity. The pre-equilibrium emission from the interaction region increases strongly when the incident energy increases and when the impact parameter decreases. It severely limits the mass and excitation energy of the equilibrated partial fusion nuclei, even in central collisions. The collective transverse momentum in the reaction plane (flow) is observed to strongly vary as a function of impact parameter and incident energy. Its value falls to zero in the range 70-80 MeV/u for central collisions. These results are compared to predictions based on the Landau-Vlasov and Boltzmann equations in order, to get information on the nucleon-nucleon cross section in medium and the equation of state of nuclear matter. 8 figs

  4. Combining generative and discriminative representation learning for lung CT analysis with convolutional restricted Boltzmann machines

    DEFF Research Database (Denmark)

    van Tulder, Gijs; de Bruijne, Marleen

    2016-01-01

    The choice of features greatly influences the performance of a tissue classification system. Despite this, many systems are built with standard, predefined filter banks that are not optimized for that particular application. Representation learning methods such as restricted Boltzmann machines may...... outperform these standard filter banks because they learn a feature description directly from the training data. Like many other representation learning methods, restricted Boltzmann machines are unsupervised and are trained with a generative learning objective; this allows them to learn representations from...... unlabeled data, but does not necessarily produce features that are optimal for classification. In this paper we propose the convolutional classification restricted Boltzmann machine, which combines a generative and a discriminative learning objective. This allows it to learn filters that are good both...

  5. Measuring Boltzmann's Constant with Carbon Dioxide

    Science.gov (United States)

    Ivanov, Dragia; Nikolov, Stefan

    2013-01-01

    In this paper we present two experiments to measure Boltzmann's constant--one of the fundamental constants of modern-day physics, which lies at the base of statistical mechanics and thermodynamics. The experiments use very basic theory, simple equipment and cheap and safe materials yet provide very precise results. They are very easy and…

  6. Lattice Boltzmann method fundamentals and engineering applications with computer codes

    CERN Document Server

    Mohamad, A A

    2014-01-01

    Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.

  7. New Poisson–Boltzmann type equations: one-dimensional solutions

    International Nuclear Information System (INIS)

    Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

    2011-01-01

    The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

  8. Lattice-Boltzmann simulation of the sedimentation of charged disks

    NARCIS (Netherlands)

    Capuani, F.; Pagonabarraga, I.; Frenkel, D.

    2006-01-01

    We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal

  9. Convection in multiphase fluid flows using lattice Boltzmann methods

    NARCIS (Netherlands)

    Biferale, L.; Perlekar, P.; Sbragaglia, M.; Toschi, F.

    2012-01-01

    We present high-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method. We first study the thermodynamical and kinematic properties of the algorithm. Then, we perform a series of 3D numerical simulations changing the

  10. Photon-hadron and photon-photon collisions in CMS (including data from p-p, p-A and A-A collisions)

    CERN Document Server

    Rebello Teles, Patricia

    2015-01-01

    Photon-nucleus and photon-photon collisions are abundantly produced at the LHC. The LHC provides a unique opportunity to study high-energy photon-photon interactions, thanks to its high energy and large integrated luminosity. In this talk two CMS analyses concerning photon-hadron and photon-photon collisions are going to be presented. The first deals with the measurement of the coherent $J/\\Psi$ photoproduction cross section in ultra-peripheral PbPb collisions at $\\sqrt{s_{NN}}$ = 2.76 TeV in conjunction with forward neutrons. The second one shows the evidence of the exclusive $\\gamma \\gamma \\to W^{+}W^{-}$ production and improvement on constraints for the anomalous gauge quartic coupling $\\gamma \\gamma WW$ parameters.

  11. Simulating colloid hydrodynamics with lattice Boltzmann methods

    International Nuclear Information System (INIS)

    Cates, M E; Stratford, K; Adhikari, R; Stansell, P; Desplat, J-C; Pagonabarraga, I; Wagner, A J

    2004-01-01

    We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy

  12. Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

    International Nuclear Information System (INIS)

    Shan Ming-Lei; Zhu Chang-Ping; Yao Cheng; Yin Cheng; Jiang Xiao-Yan

    2016-01-01

    The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. (paper)

  13. Recommended direct simulation Monte Carlo collision model parameters for modeling ionized air transport processes

    Energy Technology Data Exchange (ETDEWEB)

    Swaminathan-Gopalan, Krishnan; Stephani, Kelly A., E-mail: ksteph@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)

    2016-02-15

    A systematic approach for calibrating the direct simulation Monte Carlo (DSMC) collision model parameters to achieve consistency in the transport processes is presented. The DSMC collision cross section model parameters are calibrated for high temperature atmospheric conditions by matching the collision integrals from DSMC against ab initio based collision integrals that are currently employed in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and Data Parallel Line Relaxation (DPLR) high temperature computational fluid dynamics solvers. The DSMC parameter values are computed for the widely used Variable Hard Sphere (VHS) and the Variable Soft Sphere (VSS) models using the collision-specific pairing approach. The recommended best-fit VHS/VSS parameter values are provided over a temperature range of 1000-20 000 K for a thirteen-species ionized air mixture. Use of the VSS model is necessary to achieve consistency in transport processes of ionized gases. The agreement of the VSS model transport properties with the transport properties as determined by the ab initio collision integral fits was found to be within 6% in the entire temperature range, regardless of the composition of the mixture. The recommended model parameter values can be readily applied to any gas mixture involving binary collisional interactions between the chemical species presented for the specified temperature range.

  14. Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Melenev, Petr, E-mail: melenev@icmm.ru [Ural Federal University, 4, Turgeneva str., 620000 Ekaterinburg (Russian Federation); Institute of Continuous Media Mechanics, 1, Koroleva str., 614013 Perm (Russian Federation)

    2017-06-01

    Hydrodynamic interactions between magnetic nanoparticles suspended in the Newtonian liquid are accounted for using a combination of the lattice Boltzmann method and molecular dynamics simulations. Nanoparticle is modelled by the system of molecular dynamics material points (which form structure resembles raspberry) coupled to the lattice Boltzmann fluid. The hydrodynamic coupling between the colloids is studied by simulations of the thermo-induced rotational diffusion of two raspberry objects. It was found that for the considered range of model parameters the approaching of the raspberries leads to slight retard of the relaxation process. The presence of the weak magnetic dipolar interaction between the objects leads to modest decrease of the relaxation time and the extent of the acceleration of the diffusion is intensified along with magnetic forces. - Highlights: • The combination of molecular dynamics and lattice Boltzmann method is utilized for the reveal of the role of hydrodynamic interaction in rotational dynamics of colloid particles. • The verification of the model parameters is done based on the comparison with the results of Langevin dynamics. • For the task of free rotational diffusion of the pair of colloid particles the influence of the hydrodynamic interactions on the relaxation time is examined in the case of nonmagnetic particles and at the presence of weak dipolar interaction.

  15. Lattice Boltzmann simulations of attenuation-driven acoustic streaming

    International Nuclear Information System (INIS)

    Haydock, David; Yeomans, J M

    2003-01-01

    We show that lattice Boltzmann simulations can be used to model the attenuation-driven acoustic streaming produced by a travelling wave. Comparisons are made to analytical results and to the streaming pattern produced by an imposed body force approximating the Reynolds stresses. We predict the streaming patterns around a porous material in an attenuating acoustic field

  16. Distributional Monte Carlo Methods for the Boltzmann Equation

    Science.gov (United States)

    2013-03-01

    postulated by Ludwig Boltzmann [23] at a time when the atomic makeup of matter was not an accepted concept. Modern physics realizes Boltzmann’s vision...über Gastheorie 1898. Translated by S.G. Brush ., 1964. [24] Boyles, K.A., G.J. LeBeau, and M.A. Gallis. “DSMC Simulations in Support of the Columbia

  17. The Boltzmann constant from a snifter

    International Nuclear Information System (INIS)

    Tyukodi, B; Sárközi, Zs; Néda, Z; Tunyagi, A; Györke, E

    2012-01-01

    Evaporation of a small glass of ethylic alcohol is studied both experimentally and through an elementary thermal physics approach. For a cylindrical beaker and no air flow in the room, a simple quadratic relation is found between the evaporation time and the mass of evaporated liquid. This problem and the obtained results offer excellent possibilities for simple student experiments and for testing basic principles of thermal physics. As an example, we use the obtained results for estimating the value of the Boltzmann constant from evaporation experiments. (paper)

  18. From collision to collaboration - Integrating informal recyclers and re-use operators in Europe: A review.

    Science.gov (United States)

    Scheinberg, Anne; Nesić, Jelena; Savain, Rachel; Luppi, Pietro; Sinnott, Portia; Petean, Flaviu; Pop, Flaviu

    2016-09-01

    The European Union hosts some of the world's most developed waste management systems and an ambitious policy commitment to the circular economy. The existence of informal recycling and re-use activities in Europe has been vigorously denied until quite recently, and remains a very challenging subject for the European solid waste management sector, as well as for European government and private institutions. In countries ranging from Malta to Macedonia and from France to Turkey, informal recyclers excluded from legal recycling niches increasingly collide with formalised and controlled European Union approaches to urban waste management, packaging recovery schemes, formal re-use enterprises, and extended producer responsibility systems.This review focuses on the period from 2004 through the first half of 2016. The 78 sources on European (and neighbouring) informal recycling and re-use are contextualised with global sources and experience. The articles focus on informal recovery in and at the borders of the European Union, document the conflicts and collisions, and elaborate some constructive approaches towards legalisation, integration, and reconciliation. The overarching recommendation, to locate the issue of informal recovery and integration in the framework of the European circular economy package, is supported by four specific pillars of an integration strategy: Documentation, legalisation, occupational and enterprise recognition, and preparation for structural integration. © The Author(s) 2016.

  19. Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

    DEFF Research Database (Denmark)

    Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

    2015-01-01

    A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall. It is sh......A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall...

  20. Integrated trajectory control and collision avoidance for automated driving

    NARCIS (Netherlands)

    Verhaegh, J.; Ploeg, J.; Nunen, E. van; Teerhuis, A.

    2017-01-01

    This paper presents a method for trajectory control, based on feedback linearization to guide an Automatic Guided Vehicle (AGV). The novelty of this work, is the adaptation of a reference trajectory with respect to a desired velocity in real-time to avoid collisions using a time-scaling mechanism.

  1. Covariant transport theory

    Energy Technology Data Exchange (ETDEWEB)

    Pang, Yang [Columbia Univ., New York, NY (United States)]|[Brookhaven National Labs., Upton, NY (United States)

    1997-09-22

    Many phenomenological models for relativistic heavy ion collisions share a common framework - the relativistic Boltzmann equations. Within this framework, a nucleus-nucleus collision is described by the evolution of phase-space distributions of several species of particles. The equations can be effectively solved with the cascade algorithm by sampling each phase-space distribution with points, i.e. {delta}-functions, and by treating the interaction terms as collisions of these points. In between collisions, each point travels on a straight line trajectory. In most implementations of the cascade algorithm, each physical particle, e.g. a hadron or a quark, is often represented by one point. Thus, the cross-section for a collision of two points is just the cross-section of the physical particles, which can be quite large compared to the local density of the system. For an ultra-relativistic nucleus-nucleus collision, this could lead to a large violation of the Lorentz invariance. By using the invariance property of the Boltzmann equation under a scale transformation, a Lorentz invariant cascade algorithm can be obtained. The General Cascade Program - GCP - is a tool for solving the relativistic Boltzmann equation with any number of particle species and very general interactions with the cascade algorithm.

  2. Measurement of collision integral cross-sections of double-photon Compton effect using a single gamma ray detector: A response matrix approach

    International Nuclear Information System (INIS)

    Saddi, M.B.; Singh, Bhajan; Sandhu, B.S.

    2008-01-01

    The collision integral cross-sections of double-photon Compton process are measured experimentally for 662 keV incident gamma photons. The measurements are successfully carried out using a single gamma ray detector, and do not require the complicated slow-fast coincidence technique used till now for observing this higher order quantum electrodynamics (QED) process. The energy spectra of one of the two final photons, originating in this process, in direction of the gamma ray detector are observed as a long tail to the single-photon Compton line on lower side of the full energy peak in the observed spectra. An inverse response matrix converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. This also results in extraction of events originating from double-photon Compton interactions. The present measured values of collision integral cross-section, although of same magnitude, deviate from the corresponding values obtained from the theory. In view of the magnitude of deviations, in addition to small value of probability of occurrence of this process, the agreement of measured values with theory is reasonably acceptable

  3. LHC Report: LHC smashes collision records

    CERN Multimedia

    Sarah Charley

    2016-01-01

    The Large Hadron Collider is now producing more than a billion proton-proton collisions per second.   The LHC is colliding protons at a faster rate than ever before: approximately 1 billion times per second. Since April 2016, the LHC has delivered more than 30 inverse femtobarns (fb-1) to both ATLAS and CMS. This means that around 2.4 quadrillion (2.4 million billion) collisions have been seen by each of the experiments this year. The inverse femtobarn is the unit of measurement for integrated luminosity, indicating the cumulative number of potential collisions. This compares with the total of 33.2 fb-1 produced between 2010 and 2015. The unprecedented performance this year is the result of both the incremental increases in collision rate and the sheer amount of time the LHC has been up and running. This comes after a slow start-up in 2015, when scientists and engineers still needed to learn how to operate the machine at a much higher energy. “With more energy, the machine is much more sen...

  4. Privacy-Preserving Restricted Boltzmann Machine

    Directory of Open Access Journals (Sweden)

    Yu Li

    2014-01-01

    Full Text Available With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM. The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model.

  5. Normal solutions of the Boltzmann equation with small Knudsen number

    International Nuclear Information System (INIS)

    Ding, E.J.; Huang, Z.Q.

    1986-01-01

    A singular perturbation method is used to find the normal solutions of the Boltzmann equation with small Knudsen number. It is proved that the secular terms may be removed by improving the Hilbert expansion and the Enskog expansion

  6. Acoustic levitation and the Boltzmann-Ehrenfest principle

    Science.gov (United States)

    Putterman, S.; Rudnick, Joseph; Barmatz, M.

    1989-01-01

    The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.

  7. Implementation of the Lattice Boltzmann Method on Heterogeneous Hardware and Platforms using OpenCL

    Directory of Open Access Journals (Sweden)

    TEKIC, P. M.

    2012-02-01

    Full Text Available The Lattice Boltzmann method (LBM has become an alternative method for computational fluid dynamics with a wide range of applications. Besides its numerical stability and accuracy, one of the major advantages of LBM is its relatively easy parallelization and, hence, it is especially well fitted to many-core hardware as graphics processing units (GPU. The majority of work concerning LBM implementation on GPU's has used the CUDA programming model, supported exclusively by NVIDIA. Recently, the open standard for parallel programming of heterogeneous systems (OpenCL has been introduced. OpenCL standard matures and is supported on processors from most vendors. In this paper, we make use of the OpenCL framework for the lattice Boltzmann method simulation, using hardware accelerators - AMD ATI Radeon GPU, AMD Dual-Core CPU and NVIDIA GeForce GPU's. Application has been developed using a combination of Java and OpenCL programming languages. Java bindings for OpenCL have been utilized. This approach offers the benefits of hardware and operating system independence, as well as speeding up of lattice Boltzmann algorithm. It has been showed that the developed lattice Boltzmann source code can be executed without modification on all of the used hardware accelerators. Performance results have been presented and compared for the hardware accelerators that have been utilized.

  8. Student learning of upper-level thermal and statistical physics: The derivation and use of the Boltzmann factor

    Science.gov (United States)

    Thompson, John

    2015-04-01

    As the Physical Review Focused Collection demonstrates, recent frontiers in physics education research include systematic investigations at the upper division. As part of a collaborative project, we have examined student understanding of several topics in upper-division thermal and statistical physics. A fruitful context for research is the Boltzmann factor in statistical mechanics: the standard derivation involves several physically justified mathematical steps as well as the invocation of a Taylor series expansion. We have investigated student understanding of the physical significance of the Boltzmann factor as well as its utility in various circumstances, and identified various lines of student reasoning related to the use of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students do not use the Boltzmann factor when answering questions related to probability in applicable physical situations, even after lecture instruction. We designed an inquiry-based tutorial activity to guide students through a derivation of the Boltzmann factor and to encourage deep connections between the physical quantities involved and the mathematics. Observations of students working through the tutorial suggest that many students at this level can recognize and interpret Taylor series expansions, but they often lack fluency in creating and using Taylor series appropriately, despite previous exposure in both calculus and physics courses. Our findings also suggest that tutorial participation not only increases the prevalence of relevant invocation of the Boltzmann factor, but also helps students gain an appreciation of the physical implications and meaning of the mathematical formalism behind the formula. Supported in part by NSF Grants DUE-0817282, DUE-0837214, and DUE-1323426.

  9. Some recent studies of electron swarms in gases

    International Nuclear Information System (INIS)

    Tagashira, H.

    1992-01-01

    Some recent studies of electron swarms in gases under the action of an electric field are introduced. The studies include a new type of continuity equation for electrons having a form in which the partial derivative of the electron density with respect to position and to time are interchanged, a method to deduce the time-of-flight and arrival-time-spectrum swarm parameters based on a Fourier-transformed Boltzmann equation, an examination of the correspondence between experimental and theoretical electron drift velocities, and an automatic technique to deduce the electron-gas molecule collision cross section from electron drift velocity data. A method for the deduction of electron collision cross sections with gas molecules having vibrational excitation cross sections greater than the elastic momentum transfer cross section by using a gas mixture technique, an integral type of method for solution of the Boltzmann equation with salient numerical stability, a quantitative analysis of the effect of Penning ionisation, and the behaviour of electron swarms under radio frequency electric fields, are also briefly discussed. 28 refs., 3 figs

  10. Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

    Science.gov (United States)

    Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

    2018-05-01

    This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

  11. Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)

    2010-09-15

    In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)

  12. DeepX: Deep Learning Accelerator for Restricted Boltzmann Machine Artificial Neural Networks.

    Science.gov (United States)

    Kim, Lok-Won

    2018-05-01

    Although there have been many decades of research and commercial presence on high performance general purpose processors, there are still many applications that require fully customized hardware architectures for further computational acceleration. Recently, deep learning has been successfully used to learn in a wide variety of applications, but their heavy computation demand has considerably limited their practical applications. This paper proposes a fully pipelined acceleration architecture to alleviate high computational demand of an artificial neural network (ANN) which is restricted Boltzmann machine (RBM) ANNs. The implemented RBM ANN accelerator (integrating network size, using 128 input cases per batch, and running at a 303-MHz clock frequency) integrated in a state-of-the art field-programmable gate array (FPGA) (Xilinx Virtex 7 XC7V-2000T) provides a computational performance of 301-billion connection-updates-per-second and about 193 times higher performance than a software solution running on general purpose processors. Most importantly, the architecture enables over 4 times (12 times in batch learning) higher performance compared with a previous work when both are implemented in an FPGA device (XC2VP70).

  13. Exact solutions for some discrete models of the Boltzmann equation

    International Nuclear Information System (INIS)

    Cabannes, H.; Hong Tiem, D.

    1987-01-01

    For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

  14. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

    Science.gov (United States)

    Li, Q; He, Y L; Wang, Y; Tao, W Q

    2007-11-01

    A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

  15. Training Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Fischer, Asja

    relies on sampling based approximations of the log-likelihood gradient. I will present an empirical and theoretical analysis of the bias of these approximations and show that the approximation error can lead to a distortion of the learning process. The bias decreases with increasing mixing rate......Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can also be interpreted as stochastic neural networks. Training RBMs is known to be challenging. Computing the likelihood of the model parameters or its gradient is in general computationally intensive. Thus, training...... of the applied sampling procedure and I will introduce a transition operator that leads to faster mixing. Finally, a different parametrisation of RBMs will be discussed that leads to better learning results and more robustness against changes in the data representation....

  16. Searches for excited fermions in ep collisions at HERA

    International Nuclear Information System (INIS)

    Chekanov, S.; Derrick, M.; Krakauer, D.

    2002-01-01

    Searches in ep collisions for heavy excited fermions have been performed with the ZEUS detector at HERA. Excited states of electrons and quarks have been searched for in e + p collisions at a centre-of-mass energy of 300 GeV using an integrated luminosity of 47.7 pb -1 . Excited electrons have been sought via the decays e*→eγ, e*→eZ and e*→νW. Excited quarks have been sought via the decays q*→qγ and q*→qW. A search for excited neutrinos decaying via ν*→νγ, ν*→νZ and ν*→eW is presented using e - p collisions at 318 GeV centre-of-mass energy, corresponding to an integrated luminosity of 16.7 pb -1 . No evidence for any excited fermion is found, and limits on the characteristic couplings are derived for masses ≤250 GeV

  17. Simulating the Langevin force by simple noise in nuclear one-body dynamics

    International Nuclear Information System (INIS)

    Chomaz, Ph.; Colonna, M.; Burgio, G.F.; Toro, M. Di; Randrup, J.

    1992-01-01

    For the purpose of addressing catastrophic phenomena in nuclear dynamics, the possibility of simulating the stochastic part of the collision integral is explored in the Boltzmann-Langevin model by the numerical noise associated with the finite number of test particles in the ordinary BUU treatment. Considering idealized two-dimensional matter, for which it is practical to simulate the Boltzmann-Langevin equation directly, it is demonstrated that the number of test-particles per nucleon can be adjusted so that the corresponding BUU calculation yields a good reproduction of the spontaneous clusterization occurring inside the spinodal region. This approximate method may therefore provide a relatively easy way to introduce meaningful fluctuations in simulations of unstable nuclear dynamics. (author) 18 refs.; 3 figs

  18. Lattice-Boltzmann scheme for natural convection in porous media

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    1997-01-01

    A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore

  19. Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

    International Nuclear Information System (INIS)

    Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat

    2015-01-01

    Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)

  20. A lattice Boltzmann coupled to finite volumes method for solving phase change problems

    Directory of Open Access Journals (Sweden)

    El Ganaoui Mohammed

    2009-01-01

    Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

  1. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

    Energy Technology Data Exchange (ETDEWEB)

    Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)

    2011-04-08

    The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

  2. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

    International Nuclear Information System (INIS)

    Uchaikin, V V; Sibatov, R T

    2011-01-01

    The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

  3. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    International Nuclear Information System (INIS)

    Shafii, Mohammad Ali; Meidianti, Rahma; Wildian,; Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-01-01

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation

  4. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    Energy Technology Data Exchange (ETDEWEB)

    Shafii, Mohammad Ali, E-mail: mashafii@fmipa.unand.ac.id; Meidianti, Rahma, E-mail: mashafii@fmipa.unand.ac.id; Wildian,, E-mail: mashafii@fmipa.unand.ac.id; Fitriyani, Dian, E-mail: mashafii@fmipa.unand.ac.id [Department of Physics, Andalas University Padang West Sumatera Indonesia (Indonesia); Tongkukut, Seni H. J. [Department of Physics, Sam Ratulangi University Manado North Sulawesi Indonesia (Indonesia); Arkundato, Artoto [Department of Physics, Jember University Jember East Java Indonesia (Indonesia)

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  5. SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Hong, X; Gao, H [Shanghai Jiao Tong University, Shanghai, Shanghai (China); Paganetti, H [Massachusetts General Hospital, Boston, MA (United States)

    2015-06-15

    Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang

  6. Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

    Directory of Open Access Journals (Sweden)

    Bertrand Lods

    2015-06-01

    Full Text Available Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives.

  7. A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

    KAUST Repository

    Allen, Rebecca

    2013-01-01

    The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

  8. ROLAIDS-CPM, 1-D Slowing-Down by Collision Problems Method

    International Nuclear Information System (INIS)

    De Kruijf, W.J.M.

    2002-01-01

    1 - Description of program or function: ROLAIDS-CPM is based on the AMPX-module ROLAIDS (PSR-315). CPM stands for Collision Probability Method. ROLAIDS is a one-dimensional slowing-down code which uses the interface currents method. ROLAIDS-CPM does not need the assumption of cosine currents at the interface of the zones. Extensions: collision probability method for slab and cylinder geometry; different temperatures for a nuclide can be used; flat lethargy source can be modelled. 2 - Method of solution: Collision probabilities in cylindrical geometry are calculated according to the Carlvik Method. This means that a Gauss integration is used. 3 - Restrictions on the complexity of the problem: The maximum number of zones is 30 for the collision probability method

  9. Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem.

    Science.gov (United States)

    Frausto-Solis, Juan; Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J Javier; González-Flores, Carlos; Castilla-Valdez, Guadalupe

    2016-01-01

    A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

  10. Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

    DEFF Research Database (Denmark)

    Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S.

    2007-01-01

    compute the viscosity. This paper presents a modified parallel plate rheometer, and proposes means of calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus using an accurate numerical solution in place...

  11. Contributions to the spectral theory of the linear Boltzmann operator for various geometries

    International Nuclear Information System (INIS)

    Protopopescu, V.

    1975-01-01

    The linear monoenergetic Boltzmann operator with isotropic scattering is studied for various geometries and boundary conditions as the infinitesimal generator of a positivity preserving contractive semigroup in an appropriate Hilbert space. General results about the existence and the uniqueness of the solutions of the corresponding evolution problems are reviewed. The spectrum of the Boltzmann operator is analyzed for semi-infinite, slab and parallelepipedic geometries with vacuum, periodic, perfectly reflecting, generalized and diffusely reflecting boundary condition respectively. The main features of these spectra, their importance for determining the asymptotic evolution and possible generalizations to more realistic models are put together in a final section. (author)

  12. Metriplectic Gyrokinetics and Discretization Methods for the Landau Collision Integral

    Science.gov (United States)

    Hirvijoki, Eero; Burby, Joshua W.; Kraus, Michael

    2017-10-01

    We present two important results for the kinetic theory and numerical simulation of warm plasmas: 1) We provide a metriplectic formulation of collisional electrostatic gyrokinetics that is fully consistent with the First and Second Laws of Thermodynamics. 2) We provide a metriplectic temporal and velocity-space discretization for the particle phase-space Landau collision integral that satisfies the conservation of energy, momentum, and particle densities to machine precision, as well as guarantees the existence of numerical H-theorem. The properties are demonstrated algebraically. These two result have important implications: 1) Numerical methods addressing the Vlasov-Maxwell-Landau system of equations, or its reduced gyrokinetic versions, should start from a metriplectic formulation to preserve the fundamental physical principles also at the discrete level. 2) The plasma physics community should search for a metriplectic reduction theory that would serve a similar purpose as the existing Lagrangian and Hamiltonian reduction theories do in gyrokinetics. The discovery of metriplectic formulation of collisional electrostatic gyrokinetics is strong evidence in favor of such theory and, if uncovered, the theory would be invaluable in constructing reduced plasma models. Supported by U.S. DOE Contract Nos. DE-AC02-09-CH11466 (EH) and DE-AC05-06OR23100 (JWB) and by European Union's Horizon 2020 research and innovation Grant No. 708124 (MK).

  13. Generalized Boltzmann equations for on-shell particle production in a hot plasma

    International Nuclear Information System (INIS)

    Jakovac, A.

    2002-01-01

    A novel refinement of the conventional treatment of Kadanoff-Baym equations is suggested. In addition to the Boltzmann equation, another differential equation is used for calculating the evolution of the nonequilibrium two-point function. Although it was usually interpreted as a constraint on the solution of the Boltzmann equation, we argue that its dynamics is relevant to the determination and resummation of the particle production cut contributions. The differential equation for this new contribution is illustrated in the example of the cubic scalar model. The analogue of the relaxation time approximation is suggested. It results in the shift of the threshold location and in a smearing out of the nonanalytic threshold behavior of the spectral function. The possible consequences for the dilepton production are discussed

  14. Time-independent lattice Boltzmann method calculation of hydrodynamic interactions between two particles

    Science.gov (United States)

    Ding, E. J.

    2015-06-01

    The time-independent lattice Boltzmann algorithm (TILBA) is developed to calculate the hydrodynamic interactions between two particles in a Stokes flow. The TILBA is distinguished from the traditional lattice Boltzmann method in that a background matrix (BGM) is generated prior to the calculation. The BGM, once prepared, can be reused for calculations for different scenarios, and the computational cost for each such calculation will be significantly reduced. The advantage of the TILBA is that it is easy to code and can be applied to any particle shape without complicated implementation, and the computational cost is independent of the shape of the particle. The TILBA is validated and shown to be accurate by comparing calculation results obtained from the TILBA to analytical or numerical solutions for certain problems.

  15. Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

    CERN Document Server

    Farhat, Hassan; Kondaraju, Sasidhar

    2014-01-01

    Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

  16. Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

    NARCIS (Netherlands)

    Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

    2018-01-01

    A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute

  17. Equations for the kinetic modeling of supersonically flowing electrically excited lasers

    International Nuclear Information System (INIS)

    Lind, R.C.

    1973-01-01

    The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

  18. A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

    Energy Technology Data Exchange (ETDEWEB)

    Fakhari, Abbas, E-mail: afakhari@nd.edu [Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556 (United States); Geier, Martin [TU Braunschweig, Institute for Computational Modeling in Civil Engineering (iRMB), TU-Braunschweig, Pockelsstr. 3, 38106 Braunschweig (Germany); Lee, Taehun [Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031 (United States)

    2016-06-15

    A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

  19. A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

    International Nuclear Information System (INIS)

    Fakhari, Abbas; Geier, Martin; Lee, Taehun

    2016-01-01

    A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

  20. Podolsky electromagnetism at finite temperature: Implications on the Stefan-Boltzmann law

    International Nuclear Information System (INIS)

    Bonin, C. A.; Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.

    2010-01-01

    In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.

  1. An introduction to the Boltzmann equation and transport processes in gases

    CERN Document Server

    Kremer, Gilberto M; Colton, David

    2010-01-01

    This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

  2. Scattering theory of the linear Boltzmann operator

    International Nuclear Information System (INIS)

    Hejtmanek, J.

    1975-01-01

    In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

  3. Lattice Boltzmann methods for moving boundary flows

    International Nuclear Information System (INIS)

    Inamuro, Takaji

    2012-01-01

    The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

  4. Lattice Boltzmann methods for moving boundary flows

    Energy Technology Data Exchange (ETDEWEB)

    Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 (Japan)

    2012-04-01

    The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

  5. New Monte Carlo approach to the adjoint Boltzmann equation

    International Nuclear Information System (INIS)

    De Matteis, A.; Simonini, R.

    1978-01-01

    A class of stochastic models for the Monte Carlo integration of the adjoint neutron transport equation is described. Some current general methods are brought within this class, thus preparing the ground for subsequent comparisons. Monte Carlo integration of the adjoint Boltzmann equation can be seen as a simulation of the transport of mathematical particles with reaction kernels not normalized to unity. This last feature is a source of difficulty: It can influence the variance of the result negatively and also often leads to preparation of special ''libraries'' consisting of tables of normalization factors as functions of energy, presently used by several methods. These are the two main points that are discussed and that are taken into account to devise a nonmultigroup method of solution for a certain class of problems. Reactions considered in detail are radiative capture, elastic scattering, discrete levels and continuum inelastic scattering, for which the need for tables has been almost completely eliminated. The basic policy pursued to avoid a source of statistical fluctuations is to try to make the statistical weight of the traveling particle dependent only on its starting and current energies, at least in simple cases. The effectiveness of the sampling schemes proposed is supported by numerical comparison with other more general adjoint Monte Carlo methods. Computation of neutron flux at a point by means of an adjoint formulation is the problem taken as a test for numerical experiments. Very good results have been obtained in the difficult case of resonant cross sections

  6. A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Lin-Jie, Chen; Chang-Feng, Ma

    2010-01-01

    This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

  7. Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

    Science.gov (United States)

    Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

    2018-03-01

    In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

  8. The lattice Boltzmann method and the problem of turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Djenidi, L. [School of Engineering The University of Newcastle, Callaghan NSW 2308 (Australia)

    2015-03-10

    This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.

  9. The lattice Boltzmann method and the problem of turbulence

    International Nuclear Information System (INIS)

    Djenidi, L.

    2015-01-01

    This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence

  10. A new kinetic description for turbulent collisions including mode-coupling

    International Nuclear Information System (INIS)

    Misguich, J.H.; Tchen, C.M.

    1982-07-01

    The usual introduction of higher-order mode-coupling terms in the description of turbulent collisions beyond usual Renormalized Quasi-Linear approximation (RQL) is briefly analyzed. Here new results are derived in the framework of the general kinetic theory, and the equivalence is proved with the long time limit of simple results deduced from the Vlasov equation. The correction to the RQL turbulent collision term is analyzed and a new approximation is proposed. Turbulent collisions are also described by perturbation around the Lagrangian autocorrelation of fluctuating fields. For an homogeneous turbulence, however, the asymptotic integral of this Lagrangian autocorrelation vanishes identically, similarly to what occurs in Brownian motion. For inhomogeneous turbulence this method can nevertheless be used, and higher-order mode-coupling terms can be interpreted as a shielding of elementary Lagrangian turbulent collisions

  11. A new quantum statistical evaluation method for time correlation functions

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a system of N identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, the authors derive new formulas for correlation functions of the type C(t) = i= 1 N A i (t) Σ j=1 N B j > (where B j is diagonal in the free-particle states) in the thermodynamic limit. Thereby they apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation function C(t) is derived in a straight-forward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution

  12. Fluid moments of the nonlinear Landau collision operator

    Energy Technology Data Exchange (ETDEWEB)

    Hirvijoki, E.; Pfefferlé, D. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Lingam, M.; Bhattacharjee, A. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States); Comisso, L. [Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States); Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Candy, J. [General Atomics, San Diego, California 92186 (United States)

    2016-08-15

    An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

  13. High-Performance Computer Modeling of the Cosmos-Iridium Collision

    Energy Technology Data Exchange (ETDEWEB)

    Olivier, S; Cook, K; Fasenfest, B; Jefferson, D; Jiang, M; Leek, J; Levatin, J; Nikolaev, S; Pertica, A; Phillion, D; Springer, K; De Vries, W

    2009-08-28

    This paper describes the application of a new, integrated modeling and simulation framework, encompassing the space situational awareness (SSA) enterprise, to the recent Cosmos-Iridium collision. This framework is based on a flexible, scalable architecture to enable efficient simulation of the current SSA enterprise, and to accommodate future advancements in SSA systems. In particular, the code is designed to take advantage of massively parallel, high-performance computer systems available, for example, at Lawrence Livermore National Laboratory. We will describe the application of this framework to the recent collision of the Cosmos and Iridium satellites, including (1) detailed hydrodynamic modeling of the satellite collision and resulting debris generation, (2) orbital propagation of the simulated debris and analysis of the increased risk to other satellites (3) calculation of the radar and optical signatures of the simulated debris and modeling of debris detection with space surveillance radar and optical systems (4) determination of simulated debris orbits from modeled space surveillance observations and analysis of the resulting orbital accuracy, (5) comparison of these modeling and simulation results with Space Surveillance Network observations. We will also discuss the use of this integrated modeling and simulation framework to analyze the risks and consequences of future satellite collisions and to assess strategies for mitigating or avoiding future incidents, including the addition of new sensor systems, used in conjunction with the Space Surveillance Network, for improving space situational awareness.

  14. Polarised photon and flavoured lepton quantum Boltzmann equations in the early universe; Polarisierte Photon- und geflavourte Lepton-Quantenboltzmanngleichungen im fruehen Universum

    Energy Technology Data Exchange (ETDEWEB)

    Fidler, Christian

    2011-12-16

    Polarisation and Nongaussianity are expected to play a central role in future studies of the cosmic microwave background radiation. Polarisation can be split into a divergence-like E-mode and a curl-like B-mode, of which the later can only be induced by primordial gravitational waves (tensor fluctuations of the metric) at leading order. Nongaussianity is not generated at first order and is directly proportional to the primordial Nongaussianity of inflation. Thus B-mode polarisation and Nongaussianity constrain inflation models directly. While E-mode polarisation has already been detected and is being observed with increasing precision, B-mode polarisation and Nongaussianity remains elusive. The absence of B-mode polarisation when the primordial fluctuations are purely scalar holds, however, only in linear perturbation theory. B-mode polarisation is also generated from scalar sources in second order, which may constitute an important background to the search for primordial gravitational waves. While such an effect would naturally be expected to be relevant at tensor-to-scalar ratios of order 10{sup -5}, which is the size of perturbations in the microwave background, only a full second order calculation can tell whether there are no enhancements. For Nongaussianity the situation is analogous: At second order intrinsic Nongaussianities are induced to the spectrum, which may be an important background to the primordial Nongaussianity. After the full second-order Boltzmann equations for the cosmological evolution of the polarised radiation distribution have become available, I focused on the novel sources to B-mode polarisation that appear in the second-order collision term, which have not been calculated before. In my PHD thesis I developed a numerical code, which solves the second order Boltzmann hierarchy and calculates the C{sub l}{sup BB}-spectrum.

  15. Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

    KAUST Repository

    Allen, Rebecca

    2016-06-29

    We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

  16. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    DEFF Research Database (Denmark)

    Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

    2016-01-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

  17. A pedagogical approach to the Boltzmann factor through experiments and simulations

    International Nuclear Information System (INIS)

    Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M

    2009-01-01

    The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

  18. A pedagogical approach to the Boltzmann factor through experiments and simulations

    Energy Technology Data Exchange (ETDEWEB)

    Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M [University of Palermo Physics Education Research Group, Dipartimento di Fisica e Tecnologie Relative, Universita di Palermo (Italy)], E-mail: sperandeo@difter.unipa.it

    2009-09-15

    The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

  19. Element Free Lattice Boltzmann Method for Fluid-Flow Problems

    International Nuclear Information System (INIS)

    Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung; Kwon, Young Kwon

    2007-01-01

    The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented

  20. Element Free Lattice Boltzmann Method for Fluid-Flow Problems

    Energy Technology Data Exchange (ETDEWEB)

    Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)

    2007-10-15

    The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.

  1. Fermi-Pasta-Ulam-Tsingou problems: Passage from Boltzmann to q-statistics

    Science.gov (United States)

    Bagchi, Debarshee; Tsallis, Constantino

    2018-02-01

    The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor P(ε) ∼e-βε describes its equilibrium distribution of one-body energies, and its velocity distribution is Maxwellian, i.e., P(v) ∼e - βv2 /2. We consider here a generalized system where the quartic coupling constant between sites decays as 1 / dijα (α ≥ 0 ;dij = 1 , 2 , …) . Through first-principle molecular dynamics we demonstrate that, for large α (above α ≃ 1), i.e., short-range interactions, Boltzmann statistics (based on the additive entropic functional SB [ P(z) ] = - k ∫ dzP(z) ln P(z)) is verified. However, for small values of α (below α ≃ 1), i.e., long-range interactions, Boltzmann statistics dramatically fails and is replaced by q-statistics (based on the nonadditive entropic functional Sq [ P(z) ] = k(1 - ∫ dz[ P(z) ]q) /(q - 1) , with S1 =SB). Indeed, the one-body energy distribution is q-exponential, P(ε) ∼ eqε-βε ε ≡[ 1 +(qε - 1) βε ε ]-1 /(qε - 1) with qε > 1, and its velocity distribution is given by P(v) ∼ eqv-βvv2 / 2 with qv > 1. Moreover, within small error bars, we verify qε =qv = q, which decreases from an extrapolated value q ≃ 5 / 3 to q = 1 when α increases from zero to α ≃ 1, and remains q = 1 thereafter.

  2. Lattice Boltzmann simulation of flow across a staggered tube bundle array

    Energy Technology Data Exchange (ETDEWEB)

    Tiftikçi, A.; Kocar, C., E-mail: ckocar@hacettepe.edu.tr

    2016-04-15

    Highlights: • Large eddy simulation of the cross-flow in a staggered tube bundle array in 3D was made. • LBM and FVM are used separately as numerical solvers and the results of each method compared with experimental data. • Effect of lattice model is studied for tube bundle flow. • Filter size effects, mesh size effects are studied for VLES turbulence model. - Abstract: The decision on the magnitude of the grid size is a crucial problem in large eddy simulations. Finer mesh requires excessive memory and causes long simulation time. Large eddy simulation model becomes inefficient when the extent of the flow geometry to be simulated with the lattice-Boltzmann method is large. Thus, in this study, it is proposed to investigate the capabilities of three turbulence models, namely, very large eddy simulation, Van Driest and Smagorinsky–Lilly. As a test case, a staggered tube bundle flow experiment is used for the validation and comparison purposes. Sensitivity analyses (including mesh and filter size) have been made. Furthermore, the effect of lattice model is investigated and it is showed that the D3Q27 and D3Q19 models do not differ significantly in lattice-Boltzmann method for this type of flow. The results of turbulence model comparisons for staggered tube bundle flow showed that very large eddy simulation is superior at low resolution. This paper might be considered as a good validation of the lattice-Boltzmann method. In turbulent flow conditions, the code successfully captures the velocity and stress profiles even if the flow is quite complicated.

  3. Lattice Boltzmann method for solving the bioheat equation

    International Nuclear Information System (INIS)

    Zhang Haifeng

    2008-01-01

    In this work, we develop the lattice Boltzmann method (LBM) as a potential solver for the bioheat problems. The accuracy of the present LBM algorithm is validated through comparison with the analytical solution and the finite element simulation. The results show that the LBM can give a precise prediction of the temperature distribution, and it is efficient to deal with the space- and time-dependent heat source, which are often encountered in the treatment planning of tumor hyperthermia. (note)

  4. Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.

    Science.gov (United States)

    Cooke, Ben; Schmidler, Scott C

    2008-10-28

    We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.

  5. Lattice Boltzmann model capable of mesoscopic vorticity computation

    Science.gov (United States)

    Peng, Cheng; Guo, Zhaoli; Wang, Lian-Ping

    2017-11-01

    It is well known that standard lattice Boltzmann (LB) models allow the strain-rate components to be computed mesoscopically (i.e., through the local particle distributions) and as such possess a second-order accuracy in strain rate. This is one of the appealing features of the lattice Boltzmann method (LBM) which is of only second-order accuracy in hydrodynamic velocity itself. However, no known LB model can provide the same quality for vorticity and pressure gradients. In this paper, we design a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice. A detailed Chapman-Enskog analysis is presented to illustrate all the necessary constraints in reproducing the isothermal Navier-Stokes equations. The remaining degrees of freedom are carefully analyzed to derive a model that accommodates mesoscopic computation of all the velocity and pressure gradients from the nonequilibrium moments. This way of vorticity calculation naturally ensures a second-order accuracy, which is also proven through an asymptotic analysis. We thus show, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM. The resulting model is then validated in simulations of a three-dimensional decaying Taylor-Green flow, a lid-driven cavity flow, and a uniform flow passing a fixed sphere. Furthermore, it is shown that the mesoscopic vorticity computation can be realized even with single relaxation parameter.

  6. An evaluation of collision models in the Method of Moments for rarefied gas problems

    Science.gov (United States)

    Emerson, David; Gu, Xiao-Jun

    2014-11-01

    The Method of Moments offers an attractive approach for solving gaseous transport problems that are beyond the limit of validity of the Navier-Stokes-Fourier equations. Recent work has demonstrated the capability of the regularized 13 and 26 moment equations for solving problems when the Knudsen number, Kn (where Kn is the ratio of the mean free path of a gas to a typical length scale of interest), is in the range 0.1 and 1.0-the so-called transition regime. In comparison to numerical solutions of the Boltzmann equation, the Method of Moments has captured both qualitatively, and quantitatively, results of classical test problems in kinetic theory, e.g. velocity slip in Kramers' problem, temperature jump in Knudsen layers, the Knudsen minimum etc. However, most of these results have been obtained for Maxwell molecules, where molecules repel each other according to an inverse fifth-power rule. Recent work has incorporated more traditional collision models such as BGK, S-model, and ES-BGK, the latter being important for thermal problems where the Prandtl number can vary. We are currently investigating the impact of these collision models on fundamental low-speed problems of particular interest to micro-scale flows that will be discussed and evaluated in the presentation. Engineering and Physical Sciences Research Council under Grant EP/I011927/1 and CCP12.

  7. Lattice Boltzmann method to study the contraction of a viscous ligament

    NARCIS (Netherlands)

    Srivastava, S.; Driessen, T.W.; Jeurissen, R.J.M.; Wijshoff, H.M.A.; Toschi, F.

    2013-01-01

    We employ a recently formulated axisymmetric version of the multiphase Shan–Chen (SC) lattice Boltzmann method (LBM) [S. Srivastava et al., Phys. Rev. E88, 013309 (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ)

  8. Atoms and Ions; Universality, Singularity and Particularity:. on Boltzmann's Vision a Century Later

    Science.gov (United States)

    Fisher, Michael

    2008-12-01

    Ludwig Boltzmann died by his own hand 101 years ago last September. He was a passionate believer in atoms: underlying thermodynamics, he felt, lay a statistical world governed by the mechanics of individual particles. His struggles against critics -- "Have you ever seen an atom?" taunted Ernst Mach -- left him pessimistic. Nevertheless, following Maxwell and clarified by Gibbs, he established the science of Statistical Mechanics. But today, especially granted our understanding of critical singularities and their universality, how much do atomic particles and their charged partners, ions, really matter? The answers we have also met opposition. But Boltzmann would have welcomed the insights gained and approved of applications of statistical dynamics to biology, sociology, and other enterprises. Note from Publisher: This article contains the abstract only.

  9. Theoretical study of a weakly ionised gas in a uniform constant electric field

    International Nuclear Information System (INIS)

    Segur, Pierre.

    1974-01-01

    The collision operators of the Boltzmann equation are expressed in terms of the transition probabilities for a Lorentz gas and inelastic type collisions in the case of conservation and non-conservation of the initial number of particles. These operators are approximately expressed when the mass ratio of the present particles is weak. The expressions obtained are valid for any particle distribution functions. A series expansion in spherical harmonics is effected for these operators. The Boltzmann equation is then solved for the case of a steady homogeneous medium when the electric field effect is lower than that of collisions. A resolving method is then proposed for the case where the electric field and collisions play comparable roles. Analytical expressions are given for the distribution functions in terms of asymptotic solutions valid for any type of cross section. A steady heterogenous medium is then studied by a direct numerical solution of the Boltzmann equation, for high values of the electric field/ pressure ratio. The existence of a single lattice of characteristic directions is established as well as a distribution function representing in phase space a band structure characteristic of the presence of inelastic collisions. The electron motion is simulated using a Monte-Carlo method. The calculations being effected in helium, a bibliography of the cross sections for this gas is given [fr

  10. Global Well-Posedness of the Boltzmann Equation with Large Amplitude Initial Data

    Science.gov (United States)

    Duan, Renjun; Huang, Feimin; Wang, Yong; Yang, Tong

    2017-07-01

    The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new {L^∞_xL^1v\\cap L^∞_{x,v}} approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted {L^∞} norm under some smallness condition on the {L^1_xL^∞_v} norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the {L^∞_{x,v}} norm with explicit rates of convergence are also studied.

  11. Effective thermal conductivity estimate of heterogenous media by a lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Arab, M.R.; Pateyron, B.; El Ganaoui, M.; Labbe, J.C. [Limoges Univ., Limoges (France). Science des Procedes Ceramiques et de Traitements de Surface

    2009-07-01

    Statistical lattice Boltzmann methods (LBM) are often used to simulate isothermal fluid flow for problems with complex geometry or porous structures. This study used an LBM algorithm to evaluate the effective thermal conductivity (ETC) of simple 2-D configurations. The LBM algorithm was also used to estimate the ECT of a porous structure. The Bhatnagar-Gross-Krook approximation was used to determine the discrete form of the Boltzmann equation for a single phase flow. A comparison with the finite element method (FEM) was also conducted. Results of the study demonstrated that the LBM algorithm accurately simulates the phenomena of heat and mass transfer for both the simple 2-D configurations as well as the porous media. The tool will be used to determine the influence of thermal contact resistance on heat transfer. 6 refs., 1 tab., 7 figs.

  12. Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

    KAUST Repository

    Atanasov, Atanas

    2016-10-17

    We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.

  13. Time-dependent integral transport equation kernels, leakage rates and collision rates for plane and spherical geometry

    International Nuclear Information System (INIS)

    Henderson, D.L.

    1987-01-01

    Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered

  14. Power Laws are Disguised Boltzmann Laws

    Science.gov (United States)

    Richmond, Peter; Solomon, Sorin

    Using a previously introduced model on generalized Lotka-Volterra dynamics together with some recent results for the solution of generalized Langevin equations, we derive analytically the equilibrium mean field solution for the probability distribution of wealth and show that it has two characteristic regimes. For large values of wealth, it takes the form of a Pareto style power law. For small values of wealth, wGeneralized Lotka-Volterra type of stochastic dynamics. The power law that arises in the distribution function is identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. These are a direct consequence of the multiplicative stochastic dynamics and are absent for the usual additive stochastic processes.

  15. Lattice-Boltzmann Simulation of Tablet Disintegration

    Science.gov (United States)

    Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

    Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.

  16. The binary collision approximation: Background and introduction

    International Nuclear Information System (INIS)

    Robinson, M.T.

    1992-08-01

    The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented

  17. A maximum principle for the first-order Boltzmann equation, incorporating a potential treatment of voids

    International Nuclear Information System (INIS)

    Schofield, S.L.

    1988-01-01

    Ackroyd's generalized least-squares method for solving the first-order Boltzmann equation is adapted to incorporate a potential treatment of voids. The adaptation comprises a direct least-squares minimization allied with a suitably-defined bilinear functional. The resulting formulation gives rise to a maximum principle whose functional does not contain terms of the type that have previously led to difficulties in treating void regions. The maximum principle is derived without requiring continuity of the flux at interfaces. The functional of the maximum principle is concluded to have an Euler-Lagrange equation given directly by the first-order Boltzmann equation. (author)

  18. Identifying product order with restricted Boltzmann machines

    Science.gov (United States)

    Rao, Wen-Jia; Li, Zhenyu; Zhu, Qiong; Luo, Mingxing; Wan, Xin

    2018-03-01

    Unsupervised machine learning via a restricted Boltzmann machine is a useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from nonergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.

  19. Boltzmann equation and hydrodynamics beyond Navier-Stokes.

    Science.gov (United States)

    Bobylev, A V

    2018-04-28

    We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

  20. Photons from the early stages of relativistic heavy-ion collisions

    Science.gov (United States)

    Oliva, L.; Ruggieri, M.; Plumari, S.; Scardina, F.; Peng, G. X.; Greco, V.

    2017-07-01

    We present results about photon-production in relativistic heavy-ion collisions. The main novelty of our study is the calculation of the contribution of the early-stage photons to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photon production is then computed by including the pertinent collision processes into the collision integral. We find that the contribution of the early-stage photons to the direct photon spectrum is substantial for pT≈2 GeV and higher, the exact value depending on the collision energy; therefore, we identify this part of the photon spectrum as the sign of the early stage. Moreover, the amount of photons produced during the early stage is not negligible with respect to those produced by a thermalized quark-gluon plasma: We support the idea that there is no dark age in relativistic heavy-ion collisions.

  1. Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

    KAUST Repository

    Atanasov, Atanas; Uekermann, Benjamin; Pachajoa Mejí a, Carlos; Bungartz, Hans-Joachim; Neumann, Philipp

    2016-01-01

    to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier

  2. Impact of early stage non-equilibrium dynamics on photon production in relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Oliva, L; Plumari, S; Scardina, F; Greco, V; Ruggieri, M

    2017-01-01

    In this study we discuss our results on the spectrum of photons emitted from the quark-gluon plasma produced in heavy ion collisions at RHIC energies. Simulating the space-time evolution of the fireball by solving the relativistic Boltzmann transport equation and including two-particle scattering processes with photon emission allows us to make a first step in the description of thermal photons from the QGP as well as of those produced in the pre-equilibrium stage. Indeed, we consider not only a standard Glauber initial condition but also a model in which quarks and gluons are produced in the very early stage through the Schwinger mechanism by the decay of an initial color-electric field. In the latter approach relativistic kinetic equations are coupled in a self-consistent way to field equations. We aim at spotting the impact of early stage non-equilibrium dynamics on the photon production. (paper)

  3. A multi scale approximation solution for the time dependent Boltzmann-transport equation

    International Nuclear Information System (INIS)

    Merk, B.

    2004-03-01

    The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

  4. Using x-ray tomography and lattice Boltzmann modeling to evaluate pore-scale processes in porous media

    DEFF Research Database (Denmark)

    Christensen, Britt Stenhøj Baun

    -teknik (Computed Tomography) til at visualisere og kvantificere de eksperimentelle poreskala systemer. Både en medicinsk CT-scanner og et synkrotron baseret skanningssystem med høj billede opløselighed blev anvendt. Numerisk modellering af poreskala processerne blev gjort ved hjælp af en lattice Boltzmann model...... for testning af en Shan-Chen lattice Boltzmann model. Ved anvendelse af simple veldefinerede to-fase systemer blev en kalibreringsprocedure skitseret til identificering af de dimensionsløse modelparametre og deres kobling til overfladespænding og kontaktvinkel egenskaberne af det fysiske system. Det blev taget...

  5. A modified Poisson-Boltzmann equation applied to protein adsorption.

    Science.gov (United States)

    Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

    2018-01-05

    Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

  6. Applying recursive numerical integration techniques for solving high dimensional integrals

    International Nuclear Information System (INIS)

    Ammon, Andreas; Genz, Alan; Hartung, Tobias; Jansen, Karl; Volmer, Julia; Leoevey, Hernan

    2016-11-01

    The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.

  7. Applying recursive numerical integration techniques for solving high dimensional integrals

    Energy Technology Data Exchange (ETDEWEB)

    Ammon, Andreas [IVU Traffic Technologies AG, Berlin (Germany); Genz, Alan [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, Tobias [King' s College, London (United Kingdom). Dept. of Mathematics; Jansen, Karl; Volmer, Julia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, Hernan [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik

    2016-11-15

    The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.

  8. Interface-Resolving Simulation of Collision Efficiency of Cloud Droplets

    Science.gov (United States)

    Wang, Lian-Ping; Peng, Cheng; Rosa, Bodgan; Onishi, Ryo

    2017-11-01

    Small-scale air turbulence could enhance the geometric collision rate of cloud droplets while large-scale air turbulence could augment the diffusional growth of cloud droplets. Air turbulence could also enhance the collision efficiency of cloud droplets. Accurate simulation of collision efficiency, however, requires capture of the multi-scale droplet-turbulence and droplet-droplet interactions, which has only been partially achieved in the recent past using the hybrid direct numerical simulation (HDNS) approach. % where Stokes disturbance flow is assumed. The HDNS approach has two major drawbacks: (1) the short-range droplet-droplet interaction is not treated rigorously; (2) the finite-Reynolds number correction to the collision efficiency is not included. In this talk, using two independent numerical methods, we will develop an interface-resolved simulation approach in which the disturbance flows are directly resolved numerically, combined with a rigorous lubrication correction model for near-field droplet-droplet interaction. This multi-scale approach is first used to study the effect of finite flow Reynolds numbers on the droplet collision efficiency in still air. Our simulation results show a significant finite-Re effect on collision efficiency when the droplets are of similar sizes. Preliminary results on integrating this approach in a turbulent flow laden with droplets will also be presented. This work is partially supported by the National Science Foundation.

  9. Volumetric formulation of lattice Boltzmann models with energy conservation

    OpenAIRE

    Sbragaglia, M.; Sugiyama, K.

    2010-01-01

    We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. ...

  10. Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme

    Energy Technology Data Exchange (ETDEWEB)

    Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

    1998-03-01

    A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)

  11. Many-body problem in quantum mechanics and quantum statistical mechanics

    International Nuclear Information System (INIS)

    Lee, T.D.; Yang, C.N.

    1983-01-01

    This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/

  12. Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method

    International Nuclear Information System (INIS)

    He, Y B; Tang, X H

    2016-01-01

    In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

  13. Derivation of the Second Law of Thermodynamics from Boltzmann's Distribution Law.

    Science.gov (United States)

    Nelson, P. G.

    1988-01-01

    Shows how the thermodynamic condition for equilibrium in an isolated system can be derived by the application of Boltzmann's law to a simple physical system. States that this derivation could be included in an introductory course on chemical equilibrium to help prepare students for a statistical mechanical treatment presented in the curriculum.…

  14. Does the Boltzmann Principle Need a Dynamical Correction?

    Science.gov (United States)

    Adib, Artur B.

    2004-11-01

    In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln Ω( E) via the thermodynamic relation 1/ T=∂ S / ∂ E by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Ω( E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k ln Ф( E) via the thermodynamic relation above for systems of any number of degrees of freedom ( Ф( E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain ( N~10) of quartic oscillators are also provided to further illustrate these facts.

  15. Moving charged particles in lattice Boltzmann-based electrokinetics

    Science.gov (United States)

    Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-12-01

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms.

  16. Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

    Directory of Open Access Journals (Sweden)

    L.B.Bhuiyan

    2005-01-01

    Full Text Available The density functional and modified Poisson-Boltzmann descriptions of a spherical (electric double layer are compared and contrasted vis-a-vis existing Monte Carlo simulation data (for small ion diameter 4.25·10-10 m from the literature for a range of physical parameters such as macroion surface charge, macroion radius, valencies of the small ions, and electrolyte concentration. Overall, the theoretical predictions are seen to be remarkably consistent between themselves, being also in very good agreement with the simulations. Some modified Poisson-Boltzmann results for the zeta potential at small ion diameters of 3 and 2·10-10 m are also reported.

  17. Lattice Boltzmann simulation of flow around a confined circular cyclinder

    International Nuclear Information System (INIS)

    Ashrafizaadeh, M.; Zadehgol, A.

    2002-01-01

    A two dimensional lattice Boltzmann model (LBM) based on a single time relaxation BGK model has been developed. Several benchmark problems including the Poiseuille flow, the lid driven cavity flow and the flow around a circular cylinder have been performed employing a d2q9 lattice. The laminar flow around a circular cylinder within a channel has been extensively investigated using the present lattice Boltzmann model. Both symmetric and asymmetric placement configurations of the circular cylinder within the channel have been considered. A new treatment for the outlet velocity and pressure (density) boundary conditions has been proposed and validated. The present LBM results are in excellent agreement with those of the other existing CFD results. Careful examination of the LBM results and an appropriate calculation of the lift coefficient based on the rectangular lattice representation of the circular cylinder reveals that the periodic oscillation of the lift coefficient has a second harmonic when the cylinder is placed asymmetrically within the channel. The second harmonic could be associated with an asymmetrical shedding pattern of the vortices behind the cylinder from the upper and lower sides of the cylinder. (author)

  18. Photons in a partonic transport approach

    Energy Technology Data Exchange (ETDEWEB)

    Greif, Moritz; Senzel, Florian; Greiner, Carsten [Goethe Universitaet Frankfurt, Max-von-Laue-Str. 1 60438 Frankfurt am Main (Germany)

    2015-07-01

    Partonic transport approaches have proved to be valuable tools in describing the quark-gluon plasma, created in heavy-ion collisions. In this work, first steps towards a dynamical understanding of photonproduction in expanding heavy-ion collisions are presented. Several photon production processes are included in the partonic cascade BAMPS (Boltzmann Approach to Multi-Parton Scatterings). BAMPS provides a microscopic tool to study expanding fireballs, employing a stochastic method to solve the relativistic 3+1d Boltzmann equation. Subsequently, photon spectra can be investigated, and in particular, the influence of the quark-gluon plasma phase for the elliptic flow of photons is studied.

  19. J/ψ production in proton-lead collisions with the central barrel of ALICE at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Winn, Michael [Physikalisches Institut, Universitaet Heidelberg (Germany); Collaboration: ALICE-Collaboration

    2014-07-01

    The description of J/ψ production in proton-proton and its nuclear modification in proton-nucleus collisions remains challenging for theory based on perturbative QCD and factorization. Furthermore, the investigation of J/ψ in pp and p-A collisions represents an important reference for heavy-ion collisions, where charmonium production is seen as a key observable for deconfinement. First results of the nuclear modification factor of inclusive J/ψ in proton-lead collisions with the central barrel of ALICE, both integral as well as differential in transverse momentum, are presented. Model comparisons are discussed.

  20. Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

    KAUST Repository

    Allen, Rebecca; Reis, Tim

    2016-01-01

    moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow

  1. Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients

    International Nuclear Information System (INIS)

    Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric M.; Ji, Wei

    2015-01-01

    Electromagnetic pulse (EMP) events produce low-energy conduction electrons from Compton electron or photoelectron ionizations with air. It is important to understand how conduction electrons interact with air in order to accurately predict EMP evolution and propagation. An electron swarm model can be used to monitor the time evolution of conduction electrons in an environment characterized by electric field and pressure. Here a swarm model is developed that is based on the coupled ordinary differential equations (ODEs) described by Higgins et al. (1973), hereinafter HLO. The ODEs characterize the swarm electric field, electron temperature, electron number density, and drift velocity. Important swarm parameters, the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are calculated and compared to the previously reported fitted functions given in HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford (2005), which utilizes updated cross sections from the LXcat website created by Pancheshnyi et al. (2012). We validate the swarm model by comparing to experimental effective ionization coefficient data in Dutton (1975) and drift velocity data in Ruiz-Vargas et al. (2010). In addition, we report on electron equilibrium temperatures and times for a uniform electric field of 1 StatV/cm for atmospheric heights from 0 to 40 km. We show that the equilibrium temperature and time are sensitive to the modifications in the collision frequencies and ionization rate based on the updated electron interaction cross sections

  2. A note on the Lattice Boltzmann Method Beyond the Chapman Enskog Limits

    NARCIS (Netherlands)

    Sbragaglia, M.; Succi, S.

    2006-01-01

    A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also

  3. Jet Quenching in Relativistic Heavy Ion Collisions at the LHC

    CERN Document Server

    Angerami, Aaron

    Jet production in relativistic heavy ion collisions is studied using Pb+Pb collisions at a center of mass energy of 2.76 TeV per nucleon. The measurements reported here utilize data collected with the ATLAS detector at the LHC from the 2010 Pb ion run corresponding to a total integrated luminosity of 7 μb−1. The results are obtained using fully reconstructed jets using the anti-kt algorithm with a per-event background subtraction procedure. A centrality-dependent modification of the dijet asymmetry distribution is observed, which indicates a higher rate of asymmetric dijet pairs in central collisions relative to peripheral and pp collisions. Simultaneously the dijet angular correlations show almost no centrality dependence. These results provide the first direct observation of jet quenching. Measurements of the single inclusive jet spectrum, measured with jet radius parameters R = 0.2,0.3,0.4 and 0.5, are also presented. The spectra are unfolded to correct for the finite energy resolution introduced by bot...

  4. Poisson-Boltzmann-Nernst-Planck model

    International Nuclear Information System (INIS)

    Zheng Qiong; Wei Guowei

    2011-01-01

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  5. Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality

    Science.gov (United States)

    Ayala, Mario; Carinci, Gioia; Redig, Frank

    2018-06-01

    We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.

  6. Geocoding police collision report data from California: a comprehensive approach

    Directory of Open Access Journals (Sweden)

    Park Shin

    2009-12-01

    Full Text Available Abstract Background Collision geocoding is the process of assigning geographic descriptors, usually latitude and longitude coordinates, to a traffic collision record. On California police reports, relative collision location is recorded using a highway postmile marker or a street intersection. The objective of this study was to create a geocoded database of all police-reported, fatal and severe injury collisions in the California Statewide Integrated Traffic Records System (SWITRS for years 1997-2006 for use by public agencies. Results Geocoding was completed with a multi-step process. First, pre-processing was performed using a scripting language to clean and standardize street name information. A state highway network with postmile values was then created using a custom tool written in Visual Basic for Applications (VBA in ArcGIS software. Custom VBA functionality was also used to incorporate the offset direction and distance. Intersection and address geocoding was performed using ArcGIS, StreetMap Pro 2003 digital street network, and Google Earth Pro. A total of 142,007 fatal and severe injury collisions were identified in SWITRS. The geocoding match rate was 99.8% for postmile-coded collisions and 86% for intersection-coded collisions. The overall match rate was 91%. Conclusions The availability of geocoded collision data will be beneficial to clinicians, researchers, policymakers, and practitioners in the fields of traffic safety and public health. Potential uses of the data include studies of collision clustering on the highway system, examinations of the associations between collision occurrence and a variety of variables on environmental and social characteristics, including housing and personal demographics, alcohol outlets, schools, and parks. The ability to build maps may be useful in research planning and conduct and in the delivery of information to both technical and non-technical audiences.

  7. Fuselage mounted anti-collision lights utilizing high power LEDs

    Science.gov (United States)

    Lundberg, John; Machi, Nicolo; Mangum, Scott; Singer, Jeffrey

    2005-09-01

    As LEDs continue to improve in efficacy and total light output, they are increasingly finding their way in to new applications in the aviation industry as well as adjacent markets. One function that is particularly challenging and may reap substantial benefits from this new technology is the fuselage mounted anti-collision light. Anti-collision lights provide conspicuity for the aircraft by periodically emitting bright flashes of light. The color, light distribution and intensity levels for these lights are all closely regulated through Federal Aviation Regulation (FAR) documents. These lighting requirements, along with thermal, environmental and aerodynamic requirements, drive the overall design. In this paper, we will discuss the existing technologies used in anti-collision lights and the advantages and challenges associated with an LED solution. Particular attention will be given to the optical, thermal, electrical and aerodynamic aspects associated with an LED approach. A specific case study will be presented along with some of the challenges that have arisen during the design process. These challenges include the addition of an integrated covert anti-collision lighting.

  8. Electron-molecule collisions

    International Nuclear Information System (INIS)

    Shimamura, I.; Takayanagi, K.

    1984-01-01

    The study of collision processes plays an important research role in modern physics. Many significant discoveries have been made by means of collision experiments. Based on theoretical, experimental, and computational studies, this volume presents an overview detailing the basic processes of electron-molecule collisions. The editors have collected papers-written by a group of international experts-that consider a diverse range of phenomena occurring in electronmolecule collisions. The volume discusses first the basic formulation for scattering problems and then gives an outline of the physics of electron-molecule collisions. The main topics covered are rotational transitions, vibrational transitions, dissociation of molecules in slow collisions, the electron-molecule collision as a spectroscopic tool for studying molecular electronic structures, and experimental and computational techniques for determining the cross sections. These well-referenced chapters are self-contained and can be read independently or consecutively. Authoritative and up-to-date, Electron-Molecule Collisions is a useful addition to the libraries of students and researchers in the fields of atomic, molecular, and chemical physics, and physical chemistry

  9. Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

    Energy Technology Data Exchange (ETDEWEB)

    Uddin, Rizwan

    2012-01-01

    This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.

  10. Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

    OpenAIRE

    Wu, Lei

    2014-01-01

    We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

  11. An optimized D2Q37 Lattice Boltzmann code on GP-GPUs

    NARCIS (Netherlands)

    Biferale, L.; Mantovani, F.; Pivanti, M.; Pozzati, F.; Sbragaglia, M.; Scagliarini, Andrea; Schifano, S.F.; Toschi, F.

    2013-01-01

    We describe the implementation of a thermal compressible Lattice Boltzmann algorithm on an NVIDIA Tesla C2050 system based on the Fermi GP-GPU. We consider two different versions, including and not including reactive effects. We describe the overall organization of the algorithm and give details on

  12. A particle method with adjustable transport properties - the generalized consistent Boltzmann algorithm

    International Nuclear Information System (INIS)

    Garcia, A.L.; Alexander, F.J.; Alder, B.J.

    1997-01-01

    The consistent Boltzmann algorithm (CBA) for dense, hard-sphere gases is generalized to obtain the van der Waals equation of state and the corresponding exact viscosity at all densities except at the highest temperatures. A general scheme for adjusting any transport coefficients to higher values is presented

  13. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    NARCIS (Netherlands)

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

  14. Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

    DEFF Research Database (Denmark)

    Wacker, Andreas; Jauho, Antti-Pekka; Rott, Stephan

    1999-01-01

    the whole held range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport...

  15. U.S. stock market interaction network as learned by the Boltzmann machine

    Science.gov (United States)

    Borysov, Stanislav S.; Roudi, Yasser; Balatsky, Alexander V.

    2015-12-01

    We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model's parameters might be used as a precursor of financial instabilities.

  16. Albedo of low-energy light ions: case of anisotropic approximation of the collision integral

    International Nuclear Information System (INIS)

    Simovic, R.; Vukanic, J. . E-mail address of corresponding author: simovicr@vin.bg.ac.yu; Simovic, R.)

    2005-01-01

    For diffusion and slowing-down of low-energy light ions, the linear transport equation in the path length form was rederived taking into account a common anisotropic approximation of the collision integral. Assuming that the transport cross section depends only on the ion initial energy, the equation was Laplace-transformed over the relative path length and half-space albedo problem was considered by using the ordinary DPN technique. The Laplace-transformed reflection function was found in the lowest order of DPN flux approximation, and then was inverted analytically leading to the distribution of backscattered particles in the relative path-length. For the general power potential V(R)∞R -1/m the particle reflection coefficient was obtained as a series, while for the special case of the inverse square potential (m=1/2) this coefficient was determined in a compact form. The present approach was compared with the TRIM simulations of helium ion reflection, as well as with the Tilinin - Betz fitting formula and the MARLOWE simulations of proton reflection. (author)

  17. Quenching vibrations by collisions in cold traps: A quantum study for ...

    Indian Academy of Sciences (India)

    Scattering theory; ion-molecule collisions vibrational quenching. 1. ... Hence, considerable attention has now turned to .... computed spatial features of the interaction potential for .... radial integration of the coupled equation was extended.

  18. What can nuclear collisions teach us about the boiling of water or the formation of multi-star systems

    Science.gov (United States)

    Gross, D. H. E.

    2001-11-01

    Phase transitions in nuclei, small atomic clusters and self-gravitating systems demand the extension of thermo-statistics to "Small" systems. The main obstacle is the thermodynamic limit. It is shown how the original definition of the entropy by Boltzmann as the volume of the energy-manifold of the N-body phase space allows a geometrical definition of the entropy as function of the conserved quantities. Without invoking the thermodynamic limit the whole "zoo" of phase transitions and critical points/lines can be unambiguously defined. The relation to the Yang-Lee singularities of the grand-canonical partition sum is pointed out. It is shown that just phase transitions in non-extensive systems give the complete set of characteristic parameters of the transition including the surface tension. Nuclear heavy-ion collisions are an experimental playground to explore this extension of thermo-statistics

  19. A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

    KAUST Repository

    Allen, Rebecca; Reis, Tim; Sun, Shuyu

    2013-01-01

    -driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE

  20. Lattice Boltzmann method used to simulate particle motion in a conduit

    Czech Academy of Sciences Publication Activity Database

    Dolanský, Jindřich; Chára, Zdeněk; Vlasák, Pavel; Kysela, Bohuš

    2017-01-01

    Roč. 65, č. 2 (2017), s. 105-113 ISSN 0042-790X R&D Projects: GA ČR GA15-18870S Institutional support: RVO:67985874 Keywords : Lattice Boltzmann method * particle motion * particle–fluid interaction * PIV * particle tracking Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.654, year: 2016