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
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.
Collision group and renormalization of the Boltzmann collision integral
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.
A fast iterative scheme for the linearized Boltzmann equation
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
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
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
Lattice Boltzmann methods for global linear instability analysis
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.
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.
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
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
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.)
From Newton's Law to the Linear Boltzmann Equation Without Cut-Off
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.
Gyrokinetic linearized Landau collision operator
DEFF Research Database (Denmark)
Madsen, Jens
2013-01-01
, which is important in multiple ion-species plasmas. Second, the equilibrium operator describes drag and diffusion of the magnetic field aligned component of the vorticity associated with the E×B drift. Therefore, a correct description of collisional effects in turbulent plasmas requires the equilibrium......The full gyrokinetic electrostatic linearized Landau collision operator is calculated including the equilibrium operator, which represents the effect of collisions between gyrokinetic Maxwellian particles. First, the equilibrium operator describes energy exchange between different plasma species...... operator, even for like-particle collisions....
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
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
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
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
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
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
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.
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
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
Linear colliders for photon collisions
International Nuclear Information System (INIS)
Anon.
1994-01-01
The enthusiasm of the first international workshop on photonphoton colliders and associated physics, held at the Lawrence Berkeley Laboratory from 28 March - 1 April, could have set a ball rolling. According to proponents of this physics, the particle physics one can study with a high energy linear collider is special and complements that of a hadron supercollider
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)
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
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
PB-AM: An open-source, fully analytical linear poisson-boltzmann solver.
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.
Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.
Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray
2017-07-11
Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.
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.
A linear algebraic approach to electron-molecule collisions
International Nuclear Information System (INIS)
Collins, L.A.; Schnieder, B.I.
1982-01-01
The linear algebraic approach to electron-molecule collisions is examined by firstly deriving the general set of coupled integrodifferential equations that describe electron collisional processes and then describing the linear algebraic approach for obtaining a solution to the coupled equations. Application of the linear algebraic method to static-exchange, separable exchange and effective optical potential, is examined. (U.K.)
Linear algebraic approach to electron-molecule collisions
International Nuclear Information System (INIS)
Schneider, B.I.; Collins, L.A.
1983-01-01
The various levels of sophistication of the linear algebraic method are discussed and its application to electron-molecule collisions of H 2 , N 2 LiH, LiF and HCl is described. 13 references, 2 tables
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation
Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien
2018-04-01
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation
Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien
2018-06-01
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Ladiges, Daniel R.; Sader, John E.
2018-05-01
Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.
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.)
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.
Effects of collisions on linear and non-linear spectroscopic line shapes
International Nuclear Information System (INIS)
Berman, P.R.
1978-01-01
A fundamental physical problem is the determination of atom-atom, atom-molecule and molecule-molecule differential and total scattering cross sections. In this work, a technique for studying atomic and molecular collisions using spectroscopic line shape analysis is discussed. Collisions occurring within an atomic or molecular sample influence the sample's absorptive or emissive properties. Consequently the line shapes associated with the linear or non-linear absorption of external fields by an atomic system reflect the collisional processes occurring in the gas. Explicit line shape expressions are derived characterizing linear or saturated absorption by two-or three-level 'active' atoms which are undergoing collisions with perturber atoms. The line shapes may be broadened, shifted, narrowed, or distorted as a result of collisions which may be 'phase-interrupting' or 'velocity-changing' in nature. Systematic line shape studies can be used to obtain information on both the differential and total active atom-perturber scattering cross sections. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Lloyd, S. A. M.; Ansbacher, W. [Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada); Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada) and Department of Medical Physics, British Columbia Cancer Agency-Vancouver Island Centre, Victoria, British Columbia V8R 6V5 (Canada)
2013-01-15
Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements
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
Linear momentum, angular momentum and energy in the linear collision between two balls
Hanisch, C.; Hofmann, F.; Ziese, M.
2018-01-01
In an experiment of the basic physics laboratory, kinematical motion processes were analysed. The motion was recorded with a standard video camera having frame rates from 30 to 240 fps the videos were processed using video analysis software. Video detection was used to analyse the symmetric one-dimensional collision between two balls. Conservation of linear and angular momentum lead to a crossover from rolling to sliding directly after the collision. By variation of the rolling radius the system could be tuned from a regime in which the balls move away from each other after the collision to a situation in which they re-collide.
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.)
A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation
Directory of Open Access Journals (Sweden)
José Colmenares
2014-01-01
Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.
Transverse equilibria in linear collider beam-beam collisions
International Nuclear Information System (INIS)
Rosenzweig, J.B.; Chen, Pisin
1991-01-01
It has been observed in simulations of the beam-beam interaction in linear colliders that a near equilibrium pinched state of the colliding beams develops when the disruption parameter is large (D much-gt 1). In this state the beam transverse density distributions are peaked at center, with long tails. The authors present here an analytical model of the equilibrium approached by the beams, that of a generalized Bennett pinch which develops through collisionless damping due to the strong nonlinearity of the beam-beam interaction. In order to calculate the equilibrium pinched beam size, an estimation of the rms emittance growth is made which takes into account the partial adiabaticity of the collision. This pinched beam size is used to derive the luminosity enhancement factors whose scaling is in agreement with the simulation results for both D and thermal factor A = σ z /β * large, and explains the previously noted cubic relationship between round and flat beam enhancement factors
Molavi Tabrizi, Amirhossein; Goossens, Spencer; Mehdizadeh Rahimi, Ali; Cooper, Christopher D; Knepley, Matthew G; Bardhan, Jaydeep P
2017-06-13
We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.
Energy Technology Data Exchange (ETDEWEB)
Randrup, J.
1979-07-01
This lecture discusses a theory for the transport of mass, charge, linear, and angular momentum and energy in damped nuclear collisions, as induced by multiple transfer of individual nucleons. 11 references.
Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro
2015-04-05
The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.
Stabilizing the thermal lattice Boltzmann method by spatial filtering.
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.
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.
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.
DeLuca, R.
2006-03-01
Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.
An Eulerian description of the streaming process in the lattice Boltzmann equation
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...
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.)
Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce
2009-01-01
We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry
How (non-)linear is the hydrodynamics of heavy ion collisions?
Energy Technology Data Exchange (ETDEWEB)
Floerchinger, Stefan; Wiedemann, Urs Achim [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Beraudo, Andrea [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Dep. de Fisica de Particulas, U. de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain); Del Zanna, Luca [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze (Italy); Inghirami, Gabriele [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); Rolando, Valentina [INFN - Sezione di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy); Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy)
2014-07-30
We provide evidence from full numerical solutions that the hydrodynamical evolution of initial density fluctuations in heavy ion collisions can be understood order-by-order in a perturbative series in deviations from a smooth and azimuthally symmetric background solution. To leading linear order, modes with different azimuthal wave numbers do not mix. When quadratic and higher order corrections are numerically sizable, they can be understood as overtones with corresponding wave numbers in a perturbative series. Several findings reported in the recent literature result naturally from the general perturbative series formulated here.
Linear-algebraic approach to electron-molecule collisions: General formulation
International Nuclear Information System (INIS)
Collins, L.A.; Schneider, B.I.
1981-01-01
We present a linear-algebraic approach to electron-molecule collisions based on an integral equations form with either logarithmic or asymptotic boundary conditions. The introduction of exchange effects does not alter the basic form or order of the linear-algebraic equations for a local potential. In addition to the standard procedure of directly evaluating the exchange integrals by numerical quadrature, we also incorporate exchange effects through a separable-potential approximation. Efficient schemes are developed for reducing the number of points and channels that must be included. The method is applied at the static-exchange level to a number of molecular systems including H 2 , N 2 , LiH, and CO 2
Energy Technology Data Exchange (ETDEWEB)
Yang, R [University of Alberta, Edmonton, AB (Canada); Fallone, B [University of Alberta, Edmonton, AB (Canada); Cross Cancer Institute, Edmonton, AB (Canada); MagnetTx Oncology Solutions, Edmonton, AB (Canada); St Aubin, J [University of Alberta, Edmonton, AB (Canada); Cross Cancer Institute, Edmonton, AB (Canada)
2016-06-15
Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been
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
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...
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
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
Retrieval of collision kernels from the change of droplet size distributions with linear inversion
Energy Technology Data Exchange (ETDEWEB)
Onishi, Ryo; Takahashi, Keiko [Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama Kanagawa 236-0001 (Japan); Matsuda, Keigo; Kurose, Ryoichi; Komori, Satoru [Department of Mechanical Engineering and Science, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: onishi.ryo@jamstec.go.jp, E-mail: matsuda.keigo@t03.mbox.media.kyoto-u.ac.jp, E-mail: takahasi@jamstec.go.jp, E-mail: kurose@mech.kyoto-u.ac.jp, E-mail: komori@mech.kyoto-u.ac.jp
2008-12-15
We have developed a new simple inversion scheme for retrieving collision kernels from the change of droplet size distribution due to collision growth. Three-dimensional direct numerical simulations (DNS) of steady isotropic turbulence with colliding droplets are carried out in order to investigate the validity of the developed inversion scheme. In the DNS, air turbulence is calculated using a quasi-spectral method; droplet motions are tracked in a Lagrangian manner. The initial droplet size distribution is set to be equivalent to that obtained in a wind tunnel experiment. Collision kernels retrieved by the developed inversion scheme are compared to those obtained by the DNS. The comparison shows that the collision kernels can be retrieved within 15% error. This verifies the feasibility of retrieving collision kernels using the present inversion scheme.
Analysis of spectral methods for the homogeneous Boltzmann equation
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.
Analysis of spectral methods for the homogeneous Boltzmann equation
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.
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
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
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
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.
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
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.
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.
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
International Nuclear Information System (INIS)
Larriba-Andaluz, Carlos; Hogan, Christopher J.
2014-01-01
Structural characterization of ions in the gas phase is facilitated by measurement of ion collision cross sections (CCS) using techniques such as ion mobility spectrometry. Further information is gained from CCS measurement when comparison is made between measurements and accurately predicted CCSs for model ion structures and the gas in which measurements are made. While diatomic gases, namely molecular nitrogen and air, are being used in CCS measurement with increasingly prevalency, the majority of studies in which measurements are compared to predictions use models in which gas molecules are spherical or non-rotating, which is not necessarily appropriate for diatomic gases. Here, we adapt a momentum transfer based CCS calculation approach to consider rotating, diatomic gas molecule collisions with polyatomic ions, and compare CCS predictions with a diatomic gas molecule to those made with a spherical gas molecular for model spherical ions, tetra-alkylammonium ions, and multiply charged polyethylene glycol ions. CCS calculations are performed using both specular-elastic and diffuse-inelastic collisions rules, which mimic negligible internal energy exchange and complete thermal accommodation, respectively, between gas molecule and ion. The influence of the long range ion-induced dipole potential on calculations is also examined with both gas molecule models. In large part we find that CCSs calculated with specular-elastic collision rules decrease, while they increase with diffuse-inelastic collision rules when using diatomic gas molecules. Results clearly show the structural model of both the ion and gas molecule, the potential energy field between ion and gas molecule, and finally the modeled degree of kinetic energy exchange between ion and gas molecule internal energy are coupled to one another in CCS calculations, and must be considered carefully to obtain results which agree with measurements
Toward Precision Top Quark Measurements in $e^+e^−$ Collisions at Linear Colliders
Van Der Kolk, Naomi
2017-01-01
Linear lepton colliders offer an excellent environment for precision measurements of the top quark. An overview is given of the current prospects on the measurement of the top quark mass, rare top quark decays and top quark couplings at the International Linear Collider (ILC) and the Compact Linear Collider (CLIC).
Celebrating Cercignani's conjecture for the Boltzmann equation
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.
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)
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.)
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.
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian
2015-01-01
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
MRT Lattice Boltzmann schemes for confined suspension flows
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
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
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 ...
Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
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.
Energy Technology Data Exchange (ETDEWEB)
Hager, Robert, E-mail: rhager@pppl.gov; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States)
2016-04-15
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Towards TeV-scale electron-positron collisions: the Compact Linear Collider (CLIC)
Doebert, Steffen; Sicking, Eva
2018-02-01
The Compact Linear Collider (CLIC), a future electron-positron collider at the energy frontier, has the potential to change our understanding of the universe. Proposed to follow the Large Hardron Collider (LHC) programme at CERN, it is conceived for precision measurements as well as for searches for new phenomena.
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)
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
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
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
Towards a physical interpretation of the entropic lattice Boltzmann method
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.
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.
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)
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.
Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.
2015-11-01
We describe the implementation, and application of a time-dependent, fully nonlinear multi-species Fokker-Planck-Landau collision operator based on the single-species work of Yoon and Chang [Phys. Plasmas 21, 032503 (2014)] in the full-function gyrokinetic particle-in-cell codes XGC1 [Ku et al., Nucl. Fusion 49, 115021 (2009)] and XGCa. XGC simulations include the pedestal and scrape-off layer, where significant deviations of the particle distribution function from a Maxwellian can occur. Thus, in order to describe collisional effects on neoclassical and turbulence physics accurately, the use of a non-linear collision operator is a necessity. Our collision operator is based on a finite volume method using the velocity-space distribution functions sampled from the marker particles. Since the same fine configuration space mesh is used for collisions and the Poisson solver, the workload due to collisions can be comparable to or larger than the workload due to particle motion. We demonstrate that computing time spent on collisions can be kept affordable by applying advanced parallelization strategies while conserving mass, momentum, and energy to reasonable accuracy. We also show results of production scale XGCa simulations in the H-mode pedestal and compare to conventional theory. Work supported by US DOE OFES and OASCR.
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)
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
Directory of Open Access Journals (Sweden)
Sri Widiyantoro
2003-05-01
Full Text Available Results of seismic studies presented in previous publications depict two opposing subducted oceanic lithospheric slabs under the Molucca region. This unique structure is related to the arc-arc collision between the Halmahera and Sangihe arcs. Recently, we have revisited the complex subduction zone structure by employing a non-linear tomographic imaging technique in which 3-D ray tracing has been implemented. We have used P- as well as S-wave arrival times from carefully reprocessed global data set. The results provide some improvements in the positioning of wave-speed anomalies. Consistent with earlier results, the new P-wave model depicts the two opposing subducted slabs of the Molucca Sea plate. The intriguing new observation is that the westward dipping slab appears to penetrate into the lower mantle by taking the form of folded slab. We envisage that the folding behavior may have been caused by the shift of the whole subduction system in the Molucca region toward the Eurasian continent due to the westward thrust of the Pacific plate combined with the large left-lateral movement of the Sorong fault. The inversion of travel-time residuals of direct S phases strongly confirms the new observation.
Lattice Boltzmann model for free-surface flow and its application to filling process in casting
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 ...
Linear and non-linear flow mode in Pb-Pb collisions at root sNN=2.76 TeV
Czech Academy of Sciences Publication Activity Database
Acharya, S.; Adamová, Dagmar; Bielčík, J.; Bielčíková, Jana; Brož, M.; Contreras, J. G.; Ferencei, Jozef; Hladký, Jan; Horák, D.; Křížek, Filip; Kučera, Vít; Kushpil, Svetlana; Lavička, R.; Mareš, Jiří A.; Petráček, V.; Šumbera, Michal; Vaňát, Tomáš; Závada, Petr
2017-01-01
Roč. 773, č. 10 (2017), s. 68-80 ISSN 0370-2693 R&D Projects: GA MŠk(CZ) LG15052 Institutional support: RVO:68378271 ; RVO:61389005 Keywords : ALICE collaboration * heavy ion collisions * relativistic nuclear collisions Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders; BF - Elementary Particles and High Energy Physics (FZU-D) OBOR OECD: Nuclear physics; Particles and field physics (FZU-D) Impact factor: 4.807, year: 2016
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
International Nuclear Information System (INIS)
Galin, J.; Ingold, G.; Jahnke, U.; Hilscher, D.; Lehmann, M.; Rossner, H.; Schwinn, E.
1988-01-01
The 20 Ne+U reactions are investigated at 290 MeV bombarding energy. The linear momentum transfer and excitation energy are deduced eventwise from the respective measurements of the folding angle between correlated fission fragments and the neutron multiplicity. A simple incomplete fusion picture is shown to essentially account for the data. The sensitivity of the two measurements in order to infer the violence of a collision is discussed in details. (orig.)
Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem
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).
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)
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)
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....
Celebrating Cercignani's conjecture for the Boltzmann equation
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.
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
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
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...
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.
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.)
Energy Technology Data Exchange (ETDEWEB)
Weber, Guenter
2010-06-16
In the present thesis the linear polarization of radiation emitted in energetic ion-atom collisions at the ESR storage ring was measured by applying a novel type of position, timing and energy sensitive X-ray detector as a Compton polarimeter. In contrast to previous measurements, that mainly concentrate on studies of the spectral and angular distribution, the new detectors allowed the first polarization study of the Ly-{alpha}{sub 1} radiation (2p{sub 3/2}{yields}1s{sub 1/2}) in U{sup 91+}. Owing to the high precision of the polarimeters applied here, the experimental results indicate a significant depolarization of the Ly-{alpha}{sub 1} radiation caused by the interference of the E1 and M2 transition branches. Moreover, the current investigation shows that measurements of the linear polarization in combination with angular distribution studies provide a model-independent probe for the ratio of the E1 and M2 transition amplitudes and, consequently, of the corresponding transition probabilities. In addition, a first measurement of the linear polarization as well as an angular distribution study of the electron-nucleus Bremsstrahlung arising from ion-atom collisions was performed. The experimental results obtained were compared to exact relativistic calculations and, in case of the Bremsstrahlung, to a semirelativistic treatment. In general, good agreement was found between theoretical predictions and experimental findings. (orig.)
On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems
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.
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
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)
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.
Lattice Boltzmann simulation of antiplane shear loading of a stationary crack
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.
Joint Training of Deep Boltzmann Machines
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.
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
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.
Boltzmann Oracle for Combinatorial Systems
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.
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)
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)
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
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
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)
International Nuclear Information System (INIS)
Schneider, B.I.; Collins, L.A.
1983-01-01
We propose a method for constructing an effective optical potential through which correlation effects can be introduced into the electron-molecule scattering formulation. The optical potential is based on a nonperturbative, Feshbach projection-operator procedure and is evaluated on an L 2 basis. The optical potential is incorporated into the scattering equations by means of a separable expansion, and the resulting scattering equations are solved by a linear-algebraic method based on the integral-equation formulation. We report the results of scattering calculations, which include polarization effects, for low-energy e-H 2 and e-N 2 collisions. The agreement with other theoretical and with experimental results is quite good
Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation
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.
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
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
Generalized Stefan-Boltzmann Law
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.
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
Parallel Boltzmann machines : a mathematical model
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
The convergence of parallel Boltzmann machines
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
Combinatorial optimization on a Boltzmann machine
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.
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
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
Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows
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.
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.
Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework
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.
Open heavy flavor and other hard probes in ultra-relativistic heavy-ion collisions
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...
Three-dimensional lattice Boltzmann model for compressible flows.
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.
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
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)
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
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.
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)
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
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)
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.
International Nuclear Information System (INIS)
Delaunay, F.
1990-01-01
In this experiment performed at GANIL, the use of the gaseous multidetectors DELF and XYZT allows the detection of the heavy fragments (Z ≥ 5) whose velocity is larger than 3 cm/ns when the emission angle is lower than 30 0 and whose velocity is larger than 0.5 cm/ns when the emission angle is greater than 30 0 . For the reactions Kr + Au and Kr + Th at 43 MeV/u, we have observed with a still significative occurrence, events where 6 fragments are produced and we have studied the events where at least 3 heavy fragments were detected. In order to separate the peripheral collisions from the central ones, a collective variable measuring the dispersion of the relative velocity between each couple of fragment is used for events where 3 or 4 heavy fragments are recorded. Afterwards, a selection method is presented for the peripheral events in order to deal only with almost complete events. The atomical number of the fragment whose velocity is nearly equal to the beam velocity, is used to estimate the impact parameter. We find that for a given impact parameter, some different mechanisms are present. A method of measurement of the angular momentum is elaborated from the angular distribution of the fission fragments. A study of incomplete linear momentum transfer leads to a transfer rate of about 40%. The angular momentum of the target like fragment just before fission is also small. The results of the abrasion-ablation model and of the two-step model are quite close to the experimental results [fr
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.
Lattice Boltzmann modeling an introduction for geoscientists and engineers
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.
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.)
Boltzmann equation and hydrodynamics beyond Navier-Stokes.
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).
An introduction to the theory of the Boltzmann equation
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
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...
A topological insight into restricted Boltzmann machines
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
Lattice Boltzmann approach for complex nonequilibrium flows.
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.
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...
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
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
Boltzmann map for quantum oscillators
International Nuclear Information System (INIS)
Streater, R.F.
1987-01-01
The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega 1 , omega 2 , and omega 3 mutually irrational, but obeying a relation n 1 omega 1 + n 2 omega 2 = n 3 omega 3 , n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) β 1 , β 2 , β 3 obeying the equation n 1 omega 1 β 1 + n 2 omega 3 β 1 number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case
Essentially Entropic Lattice Boltzmann Model
Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh
2017-12-01
The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.
Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations
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.
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
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
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
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)
On the Stability of the Finite Difference based Lattice Boltzmann Method
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.
On the Stability of the Finite Difference based Lattice Boltzmann Method
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.
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
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.
Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework
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.
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)
Kinetic Boltzmann, Vlasov and Related Equations
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
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.
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
Multispeed models in off-lattice Boltzmann simulations
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.
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)
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)
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
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.)
Boltzmann machines for travelling salesman problems
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
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)
Boltzmann und das Ende des mechanistischen Weltbildes
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 ...
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
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
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
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
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
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.
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.
Boltzmann, Darwin and Directionality theory
Energy Technology Data Exchange (ETDEWEB)
Demetrius, Lloyd A., E-mail: ldemetr@oeb.harvard.edu
2013-09-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Boltzmann, Darwin and Directionality theory
International Nuclear Information System (INIS)
Demetrius, Lloyd A.
2013-01-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Observation of distorted Maxwell-Boltzmann distribution of epithermal ions in LHD
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.
Boltzmann, Darwin and Directionality theory
Demetrius, Lloyd A.
2013-09-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Recursive regularization step for high-order lattice Boltzmann methods
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.
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.
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.
Nonequilibrium thermodynamics of restricted Boltzmann machines
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.
Lattice-Boltzmann simulations of droplet evaporation
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
Lattice-Boltzmann simulations of droplet evaporation
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
Nonequilibrium thermodynamics of restricted Boltzmann machines.
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.
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
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
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
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
Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions
International Nuclear Information System (INIS)
Cordier, S.
1995-05-01
In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs
International Nuclear Information System (INIS)
Sanchez, Richard.
1975-04-01
For the one-dimensional geometries, the transport equation with linearly anisotropic scattering can be reduced to a single integral equation; this is a singular-kernel FREDHOLM equation of the second kind. When applying a conventional projective method that of GALERKIN, to the solution of this equation the well-known collision probability algorithm is obtained. Piecewise polynomial expansions are used to represent the flux. In the ANILINE code, the flux is supposed to be linear in plane geometry and parabolic in both cylindrical and spherical geometries. An integral relationship was found between the one-dimensional isotropic and anisotropic kernels; this allows to reduce the new matrix elements (issuing from the anisotropic kernel) to classic collision probabilities of the isotropic scattering equation. For cylindrical and spherical geometries used an approximate representation of the current was used to avoid an additional numerical integration. Reflective boundary conditions were considered; in plane geometry the reflection is supposed specular, for the other geometries the isotropic reflection hypothesis has been adopted. Further, the ANILINE code enables to deal with an incoming isotropic current. Numerous checks were performed in monokinetic theory. Critical radii and albedos were calculated for homogeneous slabs, cylinders and spheres. For heterogeneous media, the thermal utilization factor obtained by this method was compared with the theoretical result based upon a formula by BENOIST. Finally, ANILINE was incorporated into the multigroup APOLLO code, which enabled to analyse the MINERVA experimental reactor in transport theory with 99 groups. The ANILINE method is particularly suited to the treatment of strongly anisotropic media with considerable flux gradients. It is also well adapted to the calculation of reflectors, and in general, to the exact analysis of anisotropic effects in large-sized media [fr
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
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
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
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
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.
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.
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.
Jurneczko, Ewa; Kalapothakis, Jason; Campuzano, Iain D G; Morris, Michael; Barran, Perdita E
2012-10-16
There has been a significant increase in the use of ion mobility mass spectrometry (IM-MS) to investigate conformations of proteins and protein complexes following electrospray ionization. Investigations which employ traveling wave ion mobility mass spectrometry (TW IM-MS) instrumentation rely on the use of calibrants to convert the arrival times of ions to collision cross sections (CCS) providing "hard numbers" of use to structural biology. It is common to use nitrogen as the buffer gas in TW IM-MS instruments and to calibrate by extrapolating from CCS measured in helium via drift tube (DT) IM-MS. In this work, both DT and TW IM-MS instruments are used to investigate the effects of different drift gases (helium, neon, nitrogen, and argon) on the transport of multiply charged ions of the protein myoglobin, frequently used as a standard in TW IM-MS studies. Irrespective of the drift gas used, recorded mass spectra are found to be highly similar. In contrast, the recorded arrival time distributions and the derived CCS differ greatly. At low charge states (7 ≤ z ≤ 11) where the protein is compact, the CCS scale with the polarizability of the gas; this is also the case for higher charge states (12 ≤ z ≤ 22) where the protein is more unfolded for the heavy gases (neon, argon, and nitrogen) but not the case for helium. This is here interpreted as a different conformational landscape being sampled by the lighter gas and potentially attributable to increased field heating by helium. Under nanoelectrospray ionization (nESI) conditions, where myoglobin is sprayed from an aqueous solution buffered to pH 6.8 with 20 mM ammonium acetate, in the DT IM-MS instrument, each buffer gas can yield a different arrival time distribution (ATD) for any given charge state.
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)
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)
Identifying product order with restricted Boltzmann machines
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.
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.
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)
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup; Servis, D.P.; Zhang, Shengming
1999-01-01
The first section of the present report describes the procedures that are being programmed at DTU for evaluation of the external collision dynamics. Then follows a detailed description of a comprehensive finite element analysis of one collision scenario for MS Dextra carried out at NTUA. The last...
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
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.…
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 ...
Axisymmetric multiphase lattice Boltzmann method for generic equations of state
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
General relativistic Boltzmann equation, II: Manifestly covariant treatment
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
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...
Boltzmann machines as a model for parallel annealing
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
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
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
Exploring cluster Monte Carlo updates with Boltzmann machines
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.
Exploring cluster Monte Carlo updates with Boltzmann machines.
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.
Boltzmann equations for a binary one-dimensional ideal gas.
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.
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
CLIC: developing a linear collider
Laurent Guiraud
1999-01-01
Compact Linear Collider (CLIC) is a CERN project to provide high-energy electron-positron collisions. Instead of conventional radio-frequency klystrons, CLIC will use a low-energy, high-intensity primary beam to produce acceleration.
Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.
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.
Boltzmann babies in the proper time measure
Energy Technology Data Exchange (ETDEWEB)
Bousso, Raphael; Bousso, Raphael; Freivogel, Ben; Yang, I-Sheng
2007-12-20
After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.
Flux Limiter Lattice Boltzmann for Compressible Flows
International Nuclear Information System (INIS)
Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai
2011-01-01
In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
The Lattice Boltzmann method principles and practice
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...
Power Laws are Disguised Boltzmann Laws
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.
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
Lattice-Boltzmann Simulation of Tablet Disintegration
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.
Corner-transport-upwind lattice Boltzmann model for bubble cavitation
Sofonea, V.; Biciuşcǎ, T.; Busuioc, S.; Ambruş, Victor E.; Gonnella, G.; Lamura, A.
2018-02-01
Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 ×6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca≳0.2 .
Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine
2008-02-01
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 14x improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
Lattice Boltzmann simulation optimization on leading multicore platforms
Energy Technology Data Exchange (ETDEWEB)
Williams, S. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States); Carter, J. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, L. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Shalf, J. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yelick, K. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
2008-01-01
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of searchbased performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our autotuned LBMHD application achieves up to a 14 improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
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
Study of flow over object problems by a nodal discontinuous Galerkin-lattice Boltzmann method
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.
Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method
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.
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
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.
The Concept of Collision-Free Motion Planning Using a Dynamic Collision Map
Directory of Open Access Journals (Sweden)
Keum-Bae Cho
2014-09-01
Full Text Available In this paper, we address a new method for the collision-free motion planning of a mobile robot in dynamic environments. The motion planner is based on the concept of a conventional collision map (CCM, represented on the L(travel length-T(time plane. We extend the CCM with dynamic information about obstacles, such as linear acceleration and angular velocity, providing useful information for estimating variation in the collision map. We first analyse the effect of the dynamic motion of an obstacle in the collision region. We then define the measure of collision dispersion (MOCD. The dynamic collision map (DCM is generated by drawing the MOCD on the CCM. To evaluate a collision-free motion planner using the DCM, we extend the DCM with MOCD, then draw the unreachable region and deadlocked regions. Finally, we construct a collision-free motion planner using the information from the extended DCM.
International Nuclear Information System (INIS)
Southworth, B.
1985-01-01
The peak of the construction phase of the Stanford Linear Collider, SLC, to achieve 50 GeV electron-positron collisions has now been passed. The work remains on schedule to attempt colliding beams, initially at comparatively low luminosity, early in 1987. (orig./HSI).
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.
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.
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
Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
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.
Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2
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.
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.)
Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation
International Nuclear Information System (INIS)
Baker, C.M.J.; Buchan, A.G.; Pain, C.C.; Tollit, B.; Eaton, M.D.; Warner, P.
2012-01-01
This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.
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...
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...
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 ...
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
Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase I
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...
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
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
Lattice Boltzmann method fundamentals and engineering applications with computer codes
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.
Energy Technology Data Exchange (ETDEWEB)
Berenguer Antequera, J.
2015-07-01
Calorimetry Hadronic with semidigital reading based on camera of resistive planes of glass for experiments on collision linear e + e-. Electron-positron linear colliders have been proposed as next generation particle colliders to complement and extend the physics programme of the LHC (Large Hadron Collider) at CERN. Currently, two projects, ILC (International Linear Collider) and CLIC (Compact LInear Collider), have been suggested by the international community to reach this purpose. The requirements for a detector for both linear colliders are defined by the precision needed to fully exploit the physics potential of these colliders. In particular, one of the most important requirements is an excellent jet energy resolution. This can be achieved with the particle-flow concept in which the overall detector performance for jet reconstruction is optimised by reconstructing each particle individually. For this reason, the calorimeter system has to have unprecedented granularity fulfilling the task of shower separation and providing excellent jet energy resolution and background separation. (Author)
Maxwell iteration for the lattice Boltzmann method with diffusive scaling
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.
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
Poisson-Boltzmann-Nernst-Planck model.
Zheng, Qiong; Wei, Guo-Wei
2011-05-21
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
Boltzmann Transport in Hybrid PIC HET Modeling
2015-07-01
assumption of an electron velocity distribution function in local thermal equilibrium. Recently, work in the field of gaseous electronics has...parameters and are based on the assumption of an electron velocity distribution function in local thermal equilibrium. Recently, work in the field of gaseous ...constant νe = electron momentum exchange frequency e = elementary charge µ = scalar electron mobility ν = electron momentum exchange collision frequency Ωe
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
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
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
Ludwig Boltzmann, Albert Einstein and Franz Joseph
International Nuclear Information System (INIS)
Broda, E.
1983-01-01
Under the Emperor Francis Joseph (1848-1916) the natural sciences were less weIl supported in Austria than in other countries of Europe. This is explained by the fact that the German speaking middle classes accepted the preeminence of the feudal forces with their antiscientific attitude. The reason for this readiness to subordination was that those middle classes feIt threatened in their relatively favourable situation by Slavs and Latins. Francis Joseph was the typical representative of the aristocracy. Personally, he did his duty conscientiously and was not corrupt, but progressive ideas and scientific thought were alien to him. From his desk he treated Boltzmann benevolently, but he had no wish to meet personally the greatest mind of the Empire or in any respect to ask his views. Another famous subject of the Emperor, Albert Einstein, was apparently ignored altogether. The structural weakness of Austria, due to the national problems, led to immobilism in her scientific life, but also, up to a point, to tolerance. The impression of Victor Adler on Einstein is considered in this historical context. (author) [de
Parallelization of 2-D lattice Boltzmann codes
International Nuclear Information System (INIS)
Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo.
1996-03-01
Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author)
Extended lattice Boltzmann scheme for droplet combustion.
Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas
2017-05-01
The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.
Parallelization of 2-D lattice Boltzmann codes
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo
1996-03-01
Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author).
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.
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
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 ...
Implementing the lattice Boltzmann model on commodity graphics hardware
International Nuclear Information System (INIS)
Kaufman, Arie; Fan, Zhe; Petkov, Kaloian
2009-01-01
Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications. The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM). We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor. Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the
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
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.
International Nuclear Information System (INIS)
Combes, F.
1987-01-01
Galaxies are not isolated systems of stars and gas, ''independent universes'' as believed by astronomers about ten years ago, but galaxies are formed and evolve by interaction with their environment, and in particular with their nearest neighbors. Gravitational interactions produce enormous tides in the disk of spiral galaxies, generate spiral arms and trigger bursts of star formation. Around elliptical galaxies, the collision with a small companion produces a series of waves, or shells. A galaxy interaction leads, in most cases, to the coalescence of the two coliders; therefore all galaxies are not formed just after the Big-Bang, when matter recombines: second generation galaxies are still forming now by galaxy mergers, essentially elliptical galaxies, but also compact dwarfs. Collisions between galaxies could also trigger activity in nuclei for radiogalaxies and quasars [fr
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.)
Multidimensional intermittency in hadronic collisions
International Nuclear Information System (INIS)
Pan, J.; Hwa, R.C.
1992-06-01
The study of intermittency in high-energy hadronic collisions by the Monte Carlo code ECCO is extended to 3-dimensional phase space. Strong intermittency is found in agreement with the data. Fluctuation in the impact parameter is responsible for the intermittency in lnp T , and the transverse-momentum conservation leads to negative intermittency slopes in the azimuthal angle φ. The Ochs-Wosiek plots are linear in all dimensions having universal slopes. An exponent ν = 1.448 emerges to characterize multiparticle production in pp collisions. The properties of G moments are also examined, and the fractal dimensions determined
International Nuclear Information System (INIS)
Zhang Qing-Yu; Zhu Ming-Fang; Sun Dong-Ke
2017-01-01
A multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann (LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudo-particle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio. The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young’s equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie’s law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to
Tomography and generative training with quantum Boltzmann machines
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.
Navier-Stokes Dynamics by a Discrete Boltzmann Model
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.
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.
Lattice gas cellular automata and lattice Boltzmann models an introduction
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.
Stabilization of the Lattice Boltzmann Method Using Information Theory
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...
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
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...
On a Boltzmann-type price formation model
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.
On a Boltzmann-type price formation model
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.
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.
On the relativistic large-angle electron collision operator for runaway avalanches in plasmas
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.
Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.
2016-04-01
In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.
International Nuclear Information System (INIS)
Stoltz, G; Lazzeri, M; Mauri, F
2009-01-01
We present a study of the phononic thermal conductivity of isotopically disordered carbon nanotubes. In particular, the behaviour of the thermal conductivity as a function of the system length is investigated, using Green's function techniques to compute the transmission across the system. The method is implemented using linear scaling algorithms, which allow us to reach systems of lengths up to L = 2.5 μm (with up to 200 000 atoms). As for 1D systems, it is observed that the conductivity diverges with the system size L. We also observe a dramatic decrease of the thermal conductance for systems of experimental sizes (roughly 80% at room temperature for L = 2.5 μm), when a large fraction of isotopic disorder is introduced. The results obtained with Green's function techniques are compared to results obtained with a Boltzmann description of thermal transport. There is a good agreement between both approaches for systems of experimental sizes, even in the presence of Anderson localization. This is particularly interesting since the computation of the transmission using Boltzmann's equation is much less computationally expensive, so that larger systems may be studied with this method.
Relativistic Boltzmann theory for a plasma. II
International Nuclear Information System (INIS)
Erkelens, H. van; Leeuwen, W.A. van
1977-01-01
The linear or phenomenological laws such as Ohm's law, Fourier's law and Fick's law are derived for a relativistic plasma in an electromagnetic field. It is shown that the choice of a reference frame as proposed by Landau and Lifshitz entails - in contrast to, for instance, the choice of Eckart - the validity of Onsager's reciprocity relations. (Auth.)
Contact angle determination in multicomponent lattice Boltzmann simultations
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
Classifying images using restricted Boltzmann machines and convolutional neural networks
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.
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.
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
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...
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...
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 ...
Convection in multiphase fluid flows using lattice Boltzmann methods
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
Convection-diffusion lattice Boltzmann scheme for irregular lattices
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
Diffusion on unstructured triangular grids using Lattice Boltzmann
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
Lattice Boltzmann scheme for diffusion on triangular grids
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
Lattice-Boltzmann simulation of the sedimentation of charged disks
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
Measuring Boltzmann's Constant with Carbon Dioxide
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…
Lattice-Boltzmann scheme for natural convection in porous media
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
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.
A topological insight into restricted Boltzmann machines (extented abstract)
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.
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
Distributional Monte Carlo Methods for the Boltzmann Equation
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
Energy Technology Data Exchange (ETDEWEB)
Broda, E.
1983-07-01
Under the Emperor Francis Joseph (1848-1916) the natural sciences were less weIl supported in Austria than in other countries of Europe. This is explained by the fact that the German speaking middle classes accepted the preeminence of the feudal forces with their antiscientific attitude. The reason for this readiness to subordination was that those middle classes feIt threatened in their relatively favourable situation by Slavs and Latins. Francis Joseph was the typical representative of the aristocracy. Personally, he did his duty conscientiously and was not corrupt, but progressive ideas and scientific thought were alien to him. From his desk he treated Boltzmann benevolently, but he had no wish to meet personally the greatest mind of the Empire or in any respect to ask his views. Another famous subject of the Emperor, Albert Einstein, was apparently ignored altogether. The structural weakness of Austria, due to the national problems, led to immobilism in her scientific life, but also, up to a point, to tolerance. The impression of Victor Adler on Einstein is considered in this historical context. (author) [German] Die Naturwissenschaften wurden in Österreich unter Franz Joseph (1848-1916) weniger gefördert als in anderen Staaten Europas. Dies wird darauf zurückgeführt, daß das deutschsprechende Bürgertum sich mit der Vorherrschaft der feudalen Kräfte abfand, die nicht wissenschafts-freundlich waren. Für die Bereitschaft zur Unterordnung unter die Feudalen war maßgebend, daß das deutschsprechende Bürgertum sich durch Slawen und Romanen in seiner relativen Vorzugsstellung bedroht sah. Franz Joseph war der typische Repräsentant des konservativen Feudalismus. Er war persönlich pflichtbewußt und integer, doch waren ihm fortschrittliche Gedanken und wissenschaftliche Denkweise fremd. Boltzmann behandelte er von seinem Schreibtisch aus wohlwollend, doch hegte er keinen Wunsch, den größten Geist seines Reiches persönlich kennen zu lernen oder ihn in
Macroscopic behaviour of a charged Boltzmann gas
International Nuclear Information System (INIS)
Banyai, L.; Gartner, P.; Protopopescu, V.
1980-08-01
We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzman equation with thermaljzation on unifopmly distributed scatterers. It is shown that jf one scales the time t, the reciprocal space coordinate k vector and the Debye length l as lambda 2 t, k vector/lambda, lambda l respectively, in the lambda→infinity limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation. (author)
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
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
Lambda hyperon production and polarization in collisions of p(3.5 GeV)+Nb
Energy Technology Data Exchange (ETDEWEB)
Agakishiev, G.; Belyaev, A.V.; Chernenko, S.; Fateev, O.V.; Ierusalimov, A.; Ladygin, V.; Muentz, C.; Vasiliev, T.; Zanevsky, Y.V. [Joint Institute of Nuclear Research, Dubna (Russian Federation); Arnold, O.; Berger-Chen, J.C.; Epple, E.; Fabbietti, L.; Lalik, R.; Lapidus, K.; Schmah, A.; Siebenson, J. [Excellence Cluster ' ' Origin and Structure of the Universe' ' , Garching (Germany); Balanda, A.; Dybczak, A.; Michalska, B.; Palka, M.; Przygoda, W.; Salabura, P.; Trebacz, R. [Jagiellonian University of Cracow, Smoluchowski Institute of Physics, Krakow (Poland); Belver, D.; Cabanelas, P.; Garzon, J.A.; Kornakov, G. [Univ. de Santiago de Compostela, LabCAF F. Fisica, Santiago de Compostela (Spain); Blanco, A.; Fonte, P.; Lopes, L.; Mangiarotti, A. [LIP-Laboratorio de Instrumentacao e Fisica Experimental de Particulas, Coimbra (Portugal); Boehmer, M.; Friese, J.; Gernhaeuser, R.; Jurkovic, M.; Kruecken, R.; Maier, L.; Weber, M. [Technische Universitaet Muenchen, Physik Department E12, Garching (Germany); Boyard, J.L.; Hennino, T.; Liu, T.; Ramstein, B. [Universite Paris Sud, Institut de Physique Nucleaire (UMR 8608), CNRS/IN2P3, Orsay Cedex (France); Finocchiaro, P. [Laboratori Nazionali del Sud, INFN, Catania (Italy); Froehlich, I.; Goebel, K.; Lorenz, M.; Markert, J.; Michel, J.; Pachmayer, Y.C.; Pechenova, O.; Rustamov, A.; Stroebele, H.; Tarantola, A.; Teilab, K. [Johann Wolfgang Goethe-Universitaet, Institut fuer Kernphysik, Frankfurt (Germany); Galatyuk, T.; Gonzalez-Diaz, D. [Technische Universitaet Darmstadt, Darmstadt (Germany); Golubeva, M.; Guber, F.; Ivashkin, A.; Karavicheva, T.; Kurepin, A.; Reshetin, A.; Sadovsky, A. [Russian Academy of Science, Institute for Nuclear Research, Moscow (Russian Federation); Gumberidze, M. [Technische Universitaet Darmstadt, Darmstadt (Germany); Universite Paris Sud, Institut de Physique Nucleaire (UMR 8608), CNRS/IN2P3, Orsay Cedex (France); Heinz, T.; Holzmann, R.; Koenig, I.; Koenig, W.; Kolb, B.W.; Lang, S.; Pechenov, V.; Pietraszko, J.; Schwab, E.; Sturm, C.; Traxler, M.; Yurevich, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Iori, I. [Sezione di Milano, INFN, Milano (Italy); Kaempfer, B.; Kotte, R.; Naumann, L.; Wendisch, C.; Wuestenfeld, J. [Helmholtz-Zentrum Dresden-Rossendorf, Institut fuer Strahlenphysik, Dresden (Germany); Krasa, A.; Krizek, F.; Kugler, A.; Sobolev, Yu.G.; Tlusty, P.; Wagner, V. [Academy of Sciences of Czech Republic, Nuclear Physics Institute, Rez (Czech Republic); Kuc, H. [Jagiellonian University of Cracow, Smoluchowski Institute of Physics, Krakow (Poland); Universite Paris Sud, Institut de Physique Nucleaire (UMR 8608), CNRS/IN2P3, Orsay Cedex (France); Kuehn, W.; Metag, V.; Spataro, S.; Spruck, B. [Justus Liebig Universitaet Giessen, II.Physikalisches Institut, Giessen (Germany); Lebedev, A. [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation); Parpottas, Y.; Tsertos, H. [University of Cyprus, Department of Physics, Nicosia (Cyprus); Stroth, J. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Johann Wolfgang Goethe-Universitaet, Institut fuer Kernphysik, Frankfurt (Germany); Collaboration: HADES Collaboration
2014-05-15
Results on Λ hyperon production are reported for collisions of p(3.5 GeV) + Nb, studied with the High-Acceptance Di-Electron Spectrometer (HADES) at SIS18 at GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt. The transverse mass distributions in rapidity bins are well described by Boltzmann shapes with a maximum inverse slope parameter of about 90 MeV at a rapidity of y = 1.0, i.e. slightly below the center-of-mass rapidity for nucleon-nucleon collisions, y{sub cm} = 1.12. The rapidity density decreases monotonically with increasing rapidity within a rapidity window ranging from 0.3 to 1.3. The Λ phase-space distribution is compared with results of other experiments and with predictions of two transport approaches which are available publicly. None of the present versions of the employed models is able to fully reproduce the experimental distributions, i.e. in absolute yield and in shape. Presumably, this finding results from an insufficient modelling in the transport models of the elementary processes being relevant for Λ production, rescattering and absorption. The present high-statistics data allow for a genuine two-dimensional investigation as a function of phase space of the self-analyzing Λ polarization in the weak decay Λ → pπ{sup -}. Finite negative values of the polarization in the order of 5-20% are observed over the entire phase space studied. The absolute value of the polarization increases almost linearly with increasing transverse momentum for p{sub t} > 300 MeV/c and increases with decreasing rapidity for y < 0.8. (orig.)
Lambda hyperon production and polarization in collisions of p(3.5 GeV)+Nb
International Nuclear Information System (INIS)
Agakishiev, G.; Belyaev, A.V.; Chernenko, S.; Fateev, O.V.; Ierusalimov, A.; Ladygin, V.; Muentz, C.; Vasiliev, T.; Zanevsky, Y.V.; Arnold, O.; Berger-Chen, J.C.; Epple, E.; Fabbietti, L.; Lalik, R.; Lapidus, K.; Schmah, A.; Siebenson, J.; Balanda, A.; Dybczak, A.; Michalska, B.; Palka, M.; Przygoda, W.; Salabura, P.; Trebacz, R.; Belver, D.; Cabanelas, P.; Garzon, J.A.; Kornakov, G.; Blanco, A.; Fonte, P.; Lopes, L.; Mangiarotti, A.; Boehmer, M.; Friese, J.; Gernhaeuser, R.; Jurkovic, M.; Kruecken, R.; Maier, L.; Weber, M.; Boyard, J.L.; Hennino, T.; Liu, T.; Ramstein, B.; Finocchiaro, P.; Froehlich, I.; Goebel, K.; Lorenz, M.; Markert, J.; Michel, J.; Pachmayer, Y.C.; Pechenova, O.; Rustamov, A.; Stroebele, H.; Tarantola, A.; Teilab, K.; Galatyuk, T.; Gonzalez-Diaz, D.; Golubeva, M.; Guber, F.; Ivashkin, A.; Karavicheva, T.; Kurepin, A.; Reshetin, A.; Sadovsky, A.; Gumberidze, M.; Heinz, T.; Holzmann, R.; Koenig, I.; Koenig, W.; Kolb, B.W.; Lang, S.; Pechenov, V.; Pietraszko, J.; Schwab, E.; Sturm, C.; Traxler, M.; Yurevich, S.; Iori, I.; Kaempfer, B.; Kotte, R.; Naumann, L.; Wendisch, C.; Wuestenfeld, J.; Krasa, A.; Krizek, F.; Kugler, A.; Sobolev, Yu.G.; Tlusty, P.; Wagner, V.; Kuc, H.; Kuehn, W.; Metag, V.; Spataro, S.; Spruck, B.; Lebedev, A.; Parpottas, Y.; Tsertos, H.; Stroth, J.
2014-01-01
Results on Λ hyperon production are reported for collisions of p(3.5 GeV) + Nb, studied with the High-Acceptance Di-Electron Spectrometer (HADES) at SIS18 at GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt. The transverse mass distributions in rapidity bins are well described by Boltzmann shapes with a maximum inverse slope parameter of about 90 MeV at a rapidity of y = 1.0, i.e. slightly below the center-of-mass rapidity for nucleon-nucleon collisions, y cm = 1.12. The rapidity density decreases monotonically with increasing rapidity within a rapidity window ranging from 0.3 to 1.3. The Λ phase-space distribution is compared with results of other experiments and with predictions of two transport approaches which are available publicly. None of the present versions of the employed models is able to fully reproduce the experimental distributions, i.e. in absolute yield and in shape. Presumably, this finding results from an insufficient modelling in the transport models of the elementary processes being relevant for Λ production, rescattering and absorption. The present high-statistics data allow for a genuine two-dimensional investigation as a function of phase space of the self-analyzing Λ polarization in the weak decay Λ → pπ - . Finite negative values of the polarization in the order of 5-20% are observed over the entire phase space studied. The absolute value of the polarization increases almost linearly with increasing transverse momentum for p t > 300 MeV/c and increases with decreasing rapidity for y < 0.8. (orig.)
International Nuclear Information System (INIS)
Hou-Hui, Yi; Cai-Feng, Wang; Xiao-Feng, Yang; Hua-Bing, Li
2009-01-01
The rolling massage is one of the most important manipulations in Chinese massage, which is expected to eliminate many diseases. Here, the effect of the rolling massage on a pair of particles moving in blood vessels under rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulated results show that the motion of each particle is considerably modified by the rolling massage, and it depends on the relative rolling velocity, the rolling depth, and the distance between particle position and rolling position. Both particles' translational average velocities increase almost linearly as the rolling velocity increases, and obey the same law. The increment of the average relative angular velocity for the leading particle is smaller than that of the trailing one. The result is helpful for understanding the mechanism of the massage and to further develop the rolling techniques. (classical areas of phenomenology)
Lattice Boltzmann simulation of droplet formation in T-junction geometries
Busuioc, Sergiu; Ambruş, Victor E.; Sofonea, Victor
2017-01-01
The formation of droplets in T-junction configurations is investigated using a two-dimensional Lattice Boltzmann model for liquid-vapor systems. We use an expansion of the equilibrium distribution function with respect to Hermite polynomials and an off-lattice velocity set. To evolve the distribution functions we use the second order corner transport upwind numerical scheme and a third order scheme is used to compute the gradient operators in the force term. The droplet formation successfully recovers the squeezing, dripping and jetting regimes. We find that the droplet length decreases proportionally with the flow rate of the continuous phase and increases with the flow rate of the dispersed phase in all simulation configurations and has a linear dependency on the surface tension parameter κ.
Sarna, Neeraj; Torrilhon, Manuel
2018-01-01
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
Analytical estimation of effective charges at saturation in Poisson-Boltzmann cell models
International Nuclear Information System (INIS)
Trizac, Emmanuel; Aubouy, Miguel; Bocquet, Lyderic
2003-01-01
We propose a simple approximation scheme for computing the effective charges of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression for the effective charge in the infinite-dilution limit which is asymptotically valid for large salt concentrations; this result is then extended to finite colloidal concentration, approximating the salt partitioning effect which relates the salt content in the suspension to that of a dialysing reservoir. This leads to an analytical expression for the effective charge as a function of colloid volume fraction and salt concentration. These results compare favourably with the effective charges at saturation (i.e. in the limit of large bare charge) computed numerically following the standard prescription proposed by Alexander et al within the cell model
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.
International Nuclear Information System (INIS)
Field, J.H.
1984-01-01
The current status, both theoretical and experimental, of two photon collision physics is reviewed with special emphasis on recent experimental results from e + e - storage rings. After a complete presentation of the helicity amplitude formalism for the general process e + e - → Xe + e - , various approximations (transverse photon, Weisaecker Williams) are discussed. Beam polarisation effects and radiative corrections are also briefly considered. A number of specific processes, for which experimental results are now available, are then described. In each case existing theoretical prediction are confronted with experimental results. The processes described include single resonance production, lepton and hadron pair production, the structure functions of the photon, the production of high Psub(T) jets and the total photon photon cross section. In the last part of the review the current status of the subject is summarised and some comments are made on future prospects. These include both extrapolations of current research to higher energy machines (LEP, HERA) as well as a brief mention of both the technical realisation and the physics interest of the real γγ and eγ collisions which may be possible using linear electron colliders in the 1 TeV energy range
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.
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)
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
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
Hermite regularization of the lattice Boltzmann method for open source computational aeroacoustics.
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).
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
Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology
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.
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.
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)
Lattice Boltzmann model for three-phase viscoelastic fluid flow
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.
Riemann-Theta Boltzmann Machine arXiv
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.
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
Comparison of Einstein-Boltzmann solvers for testing general relativity
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.
Acoustic levitation and the Boltzmann-Ehrenfest principle
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.
Volumetric formulation of lattice Boltzmann models with energy conservation
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. ...
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)
Comment on ''Boltzmann equation and the conservation of particle number''
International Nuclear Information System (INIS)
Zanette, D.
1990-09-01
In a recent paper (Z. Banggu, Phys. Rev. A 42, 761 (1990)) it is argued that some solutions of the Boltzmann equation do not satisfy particle conservation as a consequence of the independence of velocity on position. In this comment, the arguments and conclusions of that paper are discussed. In particular, it is stressed that the temporal series used for solving the kinetic equation are generally divergent. A discussion about the particle conservation in its solutions is also provided. (author). 4 refs
Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation
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.
Entropic multirelaxation lattice Boltzmann models for turbulent flows
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.
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
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
International Nuclear Information System (INIS)
Liu, Haihu; Zhang, Yonghao; Valocchi, Albert J.
2015-01-01
Injection of anthropogenic carbon dioxide (CO 2 ) into geological formations is a promising approach to reduce greenhouse gas emissions into the atmosphere. Predicting the amount of CO 2 that can be captured and its long-term storage stability in subsurface requires a fundamental understanding of multiphase displacement phenomena at the pore scale. In this paper, the lattice Boltzmann method is employed to simulate the immiscible displacement of a wetting fluid by a non-wetting one in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We have identified three different displacement patterns, namely, stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number (Ca), viscosity ratio (M), and the media heterogeneity. The non-wetting fluid saturation (S nw ) is found to increase nearly linearly with logCa for each constant M. Increasing M (viscosity ratio of non-wetting fluid to wetting fluid) or decreasing the media heterogeneity can enhance the stability of the displacement process, resulting in an increase in S nw . In either pore networks, the specific interfacial length is linearly proportional to S nw during drainage with equal proportionality constant for all cases excluding those revealing considerable viscous fingering. Our numerical results confirm the previous experimental finding that the steady state specific interfacial length exhibits a linear dependence on S nw for either favorable (M ≥ 1) or unfavorable (M < 1) displacement, and the slope is slightly higher for the unfavorable displacement
Heavy quark pair production in polarized photon-photon collisions
International Nuclear Information System (INIS)
Jikia, G.; Tkabladze, A.
2000-04-01
We present the cross sections of the heavy quark-antiquark pair production in polarized photon photon collision for the general case of photon polarizations. The numerical results for top-antitop production cross sections together with production asymmetries are obtained for linearly polarized photon-photon collisions, including QCD radiative corrections. (orig.)
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)
Asinari, Pietro
2010-10-01
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both these corrections make possible to derive very accurate reference solutions for this test case. Moreover this work aims to distribute an open-source program (called HOMISBOLTZ), which can be redistributed and/or modified for dealing with different applications, under the terms of the GNU General Public License. The program has been purposely designed in order to be minimal, not only with regards to the reduced number of lines (less than 1000), but also with regards to the coding style (as simple as possible). Program summaryProgram title: HOMISBOLTZ Catalogue identifier: AEGN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 23 340 No. of bytes in distributed program, including test data, etc.: 7 635 236 Distribution format: tar
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)
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)
The Collision Repair Campaign targets meaningful risk reduction in the Collision Repair source category to reduce air toxic emissions in their communities. The Campaign also helps shops to work towards early compliance with the Auto Body Rule.
Neuromorphic UAS Collision Avoidance
National Aeronautics and Space Administration — Collision avoidance for unmanned aerial systems (UAS) traveling at high relative speeds is a challenging task. It requires both the detection of a possible collision...
Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases
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...
International Nuclear Information System (INIS)
Salzborn, Erhard; Melchert, Frank
2000-01-01
Collisions between ions belong to the elementary processes occurring in all types of plasmas. In this article we give a short overview about collisions involving one-electron systems. For collisions involving multiply-charged ions we limit the discussion to one specific quasi-one-electron system. (author)
A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models
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.
International Nuclear Information System (INIS)
Phinney, N.
1992-01-01
The SLAC Linear Collider has begun a new era of operation with the SLD detector. During 1991 there was a first engineering run for the SLD in parallel with machine improvements to increase luminosity and reliability. For the 1992 run, a polarized electron source was added and more than 10,000 Zs with an average of 23% polarization have been logged by the SLD. This paper discusses the performance of the SLC in 1991 and 1992 and the technical advances that have produced higher luminosity. Emphasis will be placed on issues relevant to future linear colliders such as producing and maintaining high current, low emittance beams and focusing the beams to the micron scale for collisions. (Author) tab., 2 figs., 18 refs
Probability of satellite collision
Mccarter, J. W.
1972-01-01
A method is presented for computing the probability of a collision between a particular artificial earth satellite and any one of the total population of earth satellites. The collision hazard incurred by the proposed modular Space Station is assessed using the technique presented. The results of a parametric study to determine what type of satellite orbits produce the greatest contribution to the total collision probability are presented. Collision probability for the Space Station is given as a function of Space Station altitude and inclination. Collision probability was also parameterized over miss distance and mission duration.
Operational derivation of Boltzmann distribution with Maxwell's demon model.
Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka
2015-11-24
The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.
Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality
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.
Phase transitions in restricted Boltzmann machines with generic priors
Barra, Adriano; Genovese, Giuseppe; Sollich, Peter; Tantari, Daniele
2017-10-01
We study generalized restricted Boltzmann machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as generalized Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore, we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalization in a teacher-student scenario of unsupervised learning.
Temperature waves and the Boltzmann kinetic equation for phonons
International Nuclear Information System (INIS)
Urushev, D.; Borisov, M.; Vavrek, A.
1988-01-01
The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs
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.
Entropy inequality and hydrodynamic limits for the Boltzmann equation.
Saint-Raymond, Laure
2013-12-28
Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as huge systems of identical and indistinguishable elementary particles. The state of a gas can therefore be described in a statistical way. The evolution, which introduces couplings, loses part of the information, which is expressed by the decay of the so-called mathematical entropy (the opposite of physical entropy!).
International Nuclear Information System (INIS)
Sun, Tao; Li, Weizhong; Yang, Shuai
2013-01-01
Highlights: • The bubble departure diameter is proportional to g −0.425 in quiescent fluid. • The bubble release frequency is proportional to g 0.678 in quiescent fluid. • The simulation result supports the transient micro-convection model. • The bubble departure diameter has exponential relation with inlet velocity. • The bubble release frequency has linear relation with inlet velocity. -- Abstract: Nucleate boiling flows on a horizontal plate are studied in this paper by a hybrid lattice Boltzmann method, where both quiescent and slowly flowing ambient are concerned. The process of a single bubble growth on and departure from the superheated wall is simulated. The simulation result supports the transient micro-convection model. The bubble departure diameter and the release frequency are investigated from the simulation result. It is found that the bubble departure diameter and the release frequency are proportional to g −0.425 and g 0.678 in quiescent fluid, respectively, where g is the gravitational acceleration. Nucleate boiling in slowly flowing ambient is also calculated in consideration of forced convection. It is presented that the bubble departure diameter and the release frequency have exponential relationship and linear relationship with inlet velocity in slowly flowing fluid, respectively
Ginzburg, Irina
2016-02-01
In this Comment on the recent work (Zhu and Ma, 2013) [11] by Zhu and Ma (ZM) we first show that all three local gray Lattice Boltzmann (GLB) schemes in the form (Zhu and Ma, 2013) [11]: GS (Chen and Zhu, 2008; Gao and Sharma, 1994) [1,4], WBS (Walsh et al., 2009) [12] and ZM, fail to get constant Darcy's velocity in series of porous blocks. This inconsistency is because of their incorrect definition of the macroscopic velocity in the presence of the heterogeneous momentum exchange, while the original WBS model (Walsh et al., 2009) [12] does this properly. We improve the GS and ZM schemes for this and other related deficiencies. Second, we show that the ;discontinuous velocity; they recover on the stratified interfaces with their WBS scheme is inherent, in different degrees, to all LBE Brinkman schemes, including ZM scheme. None of them guarantees the stress and the velocity continuity by their implicit interface conditions, even in the frame of the two-relaxation-times (TRT) collision operator where these two properties are assured in stratified Stokes flow, Ginzburg (2007) [5]. Third, the GLB schemes are presented in work (Zhu and Ma, 2013) [11] as the alternative ones to direct, Brinkman-force based (BF) schemes (Freed, 1998; Nie and Martys, 2007) [3,8]. Yet, we show that the BF-TRT scheme (Ginzburg, 2008) [6] gets the solutions of any of the improved GLB schemes for specific, viscosity-dependent choice of its one or two local relaxation rates. This provides the principal difference between the GLB and BF: while the BF may respect the linearity of the Stokes-Brinkman equation rigorously, the GLB-TRT cannot, unless it reduces to the BF via the inverse transform of the relaxation rates. Furthermore, we show that, in limited parameter space, ;gray; schemes may run one another. From the practical point of view, permeability values obtained with the GLB are viscosity-dependent, unlike with the BF. Finally, the GLB shares with the BF a so-called anisotropy (Ginzburg
International Nuclear Information System (INIS)
Silva, Goncalo; Talon, Laurent; Ginzburg, Irina
2017-01-01
The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM
Energy Technology Data Exchange (ETDEWEB)
Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com [Irstea, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex (France); Talon, Laurent, E-mail: talon@fast.u-psud.fr [CNRS (UMR 7608), Laboratoire FAST, Batiment 502, Campus University, 91405 Orsay (France); Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr [Irstea, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex (France)
2017-04-15
The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM
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
Doubly charmed baryon production in heavy ion collisions
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.
Instability of compensated beam-beam collisions
International Nuclear Information System (INIS)
Rosenzweig, J.B.; Autin, B.; Chen, Pisin.
1989-01-01
The beam-beam disruption phenomena in linear colliders are increasingly seen as a source of serious problems for these machines. A plasma compensation scheme, in which the motion of the plasma electrons in the presence of the colliding beams provides neutralizing charge and current densities, has been proposed and studied. But natural alternative to this scheme is to consider the overlapping of nearly identical high energy e + and e/sup /minus// bunches, and the collision of two such pairs - in other words, collision of two opposing relativistic positronium plasmas. It should be noticed that while the luminosity for all collisions is increased by a factor of four in this scheme, the event rate for e + e/sup /minus// collisions is only increased by a factor of two. The other factor of two corresponds to the addition of e + e + and e/sup /minus//e/sup /minus// collisions to the interaction point. This beam compensation scheme, which has been examined through computer simulation by Balakin and Solyak in the Soviet Union, promises full neutralization of beam charges and currents. These numerical investigations have shown that plasma instabilities exist in this nominally neutral system. Although the implementation of this idea seems technically daunting, the potential benefits (beamstrahlung and disruption suppression, relaxation of final focus system constraints) are such that we should consider the physics of these collisions further. In the remainder of this paper, we theoretically analyze the issues of stability and bunch parameter tolerances in this scheme. 11 refs
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...
A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation
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
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
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)
Lattice Boltzmann model capable of mesoscopic vorticity computation
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.
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
A modified Poisson-Boltzmann equation applied to protein adsorption.
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.
Moving charged particles in lattice Boltzmann-based electrokinetics
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.
Does the Boltzmann Principle Need a Dynamical Correction?
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.
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.
Detection of Hypertension Retinopathy Using Deep Learning and Boltzmann Machines
Triwijoyo, B. K.; Pradipto, Y. D.
2017-01-01
hypertensive retinopathy (HR) in the retina of the eye is disturbance caused by high blood pressure disease, where there is a systemic change of arterial in the blood vessels of the retina. Most heart attacks occur in patients caused by high blood pressure symptoms of undiagnosed. Hypertensive retinopathy Symptoms such as arteriolar narrowing, retinal haemorrhage and cotton wool spots. Based on this reasons, the early diagnosis of the symptoms of hypertensive retinopathy is very urgent to aim the prevention and treatment more accurate. This research aims to develop a system for early detection of hypertension retinopathy stage. The proposed method is to determine the combined features artery and vein diameter ratio (AVR) as well as changes position with Optic Disk (OD) in retinal images to review the classification of hypertensive retinopathy using Deep Neural Networks (DNN) and Boltzmann Machines approach. We choose this approach of because based on previous research DNN models were more accurate in the image pattern recognition, whereas Boltzmann machines selected because It requires speedy iteration in the process of learning neural network. The expected results from this research are designed a prototype system early detection of hypertensive retinopathy stage and analysed the effectiveness and accuracy of the proposed methods.
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
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.
International Nuclear Information System (INIS)
Suwono.
1978-01-01
A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)
International Nuclear Information System (INIS)
Vretenar, M
2014-01-01
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics
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.
Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.
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.
Linearization Method and Linear Complexity
Tanaka, Hidema
We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.
International Nuclear Information System (INIS)
Strugalski, Z.
1981-01-01
Qualitative picture of high energy hadron-nucleus collision process, emerging from the analysis of experimental data, is presented. Appropriate description procedure giving a possibility of reproducing various characteristics of this process in terms of the data on elementary hadron-nucleon interaction is proposed. Formula reproducing hadron-nucleus collision cross sections is derived. Inelastic collision cross sections for pion-nucleus and proton-nucleus reactions at wide energy interval are calculated for Pb, Ag, and Al targets. A-dependence of cross sections for pion-nucleus and proton-nucleus collisions at nearly 50 GeV/c momentum were calculated and compared with existing experimental data. Energy dependence of cross sections for hadron-nucleus collisions is determined simply by energy dependence of corresponding cross sections for hadron-nucleon collisions; A-dependence is determined simply by nuclear sizes and nucleon density distributions in nuclei
International Nuclear Information System (INIS)
Stancic, V.
2001-01-01
This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space
Carrete, Jesús; Vermeersch, Bjorn; Katre, Ankita; van Roekeghem, Ambroise; Wang, Tao; Madsen, Georg K. H.; Mingo, Natalio
2017-11-01
almaBTE is a software package that solves the space- and time-dependent Boltzmann transport equation for phonons, using only ab-initio calculated quantities as inputs. The program can predictively tackle phonon transport in bulk crystals and alloys, thin films, superlattices, and multiscale structures with size features in the nm- μm range. Among many other quantities, the program can output thermal conductances and effective thermal conductivities, space-resolved average temperature profiles, and heat-current distributions resolved in frequency and space. Its first-principles character makes almaBTE especially well suited to investigate novel materials and structures. This article gives an overview of the program structure and presents illustrative examples for some of its uses. PROGRAM SUMMARY Program Title:almaBTE Program Files doi:http://dx.doi.org/10.17632/8tfzwgtp73.1 Licensing provisions: Apache License, version 2.0 Programming language: C++ External routines/libraries: BOOST, MPI, Eigen, HDF5, spglib Nature of problem: Calculation of temperature profiles, thermal flux distributions and effective thermal conductivities in structured systems where heat is carried by phonons Solution method: Solution of linearized phonon Boltzmann transport equation, Variance-reduced Monte Carlo
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Diffusive limits for linear transport equations
International Nuclear Information System (INIS)
Pomraning, G.C.
1992-01-01
The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion
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)
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.
Energy Technology Data Exchange (ETDEWEB)
Liu, Haihu, E-mail: haihu.liu@mail.xjtu.edu.cn [School of Energy and Power Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049 (China); James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ (United Kingdom); Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Zhang, Yonghao [James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ (United Kingdom); Valocchi, Albert J. [Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)
2015-05-15
Injection of anthropogenic carbon dioxide (CO{sub 2}) into geological formations is a promising approach to reduce greenhouse gas emissions into the atmosphere. Predicting the amount of CO{sub 2} that can be captured and its long-term storage stability in subsurface requires a fundamental understanding of multiphase displacement phenomena at the pore scale. In this paper, the lattice Boltzmann method is employed to simulate the immiscible displacement of a wetting fluid by a non-wetting one in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We have identified three different displacement patterns, namely, stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number (Ca), viscosity ratio (M), and the media heterogeneity. The non-wetting fluid saturation (S{sub nw}) is found to increase nearly linearly with logCa for each constant M. Increasing M (viscosity ratio of non-wetting fluid to wetting fluid) or decreasing the media heterogeneity can enhance the stability of the displacement process, resulting in an increase in S{sub nw}. In either pore networks, the specific interfacial length is linearly proportional to S{sub nw} during drainage with equal proportionality constant for all cases excluding those revealing considerable viscous fingering. Our numerical results confirm the previous experimental finding that the steady state specific interfacial length exhibits a linear dependence on S{sub nw} for either favorable (M ≥ 1) or unfavorable (M < 1) displacement, and the slope is slightly higher for the unfavorable displacement.
Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions
International Nuclear Information System (INIS)
Denton, A R
2010-01-01
Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid
Holographic collisions in confining theories
International Nuclear Information System (INIS)
Cardoso, Vitor; Emparan, Roberto; Mateos, David; Pani, Paolo; Rocha, Jorge V.
2014-01-01
We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t −3/2 , the failure of Huygens’ principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation
International Nuclear Information System (INIS)
Yan-Yan, Chen; Hua-Bing, Li; Hou-Hui, Yi
2008-01-01
The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density (bulk pressure). If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows
Simulation of plume dynamics by the Lattice Boltzmann Method
Mora, Peter; Yuen, David A.
2017-09-01
The Lattice Boltzmann Method (LBM) is a semi-microscopic method to simulate fluid mechanics by modelling distributions of particles moving and colliding on a lattice. We present 2-D simulations using the LBM of a fluid in a rectangular box being heated from below, and cooled from above, with a Rayleigh of Ra = 108, similar to current estimates of the Earth's mantle, and a Prandtl number of 5000. At this Prandtl number, the flow is found to be in the non-inertial regime where the inertial terms denoted I ≪ 1. Hence, the simulations presented lie within the regime of relevance for geodynamical problems. We obtain narrow upwelling plumes with mushroom heads and chutes of downwelling fluid as expected of a flow in the non-inertial regime. The method developed demonstrates that the LBM has great potential for simulating thermal convection and plume dynamics relevant to geodynamics, albeit with some limitations.
Consistent forcing scheme in the cascaded lattice Boltzmann method
Fei, Linlin; Luo, Kai Hong
2017-11-01
In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.
Charged-particle calculations using Boltzmann transport methods
International Nuclear Information System (INIS)
Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.
1981-01-01
Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of charged particle range distributions, reflection coefficients, and sputtering yields. The Boltzmann transport approach can be implemented, with minor changes, in standard neutral particle computer codes. With the multigroup discrete ordinates code, ANISN, determination of ion and target atom distributions as functions of position, energy, and direction can be obtained without the stochastic error associated with atomistic computer codes such as MARLOWE and TRIM. With the multigroup Monte Carlo code, MORSE, charged particle effects can be obtained for problems associated with very complex geometries. Results are presented for several charged particle problems. Good agreement is obtained between quantities calculated with the multigroup approach and those obtained experimentally or by atomistic computer codes
Thermal lattice Boltzmann simulation for multispecies fluid equilibration
International Nuclear Information System (INIS)
Vahala, Linda; Wah, Darren; Vahala, George; Carter, Jonathan; Pavlo, Pavol
2000-01-01
The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society
Thermal lattice Boltzmann simulation for multispecies fluid equilibration
Energy Technology Data Exchange (ETDEWEB)
Vahala, Linda [Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529 (United States); Wah, Darren [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Vahala, George [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Carter, Jonathan [NERSC, Lawrence Berkeley Laboratory, Berkeley, California 97320 (United States); Pavlo, Pavol [Institute of Plasma Physics, Czech Academy of Science, Praha 8, (Czech Republic)
2000-07-01
The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society.
Consistent forcing scheme in the cascaded lattice Boltzmann method.
Fei, Linlin; Luo, Kai Hong
2017-11-01
In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations
Riotto, Antonio
1998-01-01
The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...
Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation
International Nuclear Information System (INIS)
Dou, Nicholas G.; Minnich, Austin J.
2016-01-01
Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials
Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.
Fürst, Martin L R; Mendl, Christian B; Spohn, Herbert
2013-07-01
The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.
Simulating condensation on microstructured surfaces using Lattice Boltzmann Method
Alexeev, Alexander; Vasyliv, Yaroslav
2017-11-01
We simulate a single component fluid condensing on 2D structured surfaces with different wettability. To simulate the two phase fluid, we use the athermal Lattice Boltzmann Method (LBM) driven by a pseudopotential force. The pseudopotential force results in a non-ideal equation of state (EOS) which permits liquid-vapor phase change. To account for thermal effects, the athermal LBM is coupled to a finite volume discretization of the temperature evolution equation obtained using a thermal energy rate balance for the specific internal energy. We use the developed model to probe the effect of surface structure and surface wettability on the condensation rate in order to identify microstructure topographies promoting condensation. Financial support is acknowledged from Kimberly-Clark.
Lattice Boltzmann model for melting with natural convection
International Nuclear Information System (INIS)
Huber, Christian; Parmigiani, Andrea; Chopard, Bastien; Manga, Michael; Bachmann, Olivier
2008-01-01
We develop a lattice Boltzmann method to couple thermal convection and pure-substance melting. The transition from conduction-dominated heat transfer to fully-developed convection is analyzed and scaling laws and previous numerical results are reproduced by our numerical method. We also investigate the limit in which thermal inertia (high Stefan number) cannot be neglected. We use our results to extend the scaling relations obtained at low Stefan number and establish the correlation between the melting front propagation and the Stefan number for fully-developed convection. We conclude by showing that the model presented here is particularly well-suited to study convection melting in geometrically complex media with many applications in geosciences
Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity
Directory of Open Access Journals (Sweden)
Deming Nie
2015-01-01
Full Text Available The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Berberian, Sterling K
2014-01-01
Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
Predicting drug-target interactions using restricted Boltzmann machines.
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
Partitioned learning of deep Boltzmann machines for SNP data.
Hess, Moritz; Lenz, Stefan; Blätte, Tamara J; Bullinger, Lars; Binder, Harald
2017-10-15
Learning the joint distributions of measurements, and in particular identification of an appropriate low-dimensional manifold, has been found to be a powerful ingredient of deep leaning approaches. Yet, such approaches have hardly been applied to single nucleotide polymorphism (SNP) data, probably due to the high number of features typically exceeding the number of studied individuals. After a brief overview of how deep Boltzmann machines (DBMs), a deep learning approach, can be adapted to SNP data in principle, we specifically present a way to alleviate the dimensionality problem by partitioned learning. We propose a sparse regression approach to coarsely screen the joint distribution of SNPs, followed by training several DBMs on SNP partitions that were identified by the screening. Aggregate features representing SNP patterns and the corresponding SNPs are extracted from the DBMs by a combination of statistical tests and sparse regression. In simulated case-control data, we show how this can uncover complex SNP patterns and augment results from univariate approaches, while maintaining type 1 error control. Time-to-event endpoints are considered in an application with acute myeloid leukemia patients, where SNP patterns are modeled after a pre-screening based on gene expression data. The proposed approach identified three SNPs that seem to jointly influence survival in a validation dataset. This indicates the added value of jointly investigating SNPs compared to standard univariate analyses and makes partitioned learning of DBMs an interesting complementary approach when analyzing SNP data. A Julia package is provided at 'http://github.com/binderh/BoltzmannMachines.jl'. binderh@imbi.uni-freiburg.de. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
Boltzmann electron PIC simulation of the E-sail effect
Directory of Open Access Journals (Sweden)
P. Janhunen
2015-12-01
Full Text Available The solar wind electric sail (E-sail is a planned in-space propulsion device that uses the natural solar wind momentum flux for spacecraft propulsion with the help of long, charged, centrifugally stretched tethers. The problem of accurately predicting the E-sail thrust is still somewhat open, however, due to a possible electron population trapped by the tether. Here we develop a new type of particle-in-cell (PIC simulation for predicting E-sail thrust. In the new simulation, electrons are modelled as a fluid, hence resembling hybrid simulation, but in contrast to normal hybrid simulation, the Poisson equation is used as in normal PIC to calculate the self-consistent electrostatic field. For electron-repulsive parts of the potential, the Boltzmann relation is used. For electron-attractive parts of the potential we employ a power law which contains a parameter that can be used to control the number of trapped electrons. We perform a set of runs varying the parameter and select the one with the smallest number of trapped electrons which still behaves in a physically meaningful way in the sense of producing not more than one solar wind ion deflection shock upstream of the tether. By this prescription we obtain thrust per tether length values that are in line with earlier estimates, although somewhat smaller. We conclude that the Boltzmann PIC simulation is a new tool for simulating the E-sail thrust. This tool enables us to calculate solutions rapidly and allows to easily study different scenarios for trapped electrons.
Straight velocity boundaries in the lattice Boltzmann method
Latt, Jonas; Chopard, Bastien; Malaspinas, Orestis; Deville, Michel; Michler, Andreas
2008-05-01
Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.
Conditional High-Order Boltzmann Machines for Supervised Relation Learning.
Huang, Yan; Wang, Wei; Wang, Liang; Tan, Tieniu
2017-09-01
Relation learning is a fundamental problem in many vision tasks. Recently, high-order Boltzmann machine and its variants have shown their great potentials in learning various types of data relation in a range of tasks. But most of these models are learned in an unsupervised way, i.e., without using relation class labels, which are not very discriminative for some challenging tasks, e.g., face verification. In this paper, with the goal to perform supervised relation learning, we introduce relation class labels into conventional high-order multiplicative interactions with pairwise input samples, and propose a conditional high-order Boltzmann Machine (CHBM), which can learn to classify the data relation in a binary classification way. To be able to deal with more complex data relation, we develop two improved variants of CHBM: 1) latent CHBM, which jointly performs relation feature learning and classification, by using a set of latent variables to block the pathway from pairwise input samples to output relation labels and 2) gated CHBM, which untangles factors of variation in data relation, by exploiting a set of latent variables to multiplicatively gate the classification of CHBM. To reduce the large number of model parameters generated by the multiplicative interactions, we approximately factorize high-order parameter tensors into multiple matrices. Then, we develop efficient supervised learning algorithms, by first pretraining the models using joint likelihood to provide good parameter initialization, and then finetuning them using conditional likelihood to enhance the discriminant ability. We apply the proposed models to a series of tasks including invariant recognition, face verification, and action similarity labeling. Experimental results demonstrate that by exploiting supervised relation labels, our models can greatly improve the performance.
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
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
Lattice Boltzmann Simulation of Permeability and Tortuosity for Flow through Dense Porous Media
Directory of Open Access Journals (Sweden)
Ping Wang
2014-01-01
Full Text Available Discrete element method (DEM is used to produce dense and fixed porous media with rigid mono spheres. Lattice Boltzmann method (LBM is adopted to simulate the fluid flow in interval of dense spheres. To simulating the same physical problem, the permeability is obtained with different lattice number. We verify that the permeability is irrelevant to the body force and the media length along flow direction. The relationships between permeability, tortuosity and porosity, and sphere radius are researched, and the results are compared with those reported by other authors. The obtained results indicate that LBM is suited to fluid flow simulation of porous media due to its inherent theoretical advantages. The radius of sphere should have ten lattices at least and the media length along flow direction should be more than twenty radii. The force has no effect on the coefficient of permeability with the limitation of slow fluid flow. For mono spheres porous media sample, the relationship of permeability and porosity agrees well with the K-C equation, and the tortuosity decreases linearly with increasing porosity.
Thermoelectric properties of fully hydrogenated graphene: Semi-classical Boltzmann theory
International Nuclear Information System (INIS)
Reshak, A. H.
2015-01-01
Based on the calculated band structure, the electronic transport coefficients of chair-/boat-like graphane were evaluated by using the semi-classical Boltzmann theory and rigid band model. The maximum value of electrical conductivity for chair (boat)-like graphane of about 1.4 (0.6) × 10 19 (Ωms) −1 is achieved at 600 K. The charge carrier concentration and the electrical conductivity linearly increase with increasing the temperature in agreement with the experimental work for graphene. The investigated materials exhibit the highest value of Seebeck coefficient at 300 K. We should emphasize that in the chemical potential between ∓0.125 μ(eV) the investigated materials exhibit minimum value of electronic thermal conductivity, therefore, maximum efficiency. As the temperature increases, the electronic thermal conductivity increases exponentially, in agreement with the experimental data of graphene. We also calculated the power factor of chair-/boat-like graphane at 300 and 600 K as a function of chemical potential between ∓0.25 μ(eV)
Use of the Boltzmann equation for calculating the scattering law in gas mixtures
International Nuclear Information System (INIS)
Eder, O.J.; Lackner, T.
1989-01-01
A new approach is presented for the calculation of the dynamical incoherent structure factor S s (q, ω) for a dilute binary gas mixture. The starting point is the linearized one-dimensional Boltzmann equation for a mixture of particles interacting via a quasi-Maxwell potential (V(r) ≅ 1/r ν , ν=4). It is shown how - in the Fourier-Laplace space (q, ω) - the solution of the Boltzman equation can be expressed as an infinite continued fraction. The well known hydrodynamic limit (q→0) and the free gas limit (q→∞) are correctly reproduced as the appropriate limits of the continued fraction. A brief comparison between S s (q, ω) for two interaction potentials (quasi-Maxwell potential, ν=4, and hard core potential, ν=∞) is presented, and it is found that, after scaling the variables to the respective diffusion coefficients, only little dependence on the potential remains. Furthermore, for a one-component system in three dimensions results are summarized for the dynamical incoherent and coherent structure factor. (orig.) [de
Optimization of a Lattice Boltzmann Computation on State-of-the-Art Multicore Platforms
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine
2009-04-10
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Xeon E5345 (Clovertown), AMD Opteron 2214 (Santa Rosa), AMD Opteron 2356 (Barcelona), Sun T5140 T2+ (Victoria Falls), as well as a QS20 IBM Cell Blade. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 15x improvement compared with the original code at a given concurrency. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
Solution of the Boltzmann equation for primary light ions and the transport of their fragments
Directory of Open Access Journals (Sweden)
J. Kempe
2010-10-01
Full Text Available The Boltzmann equation for the transport of pencil beams of light ions in semi-infinite uniform media has been calculated. The equation is solved for the practically important generalized 3D case of Gaussian incident primary light ion beams of arbitrary mean square radius, mean square angular spread, and covariance. The transport of the associated fragments in three dimensions is derived based on the known transport of the primary particles, taking the mean square angular spread of their production processes, as well as their energy loss and multiple scattering, into account. The analytical pencil and broad beam depth fluence and absorbed dose distributions are accurately expressed using recently derived analytical energy and range formulas. The contributions from low and high linear energy transfer (LET dose components were separately identified using analytical expressions. The analytical results are compared with SHIELD-HIT Monte Carlo (MC calculations and found to be in very good agreement. The pencil beam fluence and absorbed dose distributions of the primary particles are mainly influenced by an exponential loss of the primary ions combined with an increasing lateral spread due to multiple scattering and energy loss with increasing penetration depth. The associated fluence of heavy fragments is concentrated at small radii and so is the LET and absorbed dose distribution. Their transport is also characterized by the buildup of a slowing down spectrum which is quite similar to that of the primaries but with a wider energy and angular spread at increasing penetration depths. The range of the fragments is shorter or longer depending on their nuclear mass to charge ratio relative to that of the primary ions. The absorbed dose of the heavier fragments is fairly similar to that of the primary ions and also influenced by a rapidly increasing energy loss towards the end of their ranges. The present analytical solution of the Boltzmann equation
International Nuclear Information System (INIS)
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-01-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated
Modelling of a collision between two smartphones
de Jesus, V. L. B.; Sasaki, D. G. G.
2016-09-01
In the predominant approach in physics textbooks, the collision between particles is treated as a black box, where no physical quantity can be measured. This approach becomes even more evident in experimental classes where collisions are the simplest and most common way of applying the theorem of conservation of linear momentum in the asymptotic behavior. In this paper we develop and analyse an experiment on collisions using only two smartphones. The experimental setup is amazingly simple; the two devices are aligned on a horizontal table of lacquered wood, in order to slide more easily. At the edge of one of them a piece of common sponge is glued using double-sided tape. By using a free smartphone application, the values generated by the accelerometer of the two devices in full motion are measured and tabulated. Through numerical iteration, the speed graphs of the smartphones before, during, and after the collision are obtained. The main conclusions were: (i) the demonstration of the feasibility of using smartphones as an alternative to air tracks and electronic sensors employed in a teaching lab, (ii) the possibility of investigating the collision itself, its characteristics and effects; this is the great advantage of the use of smartphones over traditional experiments, (iii) the compatibility of the results with the impulse-momentum theorem, within the margin of uncertainty.
Modelling of the Internal Mechanics in Ship Collisions
DEFF Research Database (Denmark)
Paik, Jeom Kee; Pedersen, Preben Terndrup
1996-01-01
A method for analysis of the structural damage due to ship collisions is developed. The method is based on the idealized structural unit method (ISUM). Longitudinal/transverse webs which connect the outer and the inner hulls are modelled by rectangular plate units. The responses are determined...... on the stiffness and the strength is considered as well. In order to include the coupling effects between local and global failure of the structure, the usual non-linear finite-element technique is applied. In order to deal with the gap and contact conditions between the striking and the struck ships, gap......-skin plated structures in collision/grounding situations with the present solutions. As an illustrative example the procedure has been used for analyses of a side collision of a double-hull tanker. Several factors affecting ship collision response, namely the collision speed and the scantlings/ arrangements...
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)
Electron-electron scattering in linear transport in two-dimensional systems
DEFF Research Database (Denmark)
Hu, Ben Yu-Kuang; Flensberg, Karsten
1996-01-01
We describe a method for numerically incorporating electron-electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature T and density n, a symmetric matrix needs to be evaluated only...... once, and henceforth it can be used to describe electron-electron scattering in any Boltzmann equation linear-response calculation for that particular T and n. Using this method, we calculate the distribution function and mobility for electrons in a quantum well, including full finite...
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.
On the quantum Landau collision operator and electron collisions in dense plasmas
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.
A Collision-Free G2 Continuous Path-Smoothing Algorithm Using Quadratic Polynomial Interpolation
Directory of Open Access Journals (Sweden)
Seong-Ryong Chang
2014-12-01
Full Text Available Most path-planning algorithms are used to obtain a collision-free path without considering continuity. On the other hand, a continuous path is needed for stable movement. In this paper, the searched path was converted into a G2 continuous path using the modified quadratic polynomial and membership function interpolation algorithm. It is simple, unique and provides a good geometric interpretation. In addition, a collision-checking and improvement algorithm is proposed. The collision-checking algorithm can check the collisions of a smoothed path. If collisions are detected, the collision improvement algorithm modifies the collision path to a collision-free path. The collision improvement algorithm uses a geometric method. This method uses the perpendicular line between a collision position and the collision piecewise linear path. The sub-waypoint is added, and the QPMI algorithm is applied again. As a result, the collision-smoothed path is converted into a collision-free smooth path without changing the continuity.
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
International Nuclear Information System (INIS)
Alcaraz, J.
2001-01-01
After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Erickson, R.A.
1987-11-01
The final focus system of a linear collider must perform two primary functions, it must focus the two opposing beams so that their transverse dimensions at the interaction point are small enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions. In addition, the final focus system must transport the outgoing beams to a location where they can be recycled or safely dumped. Elementary optical considerations for linear collider final focus systems are discussed, followed by chromatic aberrations. The design of the final focus system of the SLAC Linear Collider (SLC) is described. Tuning and diagnostics and steering to collision are discussed. Most of the examples illustrating the concepts covered are drawn from the SLC, but the principles and conclusions are said to be generally applicable to other linear collider designs as well. 26 refs., 17 figs
Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework
Neumann, Philipp; Rohrmann, Till
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
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
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
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.
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
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
An introduction to the Boltzmann equation and transport processes in gases
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.
Border Collision Route to Quasiperiodicity: Numerical Investigation and Experimental Confirmation
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai; Mosekilde, Erik; Maity, S.
2006-01-01
Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal...... form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed...... to quasiperiodicity through a border-collision bifurcation. ©2006 American Institute of Physics...
Photon Linear Collider Gamma-Gamma Summary
International Nuclear Information System (INIS)
Gronberg, J.
2012-01-01
High energy photon - photon collisions can be achieved by adding high average power short-pulse lasers to the Linear Collider, enabling an expanded physics program for the facility. The technology required to realize a photon linear collider continues to mature. Compton back-scattering technology is being developed around the world for low energy light source applications and high average power lasers are being developed for Inertial Confinement Fusion.
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)
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)
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.
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
Physics aspects in γ-γ collision
International Nuclear Information System (INIS)
Najima, Ryuichi
1990-01-01
We investigate the possibilities of Higgs boson detection in γ-γ collision using e + e - linear colliders which are now being extensively studied at several laboratories. The cross sections of Higgs boson production and main background process are calculated and it is suggested that the reaction γγ → H → ZZ is very effective to search heavy Higgs boson in almost all the mass range from 2M Z to 1 TeV. (author)
Mass shift of charmonium states in p bar A collision
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.
Binary collision rates of relativistic thermal plasmas. I Theoretical framework
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.
Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)
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.
Towards the International Linear Collider
International Nuclear Information System (INIS)
Lopez-Fernandez, Ricardo
2006-01-01
The broad physics potential of e+e- linear colliders was recognized by the high energy physics community right after the end of LEP in 2000. In 2007, the Large Hadron Collider (LHC) now under construction at CERN will obtain its first collisions. The LHC, colliding protons with protons at 14 TeV, will discover a standard model Higgs boson over the full potential mass range, and should be sensitive to new physics into the several TeV range. The program for the Linear Collider (LC) will be set in the context of the discoveries made at the LHC. All the proposals for a Linear Collider will extend the discoveries and provide a wealth of measurements that are essential for giving deeper understanding of their meaning, and pointing the way to further evolution of particle physics in the future. For the mexican groups is the right time to join such an effort
Energy Technology Data Exchange (ETDEWEB)
Kawakami, H.; Urabe, J.; Yukimura, K. (Doshisha Univ., Kyoto (Japan))
1991-03-20
In a discharge excitation rare gas halide excima laser, uniform generation and stable maintenance of the excited discharge determines the laser characteristics. In this report, an approximate solution was obtained on the Boltzmann equation (frequently used for the theoretical analysis of this laser) to examine the nature of the solution. By optimizing the conversion of the variables, calculation of an electron swarm parameter in the hitherto uncertain range of the low conversion electric field was made possible, giving a generation mechanism of the uncertainty of the excited dischareg. The results are summarized as below. (1) The Boltzmann equation gives a linear solution for a logarithmic value of an electron energy in the range of low conversion electric field. (2) Time-wise responce ability between the measured voltage, current characteristics of the excitation discharge was clarified and the attachment and ionization coefficients calculated by Boltzmann equation. (3) Dependency of the attachment coefficient on the partial pressure of fluorine and kripton was examined, and the attachment coefficient was found to increase with the increase of the partial pressure for the both cases. 20 refs., 9 figs., 2 tabs.
DEFF Research Database (Denmark)
Loukonen, Ville; Bork, Nicolai; Vehkamaki, Hanna
2014-01-01
-principles molecular dynamics collision simulations of (sulphuric acid)1(water)0, 1 + (dimethylamine) → (sulphuric acid)1(dimethylamine)1(water)0, 1 cluster formation processes. The simulations indicate that the sticking factor in the collisions is unity: the interaction between the molecules is strong enough...... control. As a consequence, the clusters show very dynamic ion pair structure, which differs from both the static structure optimisation calculations and the equilibrium first-principles molecular dynamics simulations. In some of the simulation runs, water mediates the proton transfer by acting as a proton...... to overcome the possible initial non-optimal collision orientations. No post-collisional cluster break up is observed. The reasons for the efficient clustering are (i) the proton transfer reaction which takes place in each of the collision simulations and (ii) the subsequent competition over the proton...
Takayanagi, Kazuo
1984-01-01
Scattering phenomena play an important role in modern physics. Many significant discoveries have been made through collision experiments. Amongst diverse kinds of collision systems, this book sheds light on the collision of an electron with a molecule. The electron-molecule collision provides a basic scattering problem. It is scattering by a nonspherical, multicentered composite particle with its centers having degrees of freedom of motion. The molecule can even disintegrate, Le., dissociate or ionize into fragments, some or all of which may also be molecules. Although it is a difficult problem, the recent theoretical, experimental, and computational progress has been so significant as to warrant publication of a book that specializes in this field. The progress owes partly to technical develop ments in measurements and computations. No less important has been the great and continuing stimulus from such fields of application as astrophysics, the physics of the earth's upper atmosphere, laser physics, radiat...
1976-04-30
A simple and a more detailed mathematical model for the simulation of train collisions are presented. The study presents considerable insight as to the causes and consequences of train motions on impact. Comparison of model predictions with two full ...
International Nuclear Information System (INIS)
Burke, D.L.
1982-10-01
Studies of photon-photon collisions are reviewed with particular emphasis on new results reported to this conference. These include results on light meson spectroscopy and deep inelastic e#betta# scattering. Considerable work has now been accumulated on resonance production by #betta##betta# collisions. Preliminary high statistics studies of the photon structure function F 2 /sup #betta#/(x,Q 2 ) are given and comments are made on the problems that remain to be solved
International Nuclear Information System (INIS)
Haissinski, J.
1986-06-01
The discussions presented in this paper deal with the following points: distinctive features of gamma-gamma collisions; related processes; photon-photon elastic scattering in the continuum and γγ →gg; total cross section; γγ → V 1 V 2 (V=vector meson); radiative width measurements and light meson spectroscopy; exclusive channels at large /t/; jets and inclusive particle distribution in γγ collisions; and, the photon structure function F γ 2
Karloff, Howard
1991-01-01
To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...
Stable lattice Boltzmann model for Maxwell equations in media
Hauser, A.; Verhey, J. L.
2017-12-01
The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.
One-dimensional transient radiative transfer by lattice Boltzmann method.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2013-10-21
The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed.
Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces
Dalgamoni, Hussein; Yong, Xin
2017-11-01
Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.
Modelling viscoacoustic wave propagation with the lattice Boltzmann method.
Xia, Muming; Wang, Shucheng; Zhou, Hui; Shan, Xiaowen; Chen, Hanming; Li, Qingqing; Zhang, Qingchen
2017-08-31
In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.
Entropic Lattice Boltzmann: an implicit Large-Eddy Simulation?
Tauzin, Guillaume; Biferale, Luca; Sbragaglia, Mauro; Gupta, Abhineet; Toschi, Federico; Ehrhardt, Matthias; Bartel, Andreas
2017-11-01
We study the modeling of turbulence implied by the unconditionally stable Entropic Lattice Boltzmann Method (ELBM). We first focus on 2D homogeneous turbulence, for which we conduct numerical simulations for a wide range of relaxation times τ. For these simulations, we analyze the effective viscosity obtained by numerically differentiating the kinetic energy and enstrophy balance equations averaged over sub-domains of the computational grid. We aim at understanding the behavior of the implied sub-grid scale model and verify a formulation previously derived using Chapman-Enskog expansion. These ELBM benchmark simulations are thus useful to understand the range of validity of ELBM as a turbulence model. Finally, we will discuss an extension of the previously obtained results to the 3D case. Supported by the European Unions Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 642069 and by the European Research Council under the ERC Grant Agreement No. 339032.
Lattice Boltzmann heat transfer model for permeable voxels
Pereira, Gerald G.; Wu, Bisheng; Ahmed, Shakil
2017-12-01
We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.
High-performance reconfigurable hardware architecture for restricted Boltzmann machines.
Ly, Daniel Le; Chow, Paul
2010-11-01
Despite the popularity and success of neural networks in research, the number of resulting commercial or industrial applications has been limited. A primary cause for this lack of adoption is that neural networks are usually implemented as software running on general-purpose processors. Hence, a hardware implementation that can exploit the inherent parallelism in neural networks is desired. This paper investigates how the restricted Boltzmann machine (RBM), which is a popular type of neural network, can be mapped to a high-performance hardware architecture on field-programmable gate array (FPGA) platforms. The proposed modular framework is designed to reduce the time complexity of the computations through heavily customized hardware engines. A method to partition large RBMs into smaller congruent components is also presented, allowing the distribution of one RBM across multiple FPGA resources. The framework is tested on a platform of four Xilinx Virtex II-Pro XC2VP70 FPGAs running at 100 MHz through a variety of different configurations. The maximum performance was obtained by instantiating an RBM of 256 × 256 nodes distributed across four FPGAs, which resulted in a computational speed of 3.13 billion connection-updates-per-second and a speedup of 145-fold over an optimized C program running on a 2.8-GHz Intel processor.
Equivalence of restricted Boltzmann machines and tensor network states
Chen, Jing; Cheng, Song; Xie, Haidong; Wang, Lei; Xiang, Tao
2018-02-01
The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and customer ratings, etc. We build a bridge between RBM and tensor network states (TNS) widely used in quantum many-body physics research. We devise efficient algorithms to translate an RBM into the commonly used TNS. Conversely, we give sufficient and necessary conditions to determine whether a TNS can be transformed into an RBM of given architectures. Revealing these general and constructive connections can cross fertilize both deep learning and quantum many-body physics. Notably, by exploiting the entanglement entropy bound of TNS, we can rigorously quantify the expressive power of RBM on complex data sets. Insights into TNS and its entanglement capacity can guide the design of more powerful deep learning architectures. On the other hand, RBM can represent quantum many-body states with fewer parameters compared to TNS, which may allow more efficient classical simulations.
Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.
Li, Q; Luo, K H; Li, X J
2012-07-01
The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.
From Lattice Boltzmann to hydrodynamics in dissipative relativistic fluids
Gabbana, Alessandro; Mendoza, Miller; Succi, Sauro; Tripiccione, Raffaele
2017-11-01
Relativistic fluid dynamics is currently applied to several fields of modern physics, covering many physical scales, from astrophysics, to atomic scales (e.g. in the study of effective 2D systems such as graphene) and further down to subnuclear scales (e.g. quark-gluon plasmas). This talk focuses on recent progress in the largely debated connection between kinetic transport coefficients and macroscopic hydrodynamic parameters in dissipative relativistic fluid dynamics. We use a new relativistic Lattice Boltzmann method (RLBM), able to handle from ultra-relativistic to almost non-relativistic flows, and obtain strong evidence that the Chapman-Enskog expansion provides the correct pathway from kinetic theory to hydrodynamics. This analysis confirms recently obtained theoretical results, which can be used to obtain accurate calibrations for RLBM methods applied to realistic physics systems in the relativistic regime. Using this calibration methodology, RLBM methods are able to deliver improved physical accuracy in the simulation of the physical systems described above. European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642069.
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
Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.
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.
Strangeness in nuclear collisions
International Nuclear Information System (INIS)
Gazdzicki, M.; Roehrich, D.
1996-01-01
Data on the mean multiplicity of strange hadrons produced in minimum bias proton-proton and central nucleus-nucleus collisions at momenta between 2.8 and 400 GeV/c per nucleon have been compiled. The multiplicities for nucleon-nucleon interactions were constructed. The ratios of strange particle multiplicity to participant nucleon as well as to pion multiplicity are larger for central nucleus-nucleus collisions than for nucleon-nucleon interactions at all studied energies. The data at AGS energies suggest that the latter ratio saturates with increasing masses of the colliding nuclei. The strangeness to pion multiplicity ratio observed in nucleon-nucleon interactions increases with collision energy in the whole energy range studied. A qualitatively different behaviour is observed for central nucleus-nucleus collisions: the ratio rapidly increases when going from Dubna to AGS energies and changes little between AGS and SPS energies. This change in the behaviour can be related to the increase in the entropy production observed in central nucleus-nucleus collisions at the same energy range. The results are interpreted within a statistical approach. They are consistent with the hypothesis that the quark gluon plasma is created at SPS energies, the critical collision energy being between AGS and SPS energies. (orig.)
Dijet imbalance in hadronic collisions
International Nuclear Information System (INIS)
Boer, Danieel; Mulders, Piet J.; Pisano, Cristian
2009-01-01
The imbalance of dijets produced in hadronic collisions has been used to extract the average transverse momentum of partons inside the hadrons. In this paper we discuss new contributions to the dijet imbalance that could complicate or even hamper this extraction. They are due to polarization of initial state partons inside unpolarized hadrons that can arise in the presence of nonzero parton transverse momentum. Transversely polarized quarks and linearly polarized gluons produce specific azimuthal dependences of the two jets that in principle are not suppressed. Their effects cannot be isolated just by looking at the angular deviation from the back-to-back situation; rather they enter jet broadening observables. In this way they directly affect the extraction of the average transverse momentum of unpolarized partons that is thought to be extracted. We discuss appropriately weighted cross sections to isolate the additional contributions.
Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra
M. Khouil; N. Saber; M. Mestari
2014-01-01
In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the coll...
Linearized gyro-kinetic equation
International Nuclear Information System (INIS)
Catto, P.J.; Tsang, K.T.
1976-01-01
An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated
International Nuclear Information System (INIS)
Gelat, Pierre; Podesta, Michael de; Sutton, Gavin; Underwood, Robin; Joly, Nicolas
2009-01-01
iMERA/Euromet Project 885 is co-ordinating European effort towards a new determination of the Boltzmann constant k B to within 1 ppm with the aim of redefining the unit of thermodynamic temperature. This project will enable the National Physical Laboratory to perform primary thermometry in the region of -40 0 C (Hg) to 156 0 C (In) with sub-millikelvin uncertainties by 2012. The chosen technique relies on determining the speed of sound in a monatomic gas. Using the radial acoustic modes of a spherical resonator, consisting of a copper shell and filled with argon or helium, the speed of sound can be measured with great precision and from this measurement the Boltzmann constant can be inferred. This project draws on expertise in dimensional, density, microwave and acoustic measurements at the state-of-the-art. In order to gain further understanding of the experimental configuration a vibro-acoustic model has been developed using the finite element method. Initial calculations were carried out to ensure that predictions of the resonant frequency could be made with the required precision by comparing against an analytical model of a spherical shell filled with a gas. A more elaborate model better representing the experimental configuration was then developed. Thermo-viscous effects close to the fluid-structure boundary were accounted for using a linear acoustic formulation, from which a normal incidence admittance boundary condition was derived and imposed on the inner surface of the resonator. Acoustic pressure, particle velocity and temperature variation as a function of position may be obtained within the gas as a function of frequency. It is therefore possible to investigate how changes in the configuration affect the frequency of radial modes. It is hoped that this approach will shed a better understanding of the underlying complex physical phenomena allowing a minimization of the overall uncertainty.
Gélat, Pierre; Joly, Nicolas; de Podesta, Michael; Sutton, Gavin; Underwood, Robin
2009-11-01
iMERA/Euromet Project 885 is co-ordinating European effort towards a new determination of the Boltzmann constant kB to within 1 ppm with the aim of redefining the unit of thermodynamic temperature. This project will enable the National Physical Laboratory to perform primary thermometry in the region of -40 °C (Hg) to 156 °C (In) with sub-millikelvin uncertainties by 2012. The chosen technique relies on determining the speed of sound in a monatomic gas. Using the radial acoustic modes of a spherical resonator, consisting of a copper shell and filled with argon or helium, the speed of sound can be measured with great precision and from this measurement the Boltzmann constant can be inferred. This project draws on expertise in dimensional, density, microwave and acoustic measurements at the state-of-the-art. In order to gain further understanding of the experimental configuration a vibro-acoustic model has been developed using the finite element method. Initial calculations were carried out to ensure that predictions of the resonant frequency could be made with the required precision by comparing against an analytical model of a spherical shell filled with a gas. A more elaborate model better representing the experimental configuration was then developed. Thermo-viscous effects close to the fluid-structure boundary were accounted for using a linear acoustic formulation, from which a normal incidence admittance boundary condition was derived and imposed on the inner surface of the resonator. Acoustic pressure, particle velocity and temperature variation as a function of position may be obtained within the gas as a function of frequency. It is therefore possible to investigate how changes in the configuration affect the frequency of radial modes. It is hoped that this approach will shed a better understanding of the underlying complex physical phenomena allowing a minimization of the overall uncertainty.
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.).
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)
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
International Nuclear Information System (INIS)
Khisamutdinov, A I; Velker, N N
2014-01-01
The talk examines a system of pairwise interaction particles, which models a rarefied gas in accordance with the nonlinear Boltzmann equation, the master equations of Markov evolution of this system and corresponding numerical Monte Carlo methods. Selection of some optimal method for simulation of rarefied gas dynamics depends on the spatial size of the gas flow domain. For problems with the Knudsen number K n of order unity 'imitation', or 'continuous time', Monte Carlo methods ([2]) are quite adequate and competitive. However if K n ≤ 0.1 (the large sizes), excessive punctuality, namely, the need to see all the pairs of particles in the latter, leads to a significant increase in computational cost(complexity). We are interested in to construct the optimal methods for Boltzmann equation problems with large enough spatial sizes of the flow. Speaking of the optimal, we mean that we are talking about algorithms for parallel computation to be implemented on high-performance multi-processor computers. The characteristic property of large systems is the weak dependence of sub-parts of each other at a sufficiently small time intervals. This property is taken into account in the approximate methods using various splittings of operator of corresponding master equations. In the paper, we develop the approximate method based on the splitting of the operator of master equations system 'over groups of particles' ([7]). The essence of the method is that the system of particles is divided into spatial subparts which are modeled independently for small intervals of time, using the precise 'imitation' method. The type of splitting used is different from other well-known type 'over collisions and displacements', which is an attribute of the known Direct simulation Monte Carlo methods. The second attribute of the last ones is the grid of the 'interaction cells', which is completely absent in the imitation methods. The
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
A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
Xu, Jingjie; Lu, Benzhuo
2018-01-01
Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
International Nuclear Information System (INIS)
Berenyi, D.; Biri, S.; Gulyas, L.; Juhasz, Z.; Kover, A.; Orban, A.; Palinkas, J.; Papp, T.; Racz, R.; Ricz, S.
2009-01-01
The Section of Atomic Collisions is a research unit with extended activity in the field of atomic and molecular physics. Starting from the study of atomic processes at the beamlines of nuclear physics accelerators in the seventies, our research community became one of the centers of fundamental research in Atomki. We also have a strong connection to materials sciences especially along the line of electron and ion spectroscopy methods. Our present activity covers a wide range of topics from atomic collision mechanisms of fundamental interest, to the complex interactions of electrons, ions, photons and antiparticles with atoms, molecules, surfaces, and specific nanostructures. In the last few years, an increasing fraction of our present topics has become relevant for applications, e.g., molecular collision studies for the radiation therapy methods of tumors, or ion-nanostructure interactions for the future construction of small ion-focusing elements. Our section belongs to the Division of Atomic Physics. The other unit of the Division is the Section of Electron Spectroscopy and Materials Sciences. There are traditionally good connections and a strong collaboration between the groups of the two sections in many fields. From the very beginning of our research work in atomic collisions, external collaborations were of vital importance for us. We regularly organize international workshops in the field of fast ion-atom collisions and related small conferences in Debrecen from 1981. Recently, we organized the Conference on Radiation Damage in Biomolecular Systems (RADAM 2008, Debrecen), and coorganized the Conference on Elementary Processes in Atomic Systems (CEPAS 2008, Cluj). We have access to several large scale facilities in Europe within the framework of formal and informal collaborations. The next themes are in this article: Forward electron emission from energetic atomic collisions; Positron-atom collisions; Photon-atom interactions; Interference effects in electron
A numerical 4D Collision Risk Model
Schmitt, Pal; Culloch, Ross; Lieber, Lilian; Kregting, Louise
2017-04-01
With the growing number of marine renewable energy (MRE) devices being installed across the world, some concern has been raised about the possibility of harming mobile, marine fauna by collision. Although physical contact between a MRE device and an organism has not been reported to date, these novel sub-sea structures pose a challenge for accurately estimating collision risks as part of environmental impact assessments. Even if the animal motion is simplified to linear translation, ignoring likely evasive behaviour, the mathematical problem of establishing an impact probability is not trivial. We present a numerical algorithm to obtain such probability distributions using transient, four-dimensional simulations of a novel marine renewable device concept, Deep Green, Minesto's power plant and hereafter referred to as the 'kite' that flies in a figure-of-eight configuration. Simulations were carried out altering several configurations including kite depth, kite speed and kite trajectory while keeping the speed of the moving object constant. Since the kite assembly is defined as two parts in the model, a tether (attached to the seabed) and the kite, collision risk of each part is reported independently. By comparing the number of collisions with the number of collision-free simulations, a probability of impact for each simulated position in the cross- section of the area is considered. Results suggest that close to the bottom, where the tether amplitude is small, the path is always blocked and the impact probability is 100% as expected. However, higher up in the water column, the collision probability is twice as high in the mid line, where the tether passes twice per period than at the extremes of its trajectory. The collision probability distribution is much more complex in the upper end of the water column, where the kite and tether can simultaneously collide with the object. Results demonstrate the viability of such models, which can also incorporate empirical
Boltzmann analyses of swarm experiments over the years
Pitchford, Leanne
2013-09-01
Art Phelps was one of the ``grand old men'' in field of gaseous electronics. He was a graduate student when the GEC got started and he attended almost all of the meetings over the years. During his remarkably long career, he produced a number of the classic papers in our field as a glance at Web of Science will show. Art was my mentor and friend, and I had the privilege of working with him for many years on various topics related mainly to electron scattering and transport in weakly ionized gases. In this talk, I will discuss the originality of some of his early work on these subjects in the context of their times, focusing in particular on his publications from the mid-1960's with his colleagues from Westinghouse Research Laboratories. These report the first numerical solutions of the Boltzmann equation for electrons, to my knowledge, and they inspired much subsequent work related to the extraction of quantitative information about low-energy electron scatting with simple gases from measurements of macroscopic parameters (mobility, diffusion,..). I will outline some of the work he and I did together in this topical area using more sophisticated numerical techniques. This and other work in the field eventually led to the establishment of the ongoing GEC Plasma Data Exchange Project which now involves a number of people (the LXCat team), as discussed in Tuesday's workshop. The LXCat team had completed work on noble gases and had just started working on evaluations of cross sections for simple molecules when Art died. We are fortunate to have had his involvement on these projects. Art had ideas for future work in these areas, and some are included in a long e-mail message from Art a couple of years ago that I will share because it includes some suggestions [to the community] for future work.