Stabilizing the thermal lattice Boltzmann method by spatial filtering.

Science.gov (United States)

Gillissen, J J J

2016-10-01

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

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

CERN Document Server

Lee Tae Hun

2003-01-01

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

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.

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

International Nuclear Information System (INIS)

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

1990-01-01

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

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

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.

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

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

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

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.)

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....

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)

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

Science.gov (United States)

Pradhan, Aniruddhe; Akhavan, Rayhaneh

2017-11-01

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

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

Science.gov (United States)

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

2017-06-05

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

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis; Mouhot, Clé ment

2011-01-01

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

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis

2011-04-01

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

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

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

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

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.

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

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)

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

International Nuclear Information System (INIS)

Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki

2011-01-01

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

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

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

KAUST Repository

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

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

Linear momentum, angular momentum and energy in the linear collision between two balls

Science.gov (United States)

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.

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

MRT Lattice Boltzmann schemes for confined suspension flows

NARCIS (Netherlands)

Sman, van der R.G.M.

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-05-15

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

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

Science.gov (United States)

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-11-15

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

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

Science.gov (United States)

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

2018-06-01

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

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

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

Science.gov (United States)

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

2010-02-01

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

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

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.

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

Science.gov (United States)

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

2018-03-01

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

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

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

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...

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

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

International Nuclear Information System (INIS)

Green, B I; Vedula, Prakash

2013-01-01

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

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)

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

Science.gov (United States)

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

2018-04-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-01-15

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

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

Towards a physical interpretation of the entropic lattice Boltzmann method

Science.gov (United States)

Malaspinas, Orestis; Deville, Michel; Chopard, Bastien

2008-12-01

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

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

Science.gov (United States)

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.

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)

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

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

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Science.gov (United States)

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

Science.gov (United States)

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.

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.

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

International Nuclear Information System (INIS)

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

2006-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-05-15

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

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

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

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

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

OpenAIRE

Uphoff, Jan

2014-01-01

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

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)

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)

Celebrating Cercignani's conjecture for the Boltzmann equation

KAUST Repository

Villani, Cédric

2011-01-01

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

Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

Science.gov (United States)

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.

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

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

Science.gov (United States)

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

2017-12-01

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

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

Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants

Science.gov (United States)

Bernhoff, Niclas

2018-05-01

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

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

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

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

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.)

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

Science.gov (United States)

Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

2018-01-01

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

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

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

2013-01-01

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

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

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

Chaotic Boltzmann machines

Science.gov (United States)

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

2013-01-01

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

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 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

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

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.

Science.gov (United States)

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

2016-01-07

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

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.

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

CERN Document Server

Ginzburg, I

2003-01-01

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

Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

Science.gov (United States)

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

2006-11-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-06-01

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

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

Science.gov (United States)

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

2014-04-01

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

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

Boltzmann

International Nuclear Information System (INIS)

Lin, X.

1991-01-01

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

Three-dimensional lattice Boltzmann model for compressible flows.

Science.gov (United States)

Sun, Chenghai; Hsu, Andrew T

2003-07-01

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

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

Science.gov (United States)

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

2017-06-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-07-01

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

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

International Nuclear Information System (INIS)

Allen, P.B.; Chakraborty, B.

1981-01-01

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

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.

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

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

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

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

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

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.

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

Science.gov (United States)

Embréus, O.; Stahl, A.; Fülöp, T.

2018-02-01

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

Multiple nucleon transfer in damped nuclear collisions. [Lectures, mass charge, and linear and angular momentum transport

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.

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)

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

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.

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

International Nuclear Information System (INIS)

Wagatsuma, Kazuaki

2015-01-01

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

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)

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

Science.gov (United States)

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.

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

KAUST Repository

Neumann, Philipp

2015-09-01

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

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)

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

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

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

KAUST Repository

Neumann, Philipp

2012-01-01

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

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.

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

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.)

Kinetic theory of cross-modulation in a weakly ionized plasma

International Nuclear Information System (INIS)

Garrett, A.J.M.

1991-01-01

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

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.

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...

Gli atomi di Boltzmann

CERN Document Server

Lindley, David

2002-01-01

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

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

Science.gov (United States)

Wu, Jie; Shen, Meng; Liu, Chen

2018-04-01

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

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.

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

Lattice Boltzmann modeling an introduction for geoscientists and engineers

CERN Document Server

Sukop, Michael C

2005-01-01

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

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.

Celebrating Cercignani's conjecture for the Boltzmann equation

KAUST Repository

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

2011-01-01

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

The Boltzmann project

Science.gov (United States)

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

2018-04-01

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

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)

Multispeed models in off-lattice Boltzmann simulations

NARCIS (Netherlands)

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

2008-01-01

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

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

Science.gov (United States)

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

2017-10-01

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

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

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

Kinetic solvers with adaptive mesh in phase space

Science.gov (United States)

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

2013-12-01

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

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.

Science.gov (United States)

Bobylev, A V

2018-04-28

We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

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

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.

Fully non-linear multi-species Fokker-Planck-Landau collisions for gyrokinetic particle-in-cell simulations of fusion plasma

Science.gov (United States)

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.

An introduction to the theory of the Boltzmann equation

CERN Document Server

Harris, Stewart

2011-01-01

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

Soft-Deep Boltzmann Machines

OpenAIRE

Kiwaki, Taichi

2015-01-01

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

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...

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

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

Joint Training of Deep Boltzmann Machines

OpenAIRE

Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua

2012-01-01

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

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

Combinatorial optimization on a Boltzmann machine

NARCIS (Netherlands)

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

1989-01-01

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

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.

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.

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

International Nuclear Information System (INIS)

Nagakura, Hiroki; Sumiyoshi, Kohsuke; Yamada, Shoichi

2014-01-01

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

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)

The convergence of parallel Boltzmann machines

NARCIS (Netherlands)

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

1990-01-01

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

Parallel Boltzmann machines : a mathematical model

NARCIS (Netherlands)

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

1991-01-01

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

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)

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)

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

Science.gov (United States)

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

2017-06-01

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

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)

Exploring cluster Monte Carlo updates with Boltzmann machines.

Science.gov (United States)

Wang, Lei

2017-11-01

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

Exploring cluster Monte Carlo updates with Boltzmann machines

Science.gov (United States)

Wang, Lei

2017-11-01

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

Doubly charmed baryon production in heavy ion collisions

Science.gov (United States)

Yao, Xiaojun; Müller, Berndt

2018-04-01

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

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)

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

KAUST Repository

Ibrahem, Ahmed M.

2017-05-04

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

A note on Boltzmann brains

Energy Technology Data Exchange (ETDEWEB)

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

2015-10-07

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

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

International Nuclear Information System (INIS)

Mozolevski, I.E.

2001-01-01

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

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

KAUST Repository

Bisetti, Fabrizio; El Morsli, Mbark

2014-01-01

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

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

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

International Nuclear Information System (INIS)

Heiselberg, H.; Wang, X.

1996-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

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.)

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

Boltzmann equations for a binary one-dimensional ideal gas.

Science.gov (United States)

Boozer, A D

2011-09-01

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

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

A cryofuge for cold-collision experiments with slow polar molecules

Science.gov (United States)

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

2017-11-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Boltzmann und das Ende des mechanistischen Weltbildes

CERN Document Server

Renn, Jürgen

2007-01-01

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

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

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.

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.

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

Science.gov (United States)

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

2017-11-01

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

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.)

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.

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)

Diffusion equations and hard collisions in multiple scattering of charged particles

International Nuclear Information System (INIS)

Papiez, Lech; Tulovsky, Vladimir

1998-01-01

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

Diffusion equations and hard collisions in multiple scattering of charged particles

Energy Technology Data Exchange (ETDEWEB)

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

1998-09-01

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

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.).

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

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)

Physics of ion sputtering

International Nuclear Information System (INIS)

Robinson, M.T.

1984-04-01

The ejection of atoms by the ion bombardment of solids is discussed in terms of linear collision cascade theory. A simple argument describes the energies of the ejecta, but elaborate models are required to obtain accurate sputtering yields and related quantities. These include transport theoretical models based on linearized Boltzmann equations, computer simulation models based on the binary collision approximation, and classical many-body dynamical models. The role of each kind of model is discussed. Several aspects of sputtering are illustrated by results from the simulation code MARLOWE. 20 references, 6 figures

Boltzmann machines as a model for parallel annealing

NARCIS (Netherlands)

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

1991-01-01

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

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

Science.gov (United States)

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

2015-10-01

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

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

Science.gov (United States)

Luo, Li-Shi

1998-01-01

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

Science.gov (United States)

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.

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

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.

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

International Nuclear Information System (INIS)

Farley, David R.

2010-01-01

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

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

International Nuclear Information System (INIS)

Rohlena, K.; Ruzicka, T.

1979-01-01

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

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

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.

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

Science.gov (United States)

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

2007-03-01

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

Evaluation of an analytic linear Boltzmann transport equation solver for high-density inhomogeneities

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

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

Science.gov (United States)

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

2014-12-26

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

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

Science.gov (United States)

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

General relativistic Boltzmann equation, II: Manifestly covariant treatment

NARCIS (Netherlands)

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

2009-01-01

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

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.

Kinetic Boltzmann, Vlasov and Related Equations

CERN Document Server

Sinitsyn, Alexander; Vedenyapin, Victor

2011-01-01

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

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.

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

International Nuclear Information System (INIS)

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

2009-01-01

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

Polarised photon and flavoured lepton quantum Boltzmann equations in the early universe; Polarisierte Photon- und geflavourte Lepton-Quantenboltzmanngleichungen im fruehen Universum

Energy Technology Data Exchange (ETDEWEB)

Fidler, Christian

2011-12-16

Polarisation and Nongaussianity are expected to play a central role in future studies of the cosmic microwave background radiation. Polarisation can be split into a divergence-like E-mode and a curl-like B-mode, of which the later can only be induced by primordial gravitational waves (tensor fluctuations of the metric) at leading order. Nongaussianity is not generated at first order and is directly proportional to the primordial Nongaussianity of inflation. Thus B-mode polarisation and Nongaussianity constrain inflation models directly. While E-mode polarisation has already been detected and is being observed with increasing precision, B-mode polarisation and Nongaussianity remains elusive. The absence of B-mode polarisation when the primordial fluctuations are purely scalar holds, however, only in linear perturbation theory. B-mode polarisation is also generated from scalar sources in second order, which may constitute an important background to the search for primordial gravitational waves. While such an effect would naturally be expected to be relevant at tensor-to-scalar ratios of order 10{sup -5}, which is the size of perturbations in the microwave background, only a full second order calculation can tell whether there are no enhancements. For Nongaussianity the situation is analogous: At second order intrinsic Nongaussianities are induced to the spectrum, which may be an important background to the primordial Nongaussianity. After the full second-order Boltzmann equations for the cosmological evolution of the polarised radiation distribution have become available, I focused on the novel sources to B-mode polarisation that appear in the second-order collision term, which have not been calculated before. In my PHD thesis I developed a numerical code, which solves the second order Boltzmann hierarchy and calculates the C{sub l}{sup BB}-spectrum.

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...

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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...

Navier-Stokes Dynamics by a Discrete Boltzmann Model

Science.gov (United States)

Rubinstein, Robet

2010-01-01

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

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

International Nuclear Information System (INIS)

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

2017-01-01

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

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

International Nuclear Information System (INIS)

Schmidt, R.; Stiller, W.

1981-01-01

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

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

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

Science.gov (United States)

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

2015-10-01

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

A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

KAUST Repository

Allen, Rebecca

2013-01-01

The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

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

International Nuclear Information System (INIS)

Uphoff, Jan

2013-01-01

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

Lattice Boltzmann approach for complex nonequilibrium flows.

Science.gov (United States)

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

2015-10-01

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

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

Macroscopic plasma properties and stability theory

International Nuclear Information System (INIS)

Sakanaka, P.H.

1981-01-01

1. Two-fluid equations: (a) Boltzmann equation: complete set of equations; collision models - Vlasov, BGK, Fokker-Planck-Landau, Boltzmann. (b) Moments of the Boltzmann equation: problem of closure. (c) Two-fluid equations. 2. One-fluid equation: (a) One-fluid variables. (b) One-fluid equations: quasi-neutrality. (c) Resistive MHD equations. (d) Ideal MHD equations: one-adiabatic approximation; double-adiabatic approximation - CGL. 3. MHD stability problem - energy principle: (a) Linearized ideal MHD equations: force-operator equation. (b) Boundary conditions. (c) Self-adjointness of force operator. (d) The energy principle. 4. Stability problems: application of the energy principle; stability of sharp-boundary plasmas. 5. Thermodynamic approach for stability of plasmas: Newcomb and Rosenbluth's stability criteria. (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

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 ...

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

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

Science.gov (United States)

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

Tomography and generative training with quantum Boltzmann machines

Science.gov (United States)

Kieferová, Mária; Wiebe, Nathan

2017-12-01

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

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

Science.gov (United States)

Boozer, A. D.

2011-01-01

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

Entropy à la Boltzmann

Indian Academy of Sciences (India)

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

Axisymmetric multiphase lattice Boltzmann method for generic equations of state

NARCIS (Netherlands)

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

2016-01-01

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

Riemann-Theta Boltzmann Machine arXiv

CERN Document Server

Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

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

Cross measurements of linear momentum transfer and energy dissipation in collisions between 290 MeV 20Ne and 238U

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.)

Nuclear de-excitation processes following medium energy heavy ion collisions

International Nuclear Information System (INIS)

Blann, M.

1986-09-01

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

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

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.

On a Boltzmann-type price formation model

KAUST Repository

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

2013-01-01

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

On a Boltzmann-type price formation model

KAUST Repository

Burger, Martin

2013-06-26

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

Lattice Boltzmann simulation of droplet formation in T-junction geometries

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Gamba, Irene M.; Tharkabhushanam, Sri Harsha

2009-01-01

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

A lattice Boltzmann model for solute transport in open channel flow

Science.gov (United States)

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

2018-01-01

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

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.)

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.)

Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-07-01

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

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

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

2018-05-01

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

Classifying images using restricted Boltzmann machines and convolutional neural networks

Science.gov (United States)

Zhao, Zhijun; Xu, Tongde; Dai, Chenyu

2017-07-01

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

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

OpenAIRE

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

2010-01-01

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

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

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

2014-01-01

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

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo

2014-09-04

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

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

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)

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

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

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

International Nuclear Information System (INIS)

Suraud, E.

1990-01-01

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

On the interaction of small-scale linear waves with nonlinear solitary waves

Science.gov (United States)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow

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

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

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

Science.gov (United States)

Badino, M.

2011-11-01

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

21ST International Symposium on Rarefied Gas Dynamics, Marseille (France) 26-31 July 1998. Book of Abstracts, Volume II: Poster Sessions.

Science.gov (United States)

1998-07-30

V.L. Saveliev Institute of Ionosphere, Almaty, Kazakstan 1 Introduction function %(u) is defined by the operator of colli- sions: Last year’s steady... Saveliev V.L., Temperature and mass depen- 1). dence of the Boltzmann linear collision opera- We will call as extended collision operator the fol- tor...1817 1 IRi Sdderholm L.H. 5396 I KTM3 Saunois P. 2951 I1 IP-P Soga T. 6866 11 AA-P Saveliev V.L. 6761 11 KTM-P Soga T. 4520 I KTM5 Savin A. V. 5231 1

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

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

International Nuclear Information System (INIS)

Morel, J.E.

1987-01-01

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

Transverse and radial flow in intermediate energy nucleus-nucleus collisions

International Nuclear Information System (INIS)

Vestfall, D. Gary

1997-01-01

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

Binary collision rates of relativistic thermal plasmas. I Theoretical framework

Science.gov (United States)

Dermer, C. D.

1985-01-01

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

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

International Nuclear Information System (INIS)

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

1980-01-01

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

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

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

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

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

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

Science.gov (United States)

Daligault, Jérôme

2016-03-01

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

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

International Nuclear Information System (INIS)

Zhao, Hong; Liu, Fu-Hu

2014-01-01

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

Stabilization of the Lattice Boltzmann Method Using Information Theory

OpenAIRE

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

2018-01-01

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

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.)

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

International Nuclear Information System (INIS)

Charles, F.

2009-11-01

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

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

International Nuclear Information System (INIS)

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

2010-01-01

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

Stanford's linear collider

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).

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

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

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

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...

Boltzmann Oracle for Combinatorial Systems

OpenAIRE

Pivoteau , Carine; Salvy , Bruno; Soria , Michèle

2008-01-01

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

Thermal transport in isotopically disordered carbon nanotubes: a comparison between Green's functions and Boltzmann approaches

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.

Entropic multirelaxation lattice Boltzmann models for turbulent flows

Science.gov (United States)

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

2015-10-01

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

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

Science.gov (United States)

Pradipto; Purqon, Acep

2017-07-01

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

Boltzmann machines for travelling salesman problems

NARCIS (Netherlands)

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

1989-01-01

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

Anisotropy and linear polarization of radiative processes in energetic ion-atom collisions; Untersuchung zur Anisotropie und linearen Polarisation radiativer Prozesse in energiereichen Ion-Atom-Stoessen

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.)

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.

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.)

Nonequilibrium thermodynamics of restricted Boltzmann machines

Science.gov (United States)

Salazar, Domingos S. P.

2017-08-01

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

Nonequilibrium thermodynamics of restricted Boltzmann machines.

Science.gov (United States)

Salazar, Domingos S P

2017-08-01

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

Recursive regularization step for high-order lattice Boltzmann methods

Science.gov (United States)

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

2017-09-01

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

Mass shift of charmonium states in p bar A collision

Science.gov (United States)

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

2018-05-01

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

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

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

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

Tsallis-Pareto like distributions in hadron-hadron collisions

International Nuclear Information System (INIS)

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

2011-01-01

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

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

Science.gov (United States)

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

2017-07-01

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

Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach

Science.gov (United States)

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.

Collision cross section calculations for polyatomic ions considering rotating diatomic/linear gas molecules

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

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.

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

International Nuclear Information System (INIS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

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

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

Science.gov (United States)

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

2017-10-01

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

Electron attachment coefficient in low E/N regions and a discussion of discharge-instability in KrF laser. ; Analysis by logarithm transformed Boltzmann equation. Tei E/N ryoiki no denshi fuchaku keisu to KrF laser reiki hoden no fuanteisei ni kansuru ichi kosatsu. ; Tai su henkan Boltzmann hoteishiki ni yoru kaiseki

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.

Collision Based Blood Cell Distribution of the Blood Flow

Science.gov (United States)

Cinar, Yildirim

2003-11-01

Introduction: The goal of the study is the determination of the energy transferring process between colliding masses and the application of the results to the distribution of the cell, velocity and kinetic energy in arterial blood flow. Methods: Mathematical methods and models were used to explain the collision between two moving systems, and the distribution of linear momentum, rectilinear velocity, and kinetic energy in a collision. Results: According to decrease of mass of the second system, the velocity and momentum of constant mass of the first system are decreased, and linearly decreasing mass of the second system captures a larger amount of the kinetic energy and the rectilinear velocity of the collision system on a logarithmic scale. Discussion: The cause of concentration of blood cells at the center of blood flow an artery is not explained by Bernoulli principle alone but the kinetic energy and velocity distribution due to collision between the big mass of the arterial wall and the small mass of blood cells must be considered as well.

A topological insight into restricted Boltzmann machines

NARCIS (Netherlands)

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

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

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

Science.gov (United States)

Kwang-Hua, Chu Rainer

2018-05-01

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

CLIC: developing a linear collider

CERN Multimedia

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.

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...

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

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...

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

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

Multiple electron capture in close ion-atom collisions

International Nuclear Information System (INIS)

Schlachter, A.S.; Stearns, J.W.; Berkner, K.H.

1989-01-01

Collisions in which a fast highly charged ion passes within the orbit of K electron of a target gas atom are selected by emission of a K x-ray from the projectile or target. Measurement of the projectile charge state after the collision, in coincidence with the K x-ray, allows measurement of the charge-transfer probability during these close collisions. When the projectile velocity is approximately the same as that of target electrons, a large number of electrons can be transferred to the projectile in a single collision. The electron-capture probability is found to be a linear function of the number of vacancies in the projectile L shell for 47-MeV calcium ions in an Ar target. 18 refs., 9 figs

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

Non-linear unidimensional Debye screening in plasmas

International Nuclear Information System (INIS)

Clemente, R.A.; Martin, P.

1992-01-01

An exact analytical solution for T e = T i and an approximate solution for T e ≠ T i have been obtained for the unidimensional non-linear Debye potential. The approximate expression is a solution of the Poisson equation obtained by expanding up to third order the Boltzmann's factors. The analysis shows that the effective Debye screening length can be quite different from the usual Debye length, when the potential to thermal energy ratio of the particles is not much smaller than unity. (author)

Generalized Stefan-Boltzmann Law

Science.gov (United States)

Montambaux, Gilles

2018-03-01

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

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

Directory of Open Access Journals (Sweden)

Muneki Yasuda

2018-04-01

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

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.

almaBTE : A solver of the space-time dependent Boltzmann transport equation for phonons in structured materials

Science.gov (United States)

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

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

International Nuclear Information System (INIS)

Gan Yanbiao; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

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

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

Science.gov (United States)

Berglund, Mathias; Raiko, Tapani; Cho, Kyunghyun

2015-04-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-15

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

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 ...

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

CERN Document Server

Darrigol, Olivier

2018-01-01

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

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

Science.gov (United States)

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

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

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.

Linear electrostatic waves in a three-component electron-positron-ion plasma

Energy Technology Data Exchange (ETDEWEB)

Mugemana, A., E-mail: mugemanaa@gmail.com; Moolla, S. [School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000 (South Africa); Lazarus, I. J. [Department of Mathematics, Statistics and Physics, Durban University of Technology, Durban 4000 (South Africa)

2014-12-15

Analytical linear electrostatic waves in a magnetized three-component electron-positron-ion plasma are studied in the low-frequency limit. By using the continuity and momentum equations with Poisson's equation, the dispersion relation for the electron-positron-ion plasma consisting of cool ions, and hot Boltzmann electrons and positrons is derived. In the linear regime, the propagation of two possible modes and their evolution are studied. In the cases of parallel and perpendicular propagation, it is shown that these two possible modes are always stable. The present investigation contributes to nonlinear propagation of electrostatic waves in space and the laboratory.

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

International Nuclear Information System (INIS)

Bartolomaeus, G.; Wilhelm, J.

1983-01-01

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

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

DEFF Research Database (Denmark)

Pingen, Georg; Evgrafov, Anton; Maute, Kurt

2009-01-01

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

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

Emission characteristics of 6.78-MHz radio-frequency glow discharge plasma in a pulsed mode

Science.gov (United States)

Zhang, Xinyue; Wagatsuma, Kazuaki

2017-07-01

This paper investigated Boltzmann plots for both atomic and ionic emission lines of iron in an argon glow discharge plasma driven by 6.78-MHz radio-frequency (RF) voltage in a pulsed operation, in order to discuss how the excitation/ionization process was affected by the pulsation. For this purpose, a pulse frequency as well as a duty ratio of the pulsed RF voltage was selected as the experimenter parameters. A Grimm-style radiation source was employed at a forward RF power of 70 W and at an argon pressures of 670 Pa. The Boltzmann plot for low-lying excited levels of iron atom was on a linear relationship, which was probably attributed to thermal collisions with ultimate electrons in the negative glow region; in this case, the excitation temperature was obtained in a narrow range of 3300-3400 K, which was hardly affected by the duty ratio as well as the pulse frequency of the pulsed RF glow discharge plasma. This observation suggested that the RF plasma could be supported by a self-stabilized negative glow region, where the kinetic energy distribution of the electrons would be changed to a lesser extent. Additional non-thermal excitation processes, such as a Penning-type collision and a charge-transfer collision, led to deviations (overpopulation) of particular energy levels of iron atom or iron ion from the normal Boltzmann distribution. However, their contributions to the overall excitation/ionization were not altered so greatly, when the pulse frequency or the duty ratio was varied in the pulsed RF glow discharge plasma.

Ab initio optical potentials applied to low-energy e-H2 and e-N2 collisions in the linear-algebraic approach

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

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...

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

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

DEFF Research Database (Denmark)

Svec, Oldrich; Skoček, Jan

2013-01-01

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

Lattice gas cellular automata and lattice Boltzmann models an introduction

CERN Document Server

Wolf-Gladrow, Dieter A

2000-01-01

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

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

International Nuclear Information System (INIS)

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

2002-01-01

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

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

International Nuclear Information System (INIS)

Bang, Jin Young; Chung, Chin Wook

2009-01-01

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

Perturbation theory and collision probability formalism. Vol. 2

Energy Technology Data Exchange (ETDEWEB)

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

1996-03-01

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

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

Science.gov (United States)

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

2012-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Schade, Henry

2010-09-15

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

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

NARCIS (Netherlands)

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

2011-01-01

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

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

Science.gov (United States)

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

2018-03-05

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

Direct Probes of Linearly Polarized Gluons inside Unpolarized Hadrons

NARCIS (Netherlands)

Boer, D.; Brodsky, S. J.; Mulders, P.J.G.; Pisano, C.

2011-01-01

We show that linearly polarized gluons inside unpolarized hadrons can be directly probed in jet or heavy quark pair production in electron-hadron collisions. We discuss the simplest cos2 asymmetries and estimate their maximal value, concluding that measurements of the unknown linearly polarized

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

Structure formation with massive neutrinos. Going beyond linear theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas; Lesgourgues, Julien; Institut de Theorie Phenomenes Physiques EPFL, Lausanne; Savoie Univ., CNRS, Annecy-le-Vieux

2014-08-01

We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.

Structure formation with massive neutrinos: going beyond linear theory

CERN Document Server

Blas, Diego; Konstandin, Thomas; Lesgourgues, Julien

2014-01-01

We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.

Contact angle determination in multicomponent lattice Boltzmann simultations

NARCIS (Netherlands)

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

2011-01-01

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

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...

Convection-diffusion lattice Boltzmann scheme for irregular lattices

NARCIS (Netherlands)

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

2000-01-01

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

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.

Transport coefficients of gaseous ions in an electric field

Science.gov (United States)

Whealton, J. H.; Mason, E. A.

1974-01-01

A general theory of ion mobility formulated by Kihara (1953) is extended to ion diffusion and to mixtures of neutral gases. The theory assumes that only binary collisions between ions and neutral particles need to be taken into account and that the velocity distribution function of the neutral particles is Maxwellian. These assumptions make it possible to use a linearized Boltzmann equation. Questions of mobility are considered along with aspects of diffusion and deviations from Fick's law of diffusion.

Hyperthermal (10-500 eV) collisions of noble gases with Ni(100) surface. Comparison between light and heavy atom collisions

International Nuclear Information System (INIS)

Kim, C.

1995-01-01

Collisional events between 10-500 eV atomic beams (He, Ne, Ar, Kr, and Xe) and a Ni(100) surface are investigated by the classical trajectory method. The calculation employs a molecular dynamics approach combined with a Langevin method for treating energy dissipation to infinite solid. We find that low energy collisions of heavy atoms (Xe and Kr) are characterized by extensive many-body interactions with top layer surface atoms. On the other hand, light atom (Ne and He) collisions can be approximated as a sequence of binary collisions even at these energies. Such a difference in the collisional nature gives rise to the following consequences. Low energy heavy atoms transfer energy mostly to the surface atoms during 45 angle collision. They scatter from the surface with a narrow angular distribution centered in a supraspecular direction. The ratio of the scattered to incident particle energy rapidly decreases with increasing beam energy of heavy atoms. The sputtering yield for Ni atoms by heavy atom bombardment increases quite linearly with beam energy, which is attributed to a linear proportionality between the beam energy and the energy transfered to a surface. Near the threshold energy sputtering can occur more efficiently by light atom bombardment. The energy transfer ratio to solid continuously increases with beam energy for light atoms. For heavy projectiles, on the other hand, this ratio reaches a maximum at the energy of ca, 100 eV, above which it stays nearly constant but slightly decreases. ((orig.))

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

International Nuclear Information System (INIS)

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

1992-01-01

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

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

International Nuclear Information System (INIS)

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

2001-01-01

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

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

On the quantum dynamical foundations of collision terms

International Nuclear Information System (INIS)

Nemes, M.C.; Toledo Piza, A.F.R. de

1981-08-01

Collision terms are non-unitary corrections usually added to mean field descriptions in order to describe dissipative effects. Derivations of collision terms usually include assumptions which lack an explicit connection with a fully quantum dynamical description. Quantum dynamical foundations of collision terms are examined: they are shown to reflect the dynamics of quantum correlations. A careful study of the non-unitary aspects of the evolution of quantum correlations leads naturally to an unambiguous definition of a collision term. This collision term is shown to obey a non-linear pre-master equation, whose derivation is fully quantum-mechanical. Moreover, it is shown that quantum correlations also yield an unitary correction to the mean field description, which could be absorbed in a suitable redefinition of the mean field. Formal expressions for these corrections are derived and their connection with memory effects exhibited explicitely. The typical time of evaluation of quantum correlations allows for an analytical expression for the 'lifetime of mean field descriptions'. Finally, a quantum mechanical point of view for 'irreversibility' in deep inelastic is discussed. (Author) [pt

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)

Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

OpenAIRE

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...

Transitions from phase-locked dynamics to chaos in a piecewise-linear map

DEFF Research Database (Denmark)

Zhusubaliyev, Z.T.; Mosekilde, Erik; De, S.

2008-01-01

place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic...

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

International Nuclear Information System (INIS)

Kim, In Chan

2000-01-01

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

Diffusion on unstructured triangular grids using Lattice Boltzmann

NARCIS (Netherlands)

Sman, van der R.G.M.

2004-01-01

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

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Science.gov (United States)

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 .

Analysis and manipulation of atomic and molecular collisions using laser light

International Nuclear Information System (INIS)

Grimpe, A.

2006-01-01

Optical collisions in a crossed beam experiment are examined for the atomic collision pairs LiHe, LiNe, NaNe. Differential cross sections are measured in order to probe the quality of quantum chemical calculated and spectroscopical determined molecular potentials. The linear polarization of the excitation laser is used to manipulate the contrast of the differential cross sections for NaNe. Using elliptical polarized light total control over the angular position and the contrast of the interference pattern is demonstrated. Differential cross sections for the collision pairs LiH 2 and LiD 2 show a pronounced oscillatory structure, which for the first time is observed for atom-molecule optical collisions. (orig.)

Polarization and collision velocity dependence of associative ionization in cold Na (3p)-Na(3p) collisions

NARCIS (Netherlands)

Meijer, H.A.J.

1990-01-01

We studied the polarization dependence of the associative ionization (AI) process Na(3p) + Na(3p) → Na2+ at collision velocities between 100 and 700 m/s (5 and 200 K), using linearly and circularly polarized light for the excitation. We found that the polarization dependence varies strongly in the

Comparison of Einstein-Boltzmann solvers for testing general relativity

Science.gov (United States)

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

2018-01-01

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

Lattice Boltzmann model for three-phase viscoelastic fluid flow

Science.gov (United States)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

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

Excite fermions in polarized eγ collisions

International Nuclear Information System (INIS)

Eboli, O.J.P.

1994-01-01

We investigate some consequences of excite leptons with 1/2 and 3/2 spins predicted by compound models in eγ collisions. Also we examine the possibility of the next generation of linear accelerators, with polarized beams, to provide information on the spin and these particle coupling

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

DEFF Research Database (Denmark)

Matin, Rastin

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

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

Directory of Open Access Journals (Sweden)

Florian Thüroff

2014-11-01

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

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 ...

Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase I

Data.gov (United States)

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

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

Science.gov (United States)

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

2018-01-01

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

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...

Lattice Boltzmann scheme for diffusion on triangular grids

NARCIS (Netherlands)

Sman, van der R.G.M.

2003-01-01

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

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

International Nuclear Information System (INIS)

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

1983-09-01

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

Photon-Photon Collisions -- Past and Future

International Nuclear Information System (INIS)

Brodsky, Stanley J.

2005-01-01

I give a brief review of the history of photon-photon physics and a survey of its potential at future electron-positron colliders. Exclusive hadron production processes in photon-photon and electron-photon collisions provide important tests of QCD at the amplitude level, particularly as measures of hadron distribution amplitudes. There are also important high energy γγ and eγ tests of quantum chromodynamics, including the production of jets in photon-photon collisions, deeply virtual Compton scattering on a photon target, and leading-twist single-spin asymmetries for a photon polarized normal to a production plane. Since photons couple directly to all fundamental fields carrying the electromagnetic current including leptons, quarks, W's and supersymmetric particles, high energy γγ collisions will provide a comprehensive laboratory for Higgs production and exploring virtually every aspect of the Standard Model and its extensions. High energy back-scattered laser beams will thus greatly extend the range of physics of the International Linear Collider

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

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 ...

A topological insight into restricted Boltzmann machines (extented abstract)

NARCIS (Netherlands)

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

2016-01-01

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

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

Science.gov (United States)

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

2006-03-01

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

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

Science.gov (United States)

Meng, Xuhui; Guo, Zhaoli

2015-10-01

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

A new kinetic description for turbulent collisions including mode-coupling

International Nuclear Information System (INIS)

Misguich, J.H.; Tchen, C.M.

1982-07-01

The usual introduction of higher-order mode-coupling terms in the description of turbulent collisions beyond usual Renormalized Quasi-Linear approximation (RQL) is briefly analyzed. Here new results are derived in the framework of the general kinetic theory, and the equivalence is proved with the long time limit of simple results deduced from the Vlasov equation. The correction to the RQL turbulent collision term is analyzed and a new approximation is proposed. Turbulent collisions are also described by perturbation around the Lagrangian autocorrelation of fluctuating fields. For an homogeneous turbulence, however, the asymptotic integral of this Lagrangian autocorrelation vanishes identically, similarly to what occurs in Brownian motion. For inhomogeneous turbulence this method can nevertheless be used, and higher-order mode-coupling terms can be interpreted as a shielding of elementary Lagrangian turbulent collisions

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

International Nuclear Information System (INIS)

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

2011-01-01

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

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...

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

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

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.

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)

Linear and nonlinear verification of gyrokinetic microstability codes

Science.gov (United States)

Bravenec, R. V.; Candy, J.; Barnes, M.; Holland, C.

2011-12-01

Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set of parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2 [W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of

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

International Nuclear Information System (INIS)

Jin Licong; Zhang Xinrong; Niu Xiaodong

2012-01-01

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

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

International Nuclear Information System (INIS)

Peter, J.

1990-10-01

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

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

DEFF Research Database (Denmark)

van Tulder, Gijs; de Bruijne, Marleen

2016-01-01

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

Measuring Boltzmann's Constant with Carbon Dioxide

Science.gov (United States)

Ivanov, Dragia; Nikolov, Stefan

2013-01-01

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

Lattice Boltzmann method fundamentals and engineering applications with computer codes

CERN Document Server

Mohamad, A A

2014-01-01

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

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

Lattice-Boltzmann simulation of the sedimentation of charged disks

NARCIS (Netherlands)

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

2006-01-01

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

Convection in multiphase fluid flows using lattice Boltzmann methods

NARCIS (Netherlands)

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

2012-01-01

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

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-06-01

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

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

Science.gov (United States)

2013-03-01

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

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

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)

Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

DEFF Research Database (Denmark)

Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

2015-01-01

A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall. It is sh......A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall...

Covariant transport theory

Energy Technology Data Exchange (ETDEWEB)

Pang, Yang [Columbia Univ., New York, NY (United States)]|[Brookhaven National Labs., Upton, NY (United States)

1997-09-22

Many phenomenological models for relativistic heavy ion collisions share a common framework - the relativistic Boltzmann equations. Within this framework, a nucleus-nucleus collision is described by the evolution of phase-space distributions of several species of particles. The equations can be effectively solved with the cascade algorithm by sampling each phase-space distribution with points, i.e. {delta}-functions, and by treating the interaction terms as collisions of these points. In between collisions, each point travels on a straight line trajectory. In most implementations of the cascade algorithm, each physical particle, e.g. a hadron or a quark, is often represented by one point. Thus, the cross-section for a collision of two points is just the cross-section of the physical particles, which can be quite large compared to the local density of the system. For an ultra-relativistic nucleus-nucleus collision, this could lead to a large violation of the Lorentz invariance. By using the invariance property of the Boltzmann equation under a scale transformation, a Lorentz invariant cascade algorithm can be obtained. The General Cascade Program - GCP - is a tool for solving the relativistic Boltzmann equation with any number of particle species and very general interactions with the cascade algorithm.

Transverse energy distribution and hard constituent scattering in hadronic collisions

Directory of Open Access Journals (Sweden)

Torsten Åkesson

1983-01-01

Full Text Available We estimate the contributions to the total transverse energy spectrum from hard constituent scattering and the soft hadronic spectrum in hadron collisions. The transverse energy at which jet production starts to dominate is found to be essentially independent of the cms-energy (for large enough s and roughly a linear function of rapidity and azimuthal angle interval included. Calculations are presented for pp collisions at s= 25and60GeV, andp¯p interactions at s= 540GeV.

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

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.

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

Jet-induced medium excitation in heavy-ion collisions

Energy Technology Data Exchange (ETDEWEB)

Chen, Wei [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Pang, Long-Gang [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany); Stoecker, Horst [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany); Gesellschaft für Schwehrionenforschung, Planckstr. 1, Darmstadt (Germany); Luo, Tan; 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 a Linear Boltzmann Transport (LBT) model coupled to the (3+1)D ideal hydrodynamic evolution in real time with fluctuating initial conditions to simulate both the transport of jet shower partons and jet-induced medium excitation. In this coupled approach, propagation of energetic shower partons are treated in the LBT model with the 3+1D hydrodynamic model providing the evolving bulk medium. Soft partons from both elastic and inelastic processes in the LBT are fed back into the medium as a source term in the 3+1D hydrodynamics leading to induced medium excitation. We study the effect of jet-induced medium excitation via γ-hadron correlation within this coupled LBT-hydro (CoLBT-hydro) approach.

Acoustic levitation and the Boltzmann-Ehrenfest principle

Science.gov (United States)

Putterman, S.; Rudnick, Joseph; Barmatz, M.

1989-01-01

The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.

Implementation of the Lattice Boltzmann Method on Heterogeneous Hardware and Platforms using OpenCL

Directory of Open Access Journals (Sweden)

TEKIC, P. M.

2012-02-01

Full Text Available The Lattice Boltzmann method (LBM has become an alternative method for computational fluid dynamics with a wide range of applications. Besides its numerical stability and accuracy, one of the major advantages of LBM is its relatively easy parallelization and, hence, it is especially well fitted to many-core hardware as graphics processing units (GPU. The majority of work concerning LBM implementation on GPU's has used the CUDA programming model, supported exclusively by NVIDIA. Recently, the open standard for parallel programming of heterogeneous systems (OpenCL has been introduced. OpenCL standard matures and is supported on processors from most vendors. In this paper, we make use of the OpenCL framework for the lattice Boltzmann method simulation, using hardware accelerators - AMD ATI Radeon GPU, AMD Dual-Core CPU and NVIDIA GeForce GPU's. Application has been developed using a combination of Java and OpenCL programming languages. Java bindings for OpenCL have been utilized. This approach offers the benefits of hardware and operating system independence, as well as speeding up of lattice Boltzmann algorithm. It has been showed that the developed lattice Boltzmann source code can be executed without modification on all of the used hardware accelerators. Performance results have been presented and compared for the hardware accelerators that have been utilized.

Student learning of upper-level thermal and statistical physics: The derivation and use of the Boltzmann factor

Science.gov (United States)

Thompson, John

2015-04-01

As the Physical Review Focused Collection demonstrates, recent frontiers in physics education research include systematic investigations at the upper division. As part of a collaborative project, we have examined student understanding of several topics in upper-division thermal and statistical physics. A fruitful context for research is the Boltzmann factor in statistical mechanics: the standard derivation involves several physically justified mathematical steps as well as the invocation of a Taylor series expansion. We have investigated student understanding of the physical significance of the Boltzmann factor as well as its utility in various circumstances, and identified various lines of student reasoning related to the use of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students do not use the Boltzmann factor when answering questions related to probability in applicable physical situations, even after lecture instruction. We designed an inquiry-based tutorial activity to guide students through a derivation of the Boltzmann factor and to encourage deep connections between the physical quantities involved and the mathematics. Observations of students working through the tutorial suggest that many students at this level can recognize and interpret Taylor series expansions, but they often lack fluency in creating and using Taylor series appropriately, despite previous exposure in both calculus and physics courses. Our findings also suggest that tutorial participation not only increases the prevalence of relevant invocation of the Boltzmann factor, but also helps students gain an appreciation of the physical implications and meaning of the mathematical formalism behind the formula. Supported in part by NSF Grants DUE-0817282, DUE-0837214, and DUE-1323426.

Modelling of a collision between two smartphones

Science.gov (United States)

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.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

Science.gov (United States)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)

2010-09-15

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)

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

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

Jeans instability in collisional strongly coupled dusty plasma with radiative condensation and polarization force

International Nuclear Information System (INIS)

Prajapati, R. P.; Bhakta, S.; Chhajlani, R. K.

2016-01-01

The influence of dust-neutral collisions, polarization force, and electron radiative condensation is analysed on the Jeans (gravitational) instability of partially ionized strongly coupled dusty plasma (SCDP) using linear perturbation (normal mode) analysis. The Boltzmann distributed ions, dynamics of inertialess electrons, charged dust and neutral particles are considered. Using the plane wave solutions, a general dispersion relation is derived which is modified due to the presence of dust-neutral collisions, strong coupling effect, polarization force, electron radiative condensation, and Jeans dust/neutral frequencies. In the long wavelength perturbations, the Jeans instability criterion depends upon strong coupling effect, polarization interaction parameter, and thermal loss, but it is independent of dust-neutral collision frequency. The stability of the considered configuration is analysed using the Routh–Hurwitz criterion. The growth rates of Jeans instability are illustrated, and stabilizing influence of viscoelasticity and dust-neutral collision frequency while destabilizing effect of electron radiative condensation, polarization force, and Jeans dust-neutral frequency ratio is observed. This work is applied to understand the gravitational collapse of SCDP with dust-neutral collisions.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

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....

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

Science.gov (United States)

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.

Lattice-Boltzmann scheme for natural convection in porous media

NARCIS (Netherlands)

Sman, van der R.G.M.

1997-01-01

A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore

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

Science.gov (United States)

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

2017-12-01

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

Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

International Nuclear Information System (INIS)

Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat

2015-01-01

Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)

A lattice Boltzmann coupled to finite volumes method for solving phase change problems

Directory of Open Access Journals (Sweden)

El Ganaoui Mohammed

2009-01-01

Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

Energy Technology Data Exchange (ETDEWEB)

Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)

2011-04-08

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

International Nuclear Information System (INIS)

Uchaikin, V V; Sibatov, R T

2011-01-01

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

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

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.

A numerical 4D Collision Risk Model

Science.gov (United States)

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

Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem.

Science.gov (United States)

Frausto-Solis, Juan; Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J Javier; González-Flores, Carlos; Castilla-Valdez, Guadalupe

2016-01-01

A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

DEFF Research Database (Denmark)

Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S.

2007-01-01

compute the viscosity. This paper presents a modified parallel plate rheometer, and proposes means of calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus using an accurate numerical solution in place...

Kinetic coefficients for quark-antiquark plasma

International Nuclear Information System (INIS)

Czyz, W.; Florkowski, W.

1986-03-01

The quark-antiquark plasma near equilibrium is studied. The results are based on the Heinz kinetic equations with the Boltzmann collision operator approximated by a relaxation term with the relaxation time, τ, treated as a small parameter. Linear in τ solutions of these equations are used to calculate the transport coefficients: the non-abelian version of Ohm's law, and the shear and volume viscosities. We introduce new chemical potentials which determine the color density matrix of quarks (antiquarks). Gradients of these potentials generate color currents. 12 refs. (author)

Heterotic Pomeron: high energy hadronic collisions in QCD

International Nuclear Information System (INIS)

Chung-I Tan

1993-01-01

A unified treatment of high energy collisions in QCD is presented. Using a probabilistic approach, both perturbative (hard) and non-perturbative (soft) components are incorporated in a consistent fashion, leading to a ''Heterotic Pomeron''. As a Regge trajectory, it is non linear, approaching 1 in the limit t → -∞. 2 tabs., 9 refs

Photon-photon collisions

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

Integrated trajectory control and collision avoidance for automated driving

NARCIS (Netherlands)

Verhaegh, J.; Ploeg, J.; Nunen, E. van; Teerhuis, A.

2017-01-01

This paper presents a method for trajectory control, based on feedback linearization to guide an Automatic Guided Vehicle (AGV). The novelty of this work, is the adaptation of a reference trajectory with respect to a desired velocity in real-time to avoid collisions using a time-scaling mechanism.

Lattice Boltzmann simulation of behaviour of particles moving in blood vessels under the rolling massage

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)

Generalized Boltzmann equations for on-shell particle production in a hot plasma

International Nuclear Information System (INIS)

Jakovac, A.

2002-01-01

A novel refinement of the conventional treatment of Kadanoff-Baym equations is suggested. In addition to the Boltzmann equation, another differential equation is used for calculating the evolution of the nonequilibrium two-point function. Although it was usually interpreted as a constraint on the solution of the Boltzmann equation, we argue that its dynamics is relevant to the determination and resummation of the particle production cut contributions. The differential equation for this new contribution is illustrated in the example of the cubic scalar model. The analogue of the relaxation time approximation is suggested. It results in the shift of the threshold location and in a smearing out of the nonanalytic threshold behavior of the spectral function. The possible consequences for the dilepton production are discussed

Time-independent lattice Boltzmann method calculation of hydrodynamic interactions between two particles

Science.gov (United States)

Ding, E. J.

2015-06-01

The time-independent lattice Boltzmann algorithm (TILBA) is developed to calculate the hydrodynamic interactions between two particles in a Stokes flow. The TILBA is distinguished from the traditional lattice Boltzmann method in that a background matrix (BGM) is generated prior to the calculation. The BGM, once prepared, can be reused for calculations for different scenarios, and the computational cost for each such calculation will be significantly reduced. The advantage of the TILBA is that it is easy to code and can be applied to any particle shape without complicated implementation, and the computational cost is independent of the shape of the particle. The TILBA is validated and shown to be accurate by comparing calculation results obtained from the TILBA to analytical or numerical solutions for certain problems.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

CERN Document Server

Farhat, Hassan; Kondaraju, Sasidhar

2014-01-01

Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

NARCIS (Netherlands)

Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

2018-01-01

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute

Numerical analysis of energy density and particle density in high energy heavy-ion collisions

International Nuclear Information System (INIS)

Fu Yuanyong; Lu Zhongdao

2004-01-01

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared. The results show that Gauss-Laguerre formulas is a good method in calculations of high energy heavy-ion collisions. (author)

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

International Nuclear Information System (INIS)

Lind, R.C.

1973-01-01

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Fakhari, Abbas, E-mail: afakhari@nd.edu [Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556 (United States); Geier, Martin [TU Braunschweig, Institute for Computational Modeling in Civil Engineering (iRMB), TU-Braunschweig, Pockelsstr. 3, 38106 Braunschweig (Germany); Lee, Taehun [Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031 (United States)

2016-06-15

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

International Nuclear Information System (INIS)

Fakhari, Abbas; Geier, Martin; Lee, Taehun

2016-01-01

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

Podolsky electromagnetism at finite temperature: Implications on the Stefan-Boltzmann law

International Nuclear Information System (INIS)

Bonin, C. A.; Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.

2010-01-01

In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.

An introduction to the Boltzmann equation and transport processes in gases

CERN Document Server

Kremer, Gilberto M; Colton, David

2010-01-01

This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

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)

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

Energy Technology Data Exchange (ETDEWEB)

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

1960-07-01

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

Nonlinear effect of pion production in collisions of atomic nuclei

International Nuclear Information System (INIS)

Grin', Yu.T.

1982-01-01

The phenomenon of pion production in relativistic nucleon-nucleus and nucleus-nucleus interactions is investigated. The present experimental data are analyzed. It is shown that average multiplicity of pions in the (p, C), (C, C) collision reactions with the momentum p=4.2 GeV/cA and (p, Ar), (Ar, KCl) with the momentum p=2.3 GeV/cA non-linearly depends on the nucleon number. The calculated values of average multiplicity of negative pions per one nucleon of nucleus-pro ectile, probability of pion production and number of nucleon interactions for the investigated reactions are presented as a table. A comparative analysis of average multiplicities of pions per nucleon-participant in the nucleon-nucleus and nucleus-nucleus reactions at the p=2.3 GeV/cA momentum for argon and at the p=4.2 GeV/cA for carbon reveals that decrease of multiplicity by 30-35% is observed in nucleus-nucleus collision. Non-linearity is associated with decrease of effective interaction of each incident nucleon in the collision of nuclei as compared with the number of nucleon interactions in the ''elementary'' nucleon-nucleus reaction. Knock-out of nucleons from the colliding nuclei is the most probable reason for the decrease of the number of interactions

Disoriented Chiral Condensates in High-Energy Nuclear Collisions

Energy Technology Data Exchange (ETDEWEB)

Randrup, Jorgen

2000-10-18

This brief lecture series discusses how our current understanding of chiral symmetry may be tested more globally in high-energy nuclear collisions by suitable extraction of pionic observables. After briefly recalling the general features of chiral symmetry, we focus on the SU(2) linear sigma model and show how a semi-classical mean-field treatment makes it possible to calculate its statistical properties, including the chiral phase diagram. Subsequently, we consider scenarios of relevance to high-energy collisions and discuss the features of the ensuing non-equilibrium dynamics and the associated characteristic signals. Finally, we illustrate how the presence of vacuum fluctuations or the inclusion of strangeness may affect the results quantitatively.

Discrepant Results in a 2-D Marble Collision

Science.gov (United States)

Kalajian, Peter

2013-01-01

Video analysis of 2-D collisions is an excellent way to investigate conservation of linear momentum. The often-desired experimental design goal is to minimize the momentum loss in order to demonstrate the conservation law. An air table with colliding pucks is an ideal medium for this experiment, but such equipment is beyond the budget of many…

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)

The SLAC linear collider

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

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

Science.gov (United States)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

Electroproduction of pairs at beam-beam collision

International Nuclear Information System (INIS)

Bajer, V.N.; Katkov, V.M.; Strakhovenko, V.M.

1989-01-01

Charged particle pair production at beam-beam collision in electron-positron linear colliders has been discussed taking into account a finite size of the beams (both longitudinal and transverse) and end effects. Contributions of the main acting mechanisms are singled out which depend on the energy of initial particles and the masses of created particles. A spectral distribution of produced particles is presented. 15 refs

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

Numerical simulation of bubble growth and departure during flow boiling period by lattice Boltzmann method

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

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Beamstrahlung spectra in next generation linear colliders

Energy Technology Data Exchange (ETDEWEB)

Barklow, T.; Chen, P. (Stanford Linear Accelerator Center, Menlo Park, CA (United States)); Kozanecki, W. (DAPNIA-SPP, CEN-Saclay (France))

1992-04-01

For the next generation of linear colliders, the energy loss due to beamstrahlung during the collision of the e{sup +}e{sup {minus}} beams is expected to substantially influence the effective center-of-mass energy distribution of the colliding particles. In this paper, we first derive analytical formulae for the electron and photon energy spectra under multiple beamstrahlung processes, and for the e{sup +}e{sup {minus}} and {gamma}{gamma} differential luminosities. We then apply our formulation to various classes of 500 GeV e{sup +}e{sup {minus}} linear collider designs currently under study.

Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

KAUST Repository

Allen, Rebecca

2016-06-29

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

Orbital alignment effects in near-resonant Rydberg atoms-rare gas collisions

International Nuclear Information System (INIS)

Isaacs, W.A.; Morrison, M.A.

1993-01-01

Recent experimental and theoretical studies of near-resonant energy transfer collisions involving rare-gas atoms and alkali or alkaline earth atoms which have been initially excited to an aligned state via one or more linearly polarized rasters have yielded a wealth of insight into orbital alignment and related effects. We have extended this inquiry to initially aligned Rydberg states, examining state-to-state and alignment-selected cross sections using quantum collision theory augmented by approximations appropriate to the special characteristics of the Rydberg state (e.g., the quasi-free-electron model and the impulse approximation)

Topology optimization of unsteady flow problems using the lattice Boltzmann method

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

2016-01-01

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

Linearly Polarized Gluons and the Higgs Transverse Momentum Distribution

NARCIS (Netherlands)

Boer, Daniel; den Dunnen, Wilco J.; Pisano, Cristian; Schlegel, Marc; Vogelsang, Werner

2012-01-01

We study how gluons carrying linear polarization inside an unpolarized hadron contribute to the transverse momentum distribution of Higgs bosons produced in hadronic collisions. They modify the distribution produced by unpolarized gluons in a characteristic way that could be used to determine

A pedagogical approach to the Boltzmann factor through experiments and simulations

International Nuclear Information System (INIS)

Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M

2009-01-01

The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

A pedagogical approach to the Boltzmann factor through experiments and simulations

Energy Technology Data Exchange (ETDEWEB)

Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M [University of Palermo Physics Education Research Group, Dipartimento di Fisica e Tecnologie Relative, Universita di Palermo (Italy)], E-mail: sperandeo@difter.unipa.it

2009-09-15

The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

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.

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

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.

Complex Morphology of Subducted Lithosphere in the Mantle below the Molucca Collision Zone from Non-linear Seismic Tomography

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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.

Fermi-Pasta-Ulam-Tsingou problems: Passage from Boltzmann to q-statistics

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Bagchi, Debarshee; Tsallis, Constantino

2018-02-01

The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor P(ε) ∼e-βε describes its equilibrium distribution of one-body energies, and its velocity distribution is Maxwellian, i.e., P(v) ∼e - βv2 /2. We consider here a generalized system where the quartic coupling constant between sites decays as 1 / dijα (α ≥ 0 ;dij = 1 , 2 , …) . Through first-principle molecular dynamics we demonstrate that, for large α (above α ≃ 1), i.e., short-range interactions, Boltzmann statistics (based on the additive entropic functional SB [ P(z) ] = - k ∫ dzP(z) ln P(z)) is verified. However, for small values of α (below α ≃ 1), i.e., long-range interactions, Boltzmann statistics dramatically fails and is replaced by q-statistics (based on the nonadditive entropic functional Sq [ P(z) ] = k(1 - ∫ dz[ P(z) ]q) /(q - 1) , with S1 =SB). Indeed, the one-body energy distribution is q-exponential, P(ε) ∼ eqε-βε ε ≡[ 1 +(qε - 1) βε ε ]-1 /(qε - 1) with qε > 1, and its velocity distribution is given by P(v) ∼ eqv-βvv2 / 2 with qv > 1. Moreover, within small error bars, we verify qε =qv = q, which decreases from an extrapolated value q ≃ 5 / 3 to q = 1 when α increases from zero to α ≃ 1, and remains q = 1 thereafter.

Lattice Boltzmann simulation of flow across a staggered tube bundle array

Energy Technology Data Exchange (ETDEWEB)

Tiftikçi, A.; Kocar, C., E-mail: ckocar@hacettepe.edu.tr

2016-04-15

Highlights: • Large eddy simulation of the cross-flow in a staggered tube bundle array in 3D was made. • LBM and FVM are used separately as numerical solvers and the results of each method compared with experimental data. • Effect of lattice model is studied for tube bundle flow. • Filter size effects, mesh size effects are studied for VLES turbulence model. - Abstract: The decision on the magnitude of the grid size is a crucial problem in large eddy simulations. Finer mesh requires excessive memory and causes long simulation time. Large eddy simulation model becomes inefficient when the extent of the flow geometry to be simulated with the lattice-Boltzmann method is large. Thus, in this study, it is proposed to investigate the capabilities of three turbulence models, namely, very large eddy simulation, Van Driest and Smagorinsky–Lilly. As a test case, a staggered tube bundle flow experiment is used for the validation and comparison purposes. Sensitivity analyses (including mesh and filter size) have been made. Furthermore, the effect of lattice model is investigated and it is showed that the D3Q27 and D3Q19 models do not differ significantly in lattice-Boltzmann method for this type of flow. The results of turbulence model comparisons for staggered tube bundle flow showed that very large eddy simulation is superior at low resolution. This paper might be considered as a good validation of the lattice-Boltzmann method. In turbulent flow conditions, the code successfully captures the velocity and stress profiles even if the flow is quite complicated.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

An overheight vehicle bridge collision monitoring system using piezoelectric transducers

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Song, G.; Olmi, C.; Gu, H.

2007-04-01

With increasing traffic volume follows an increase in the number of overheight truck collisions with highway bridges. The detection of collision impact and evaluation of the impact level is a critical issue in the maintenance of a concrete bridge. In this paper, an overheight collision detection and evaluation system is developed for concrete bridge girders using piezoelectric transducers. An electric circuit is designed to detect the impact and to activate a digital camera to take photos of the offending truck. Impact tests and a health monitoring test were conducted on a model concrete bridge girder by using three piezoelectric transducers embedded before casting. From the experimental data of the impact test, it can be seen that there is a linear relation between the output of sensor energy and the impact energy. The health monitoring results show that the proposed damage index indicates the level of damage inside the model concrete bridge girder. The proposed overheight truck-bridge collision detection and evaluation system has the potential to be applied to the safety monitoring of highway bridges.

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)

ZERO IMPACT PARAMETER WHITE DWARF COLLISIONS IN FLASH

International Nuclear Information System (INIS)

Hawley, W. P.; Athanassiadou, T.; Timmes, F. X.

2012-01-01

We systematically explore zero impact parameter collisions of white dwarfs (WDs) with the Eulerian adaptive grid code FLASH for 0.64 + 0.64 M ☉ and 0.81 + 0.81 M ☉ mass pairings. Our models span a range of effective linear spatial resolutions from 5.2 × 10 7 to 1.2 × 10 7 cm. However, even the highest resolution models do not quite achieve strict numerical convergence, due to the challenge of properly resolving small-scale burning and energy transport. The lack of strict numerical convergence from these idealized configurations suggests that quantitative predictions of the ejected elemental abundances that are generated by binary WD collision and merger simulations should be viewed with caution. Nevertheless, the convergence trends do allow some patterns to be discerned. We find that the 0.64 + 0.64 M ☉ head-on collision model produces 0.32 M ☉ of 56 Ni and 0.38 M ☉ of 28 Si, while the 0.81 + 0.81 M ☉ head-on collision model produces 0.39 M ☉ of 56 Ni and 0.55 M ☉ of 28 Si at the highest spatial resolutions. Both mass pairings produce ∼0.2 M ☉ of unburned 12 C+ 16 O. We also find the 0.64 + 0.64 M ☉ head-on collision begins carbon burning in the central region of the stalled shock between the two WDs, while the more energetic 0.81 + 0.81 M ☉ head-on collision raises the initial post-shock temperature enough to burn the entire stalled shock region to nuclear statistical equilibrium.

Lattice Boltzmann model capable of mesoscopic vorticity computation

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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.

An evaluation of collision models in the Method of Moments for rarefied gas problems

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Emerson, David; Gu, Xiao-Jun

2014-11-01

The Method of Moments offers an attractive approach for solving gaseous transport problems that are beyond the limit of validity of the Navier-Stokes-Fourier equations. Recent work has demonstrated the capability of the regularized 13 and 26 moment equations for solving problems when the Knudsen number, Kn (where Kn is the ratio of the mean free path of a gas to a typical length scale of interest), is in the range 0.1 and 1.0-the so-called transition regime. In comparison to numerical solutions of the Boltzmann equation, the Method of Moments has captured both qualitatively, and quantitatively, results of classical test problems in kinetic theory, e.g. velocity slip in Kramers' problem, temperature jump in Knudsen layers, the Knudsen minimum etc. However, most of these results have been obtained for Maxwell molecules, where molecules repel each other according to an inverse fifth-power rule. Recent work has incorporated more traditional collision models such as BGK, S-model, and ES-BGK, the latter being important for thermal problems where the Prandtl number can vary. We are currently investigating the impact of these collision models on fundamental low-speed problems of particular interest to micro-scale flows that will be discussed and evaluated in the presentation. Engineering and Physical Sciences Research Council under Grant EP/I011927/1 and CCP12.

Lattice Boltzmann method to study the contraction of a viscous ligament

NARCIS (Netherlands)

Srivastava, S.; Driessen, T.W.; Jeurissen, R.J.M.; Wijshoff, H.M.A.; Toschi, F.

2013-01-01

We employ a recently formulated axisymmetric version of the multiphase Shan–Chen (SC) lattice Boltzmann method (LBM) [S. Srivastava et al., Phys. Rev. E88, 013309 (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ)

Atoms and Ions; Universality, Singularity and Particularity:. on Boltzmann's Vision a Century Later

Science.gov (United States)

Fisher, Michael

2008-12-01

Ludwig Boltzmann died by his own hand 101 years ago last September. He was a passionate believer in atoms: underlying thermodynamics, he felt, lay a statistical world governed by the mechanics of individual particles. His struggles against critics -- "Have you ever seen an atom?" taunted Ernst Mach -- left him pessimistic. Nevertheless, following Maxwell and clarified by Gibbs, he established the science of Statistical Mechanics. But today, especially granted our understanding of critical singularities and their universality, how much do atomic particles and their charged partners, ions, really matter? The answers we have also met opposition. But Boltzmann would have welcomed the insights gained and approved of applications of statistical dynamics to biology, sociology, and other enterprises. Note from Publisher: This article contains the abstract only.