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Sample records for boltzmann event

  1. Boltzmann

    International Nuclear Information System (INIS)

    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

  2. Boltzmann's Concept of Reality

    OpenAIRE

    Ribeiro, Marcelo B.; Videira, Antonio A. P.

    2007-01-01

    In this article we describe and analyze the concept of reality developed by the Austrian theoretical physicist Ludwig Boltzmann. It is our thesis that Boltzmann was fully aware that reality could, and actually was, described by different points of view. In spite of this, Boltzmann did not renounce the idea that reality is real. We also discuss his main motivations to be strongly involved with philosophy of science, as well as further developments made by Boltzmann himself of his main philosop...

  3. Ludwig Boltzmann: Atomic genius

    International Nuclear Information System (INIS)

    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.)

  4. Training Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Fischer, Asja

    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...

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

    International Nuclear Information System (INIS)

    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

  6. Crystallographic Lattice Boltzmann Method

    Science.gov (United States)

    Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

    2016-01-01

    Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098

  7. Crystallographic Lattice Boltzmann Method

    Science.gov (United States)

    Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

    2016-06-01

    Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.

  8. Temperature based Restricted Boltzmann Machines

    Science.gov (United States)

    Li, Guoqi; Deng, Lei; Xu, Yi; Wen, Changyun; Wang, Wei; Pei, Jing; Shi, Luping

    2016-01-01

    Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.

  9. A Note on Boltzmann Brains

    CERN Document Server

    Nomura, Yasunori

    2015-01-01

    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 possibly the one imposed by the Poincare recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.

  10. A note on Boltzmann brains

    Science.gov (United States)

    Nomura, Yasunori

    2015-10-01

    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.

  11. 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.

  12. Events

    Directory of Open Access Journals (Sweden)

    Igor V. Karyakin

    2016-02-01

    Full Text Available The 9th ARRCN Symposium 2015 was held during 21st–25th October 2015 at the Novotel Hotel, Chumphon, Thailand, one of the most favored travel destinations in Asia. The 10th ARRCN Symposium 2017 will be held during October 2017 in the Davao, Philippines. International Symposium on the Montagu's Harrier (Circus pygargus «The Montagu's Harrier in Europe. Status. Threats. Protection», organized by the environmental organization «Landesbund für Vogelschutz in Bayern e.V.» (LBV was held on November 20-22, 2015 in Germany. The location of this event was the city of Wurzburg in Bavaria.

  13. Ludwig Boltzmann A Pioneer of Modern Physics

    CERN Document Server

    Flamm, D

    1997-01-01

    In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus broke with the classical prejudice, that fundamental laws have to be strictly deterministic. Even Max Planck had not been ready to accept Boltzmann's statistical methods until 1900. With Boltzmann's pioneering work the probabilistic interpretation of quantum mechanics had already a precedent. In fact in a paper in 1897 Boltzmann had already suggested to Planck to use his statistical methods for the treatment of black body radiation. The second pioneering step towards quantum mechanics was Boltzmann's introduction of discrete energy levels. Boltzmann used this method already in his 1872 paper on the H-theorem. One may ask whether Boltzmann considered this procedure only as a mathematical device or whether he attributed physical significance to it. In this connection Ostwald repo...

  14. Quantum corrections for Boltzmann equation

    Institute of Scientific and Technical Information of China (English)

    M.; Levy; PETER

    2008-01-01

    We present the lowest order quantum correction to the semiclassical Boltzmann distribution function,and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation,and the quantum Wigner distribution function is expanded in pow-ers of Planck constant,too. The negative quantum correlation in the Wigner dis-tribution function which is just the quantum correction terms is naturally singled out,thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework.

  15. On Training Deep Boltzmann Machines

    OpenAIRE

    Desjardins, Guillaume; Courville, Aaron; Bengio, Yoshua

    2012-01-01

    The deep Boltzmann machine (DBM) has been an important development in the quest for powerful "deep" probabilistic models. To date, simultaneous or joint training of all layers of the DBM has been largely unsuccessful with existing training methods. We introduce a simple regularization scheme that encourages the weight vectors associated with each hidden unit to have similar norms. We demonstrate that this regularization can be easily combined with standard stochastic maximum likelihood to yie...

  16. Boltzmann equation and hydrodynamic fluctuations.

    Science.gov (United States)

    Colangeli, Matteo; Kröger, Martin; Ottinger, Hans Christian

    2009-11-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics. PMID:20364972

  17. Boltzmann equation and hydrodynamic fluctuations

    OpenAIRE

    Colangeli, M.; Kroger, M.; Ottinger, H. C.

    2009-01-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.

  18. Student understanding of the Boltzmann factor

    CERN Document Server

    Smith, Trevor I; Thompson, John R

    2015-01-01

    We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann f...

  19. Pruning Boltzmann networks and hidden Markov models

    DEFF Research Database (Denmark)

    Pedersen, Morten With; Stork, D.

    1996-01-01

    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...

  20. Multiphase lattice Boltzmann methods theory and application

    CERN Document Server

    Huang, Haibo; Lu, Xiyun

    2015-01-01

    Theory and Application of Multiphase Lattice Boltzmann Methods presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods developed thus far and is aimed at researchers and practitioners within relevant Earth Science disciplines as well as Petroleum, Chemical, Mechanical and Geological Engineering. Clearly structured throughout, this book will be an invaluable reference  on the current state of all popular multiphase Lattice Boltzmann Methods (LBMs). The advantages and disadvantages of each model are presented in an accessible manner to enable the reader to choose the

  1. Relativistic Boltzmann theory for a plasma

    International Nuclear Information System (INIS)

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

  2. Relativistic Entropy and Related Boltzmann Kinetics

    CERN Document Server

    Kaniadakis, G

    2009-01-01

    It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitely remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle, suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativ...

  3. 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

  4. Student understanding of the Boltzmann factor

    Science.gov (United States)

    Smith, Trevor I.; Mountcastle, Donald B.; Thompson, John R.

    2015-12-01

    [This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.

  5. Thermal Lattice Boltzmann Model for Compressible Fluid

    Institute of Scientific and Technical Information of China (English)

    SUN Cheng-Hai

    2000-01-01

    We formulate a new thermal lattice Boltzmann model to simulate compressible flows with a high Mach number.The main difference from the standard lattice Boltzmann models is that the particle velocities are no longer a constant, varying with the mean velocity and internal energy. The proper heat conduction term in the energy equation is recovered by modification of the fluctuating kinetic energy transported by particles. The simulation of Couette flow is in good agreement with the analytical solutions.

  6. A Viscosity Adaptive Lattice Boltzmann Method

    OpenAIRE

    Conrad, Daniel

    2015-01-01

    The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice. By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics methods. The LBM has been shown to be an accurate and efficient tool for the numerical...

  7. 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. PMID:26565365

  8. Matrix-valued Quantum Lattice Boltzmann Method

    CERN Document Server

    Mendl, Christian B

    2013-01-01

    We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM), with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function. To accommodate the spin density matrix, the distribution functions become 2x2-matrix valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The framework could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.

  9. Boltzmann map for quantum oscillators

    International Nuclear Information System (INIS)

    The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega1, omega2, and omega3 mutually irrational, but obeying a relation n1omega1 + n2omega2 = n3omega3, n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) β1, β2, β3 obeying the equation n1omega1β1 + n2omega3β1number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case

  10. The generalized Stefan-Boltzmann law of a rectilinear non-uniformly accelerating Kinnersley black hole

    Institute of Scientific and Technical Information of China (English)

    Jiang Ji-Jian; Meng Qing-Miao; Wang Shuai

    2009-01-01

    Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan Boltzmann law. In addition, the derived generalized Stefan-Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space-time metric near the event horizon and the changing rate of the event horizon in black holes.

  11. Phantom cosmology and Boltzmann brains problem

    CERN Document Server

    Astashenok, Artyom V; Yurov, Valerian V

    2013-01-01

    We consider the well-known Boltzmann brains problem in frames of simple phantom energy models with little rip, big rip and big freeze singularity. It is showed that these models (i) satisfy to observational data and (ii) may be free from Boltzmann brains problem. The human observers in phantom models can exist only in during for a certain period $tBoltzmann brains problem doesn't appear. The bounds on model parameters derived from such requirement don't contradict to allowable range from observational data.

  12. Boltzmann-Electron Model in Aleph.

    Energy Technology Data Exchange (ETDEWEB)

    Hughes, Thomas Patrick; Hooper, Russell

    2014-11-01

    We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical %22grid instability%22 that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model

  13. 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.

  14. 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

  15. Grid refinement for entropic lattice Boltzmann models

    CERN Document Server

    Dorschner, B; Chikatamarla, S S; Karlin, I V

    2016-01-01

    We propose a novel multi-domain grid refinement technique with extensions to entropic incompressible, thermal and compressible lattice Boltzmann models. Its validity and accuracy are accessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the set-ups of turbulent channel flow, flow past a sphere, Rayleigh-Benard convection as well as the supersonic flow around an airfoil. Special attention is payed to analyzing the adaptive features of entropic lattice Boltzmann models for multi-grid simulations.

  16. Rigorous Navier-Stokes Limit of the Lattice Boltzmann Equation

    OpenAIRE

    Junk, Michael; Yong, Wen-An

    2001-01-01

    Here we riqorously investigate the diffusive limit of a velocity-discrete Boltzmann equation which is used in the lattice Boltzmann method to construct approximate solutions of the incompressible Navier-Stokes equation.

  17. A Fluctuating Lattice Boltzmann Method for the Diffusion Equation

    CERN Document Server

    Wagner, Alexander J

    2016-01-01

    We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

  18. Test of Information Theory on the Boltzmann Equation

    OpenAIRE

    Hyeon-Deuk, Kim; Hayakawa, Hisao

    2002-01-01

    We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.

  19. Test of Information Theory on the Boltzmann Equation

    OpenAIRE

    Kim, Hyeon-Deuk; Hayakawa, Hisao

    2003-01-01

    We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.

  20. Deriving thermal lattice-Boltzmann models from the continuous Boltzmann equation: theoretical aspects

    CERN Document Server

    Philippi, P C; Surmas, R; Philippi, Paulo Cesar; Santos, Luis Orlando Emerich dos; Surmas, Rodrigo

    2005-01-01

    The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its conceptual support: the continuous Boltzmann equation (BE). Most collision models are based on the BGK, single parameter, relaxation-term leading to constant Prandtl numbers. The polynomial expansion used for the equilibrium distribution introduces an upper-bound in the local macroscopic speed. Most widely used time discretization procedures give an explicit numerical scheme with second-order time step errors. In thermal problems, quadrature did not succeed in giving discrete velocity sets able to generate multi-speed regular lattices. All these problems, greatly, difficult the numerical simulation of LBM based algorithms. In present work, the systematic derivation of lattice-Boltzmann models from the continuous Boltzmann equation is discussed. The collision term in the li...

  1. Pair Production in the Quantum Boltzmann Equation

    OpenAIRE

    Rau, Jochen

    1994-01-01

    A source term in the quantum Boltzmann equation, which accounts for the spontaneous creation of $e^+e^-$-pairs in external electric fields, is derived from first principles and evaluated numerically. Careful analysis of time scales reveals that this source term is generally non-Markovian. This implies in particular that there may be temporary violations of the $H$-theorem.

  2. The Quantum Boltzmann Equation in Semiconductor Physics

    OpenAIRE

    Snoke, D. W.

    2010-01-01

    The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases.

  3. Lattice Boltzmann Models for Complex Fluids

    OpenAIRE

    Flekkoy, E. G.; Herrmann, H. J.

    1993-01-01

    We present various Lattice Boltzmann Models which reproduce the effects of rough walls, shear thinning and granular flow. We examine the boundary layers generated by the roughness of the walls. Shear thinning produces plug flow with a sharp density contrast at the boundaries. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.

  4. 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 ...

  5. The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation

    CERN Document Server

    Frank, Martin; Larsen, Edward W; Vasques, Richard

    2014-01-01

    We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo, with only statistical errors - no truncation errors.

  6. Lattice Boltzmann approaches to magnetohydrodynamics and electromagnetism

    Science.gov (United States)

    Dellar, Paul

    2010-03-01

    J u B E g We present a lattice Boltzmann approach for magnetohydrodynamics and electromagnetism that expresses the magnetic field using a discrete set of vector distribution functions i. The i were first postulated to evolve according to a vector Boltzmann equation of the form ti+ ξi.∇i= - 1τ ( i- i^(0) ), where the ξi are a discrete set of velocities. The right hand side relaxes the i towards some specified functions i^(0) of the fluid velocity , and of the macroscopic magnetic field given by = ∑ii. Slowly varying solutions obey the equations of resistive magnetohydrodynamics. This lattice Boltzmann formulation has been used in large-scale (up to 1800^3 resolution) simulations of magnetohydrodynamic turbulence. However, this is only the simplest form of Ohm's law. We may simulate more realistic extended forms of Ohm's law using more complex collision operators. A current-dependent relaxation time yields a current-dependent resistivity η(|∇x|), as used to model ``anomalous'' resistivity created by small-scale plasma processes. Using a hydrodynamic matrix collision operator that depends upon the magnetic field , we may simulate Braginskii's magnetohydrodynamics, in which the viscosity for strains parallel to the magnetic field lines is much larger than the viscosity for strains in perpendicular directions. Changing the collision operator again, from the above vector Boltzmann equation we may derive the full set of Maxwell's equations, including the displacement current, and Ohm's law, - 1c^2 tE+ ∇x= μo,= σ( E + x). The original lattice Boltzmann scheme was designed to reproduce resistive magnetohydrodynamics in the non-relativistic limit. However, the kinetic formulation requires a system of first order partial differential equations with collision terms. This system coincides with the full set of Maxwell's equations and Ohm's law, so we capture a much wider range of electromagnetic phenomena, including electromagnetic waves.

  7. 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

  8. Lattice Boltzmann model for wave propagation.

    Science.gov (United States)

    Zhang, Jianying; Yan, Guangwu; Shi, Xiubo

    2009-08-01

    A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation. PMID:19792280

  9. Classical non-Markovian Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Alexanian, Moorad, E-mail: alexanian@uncw.edu [Department of Physics and Physical Oceanography, University of North Carolina Wilmington, Wilmington, North Carolina 28403-5606 (United States)

    2014-08-01

    The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

  10. Nuclear Flow in Consistent Boltzmann Algorithm Models

    OpenAIRE

    Kortemeyer, G.; Daffin, F.; Bauer, W.

    1995-01-01

    We investigate the stochastic Direct Simulation Monte Carlo method (DSMC) for numerically solving the collision-term in heavy-ion transport theories of the Boltzmann-Uehling-Uhlenbeck (BUU) type. The first major modification we consider is changes in the collision rates due to excluded volume and shadowing/screening effects (Enskog theory). The second effect studied by us is the inclusion of an additional advection term. These modifications ensure a non-vanishing second virial and change the ...

  11. Privacy-Preserving Restricted Boltzmann Machine

    OpenAIRE

    Yu Li; Yuan Zhang; Yue Ji

    2014-01-01

    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 provi...

  12. Lattice Boltzmann Model and Geophysical Hydrodynamic Equation

    Institute of Scientific and Technical Information of China (English)

    冯士德; 杨京龙; 郜宪林; 季仲贞

    2002-01-01

    A lattice Boltzmann equation model in a rotating system is developed by introducing the Coriolis force effect.The geophysical hydrodynamic equation can be derived from this model. Numerical computations are performed to simulate the cylindrical annulus experiment and Benard convection. The numerical results have shown the flow behaviour of large-scale geostrophic current and Benard convection cells, which verifies the applicability of this model to both theory and experiment.

  13. 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.

  14. The Boltzmann equation in the difference formulation

    International Nuclear Information System (INIS)

    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.

  15. Geometry of the restricted Boltzmann machine

    OpenAIRE

    Cueto, Maria Angelica; Morton, Jason; Sturmfels, Bernd

    2009-01-01

    The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the first secant variety of the Segre variety of projective lines. We derive a dimension formula for the ...

  16. The Milne problem for the Boltzmann equation

    International Nuclear Information System (INIS)

    Existence, uniqueness and asymptotic properties are proved for the solution of the Milne problem for the Boltzmann equation, in which the incoming velocity distribution and the total mass flux are specified arbitrarily. The collision law corresponds to a hard sphere gas. The solution uses energy estimates and is similar to that of Bardos, Santos and Sentis for neutron transport. From the Milne problem one can then easily deduce the solution of the Kramers problem

  17. Nonlocal Boltzmann theory of plasma channels

    Energy Technology Data Exchange (ETDEWEB)

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

    1983-01-03

    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.

  18. Nonlocal Boltzmann theory of plasma channels

    International Nuclear Information System (INIS)

    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

  19. Improved learning algorithms for restricted Boltzmann machines

    OpenAIRE

    Cho, Kyunghyun

    2011-01-01

    A restricted Boltzmann machine (RBM) is often used as a building block for constructing deep neural networks and deep generative models which have gained popularity recently as one way to learn complex and large probabilistic models. In these deep models, it is generally known that the layer-wise pretraining of RBMs facilitates finding a more accurate model for the data. It is, hence, important to have an efficient learning method for RBM. The conventional learning is mostly performed us...

  20. On the full Boltzmann equations for Leptogenesis

    CERN Document Server

    Garayoa, J; Pinto, T; Rius, N; Vives, O

    2009-01-01

    We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous...

  1. An efficient annealing in Boltzmann machine in Hopfield neural network

    Science.gov (United States)

    Kin, Teoh Yeong; Hasan, Suzanawati Abu; Bulot, Norhisam; Ismail, Mohammad Hafiz

    2012-09-01

    This paper proposes and implements Boltzmann machine in Hopfield neural network doing logic programming based on the energy minimization system. The temperature scheduling in Boltzmann machine enhancing the performance of doing logic programming in Hopfield neural network. The finest temperature is determined by observing the ratio of global solution and final hamming distance using computer simulations. The study shows that Boltzmann Machine model is more stable and competent in term of representing and solving difficult combinatory problems.

  2. Boltzmann equation integration in thermionic converter conditions. Part II. Terms in Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Stoenescu, M.L.

    1977-06-01

    The terms in Boltzmann kinetic equation corresponding to elastic short range collisions, inelastic excitational collisions, coulomb interactions and electric field acceleration are evaluated numerically for a standard distribution function minimizing the computational volume by expressing the terms as linear combinations with recalculable coefficients, of the distribution function and its derivatives. The present forms are suitable for spatial distribution calculations.

  3. 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.

  4. Privacy-preserving restricted boltzmann machine.

    Science.gov (United States)

    Li, Yu; Zhang, Yuan; Ji, Yue

    2014-01-01

    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. PMID:25101139

  5. Application of lattice Boltzmann scheme to nanofluids

    Institute of Scientific and Technical Information of China (English)

    XUAN; Yimin; LI; Qiang; YAO; Zhengping

    2004-01-01

    A nanofluid is a particle suspension that consists of base liquids and nanoparticles. Nanofluid has greater potential for heat transfer enhancement than traditional solid-liquid mixture. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles,a lattice Boltzmann model for simulating flow and energy transport processes inside the nanofluids is proposed. The irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids are discussed. The distributions of suspended nanoparticles inside nanofluids are calculated.

  6. 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)

  7. Lattice Boltzmann methods for moving boundary flows

    International Nuclear Information System (INIS)

    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)

  8. Scattering theory of the linear Boltzmann operator

    International Nuclear Information System (INIS)

    In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.)

  9. Celebrating Cercignani's conjecture for the Boltzmann equation

    CERN Document Server

    Desvillettes, Laurent; Villani, Cédric

    2010-01-01

    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.

  10. Convolution Inequalities for the Boltzmann Collision Operator

    Science.gov (United States)

    Alonso, Ricardo J.; Carneiro, Emanuel; Gamba, Irene M.

    2010-09-01

    We study integrability properties of a general version of the Boltzmann collision operator for hard and soft potentials in n-dimensions. A reformulation of the collisional integrals allows us to write the weak form of the collision operator as a weighted convolution, where the weight is given by an operator invariant under rotations. Using a symmetrization technique in L p we prove a Young’s inequality for hard potentials, which is sharp for Maxwell molecules in the L 2 case. Further, we find a new Hardy-Littlewood-Sobolev type of inequality for Boltzmann collision integrals with soft potentials. The same method extends to radially symmetric, non-increasing potentials that lie in some {Ls_{weak}} or L s . The method we use resembles a Brascamp, Lieb and Luttinger approach for multilinear weighted convolution inequalities and follows a weak formulation setting. Consequently, it is closely connected to the classical analysis of Young and Hardy-Littlewood-Sobolev inequalities. In all cases, the inequality constants are explicitly given by formulas depending on integrability conditions of the angular cross section (in the spirit of Grad cut-off). As an additional application of the technique we also obtain estimates with exponential weights for hard potentials in both conservative and dissipative interactions.

  11. Thermal equation of state for lattice Boltzmann gases

    Institute of Scientific and Technical Information of China (English)

    Ran Zheng

    2009-01-01

    The Galilean invaxiance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model axe 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.

  12. Thermal equation of state for lattice Boltzmann gases

    Science.gov (United States)

    Ran, Zheng

    2009-06-01

    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.

  13. Droplet collision simulation by multi-speed lattice Boltzmann method

    OpenAIRE

    Lycett-Brown, D.; Karlin, I.V.; Luo, K. H.

    2011-01-01

    Realization of the Shan-Chen multiphase flow lattice Boltzmann model is considered in the framework of the higher-order Galilean invariant lattices. The present multiphase lattice Boltzmann model is used in two dimensional simulation of droplet collisions at high Weber numbers. Results are found to be in a good agreement with experimental findings.

  14. Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics

    OpenAIRE

    Ahmad, Mushfiq; Talukder, Muhammad O. G.

    2007-01-01

    The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The solutions of this equation come in Boson-Fermion pairs. Reciprocal symmetric Boltzmann's function, thus, unifies both Bosonic and Fermionic distributions.

  15. A probabilistic view on the general relativistic Boltzmann equation

    CERN Document Server

    Bailleul, Ismael

    2011-01-01

    A new probalistic approach to general relativistic kinetic theory is proposed. The general relativistic Boltzmann equation is linked to a new Markov process in a completely intrinsic way. This treatment is then used to prove the causal character of the relativistic Boltzmann model.

  16. The possible resolution of Boltzmann brains problem in phantom cosmology

    OpenAIRE

    Astashenok, Artyom V.; Yurov, Artyom V.; Yurov, Valerian V.

    2013-01-01

    We consider the well-known Boltzmann brains problem in frames of simple phantom energy models with little rip and big rip singularity. It is showed that these models (i) satisfy to observational data and (ii) may be free from Boltzmann brains problem. The human observers in phantom models can exist only in during for a certain period $t

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

    International Nuclear Information System (INIS)

    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

  18. Training Restricted Boltzmann Machines on Word Observations

    CERN Document Server

    Dahl, George E; Larochelle, Hugo

    2012-01-01

    The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language processing applications, words are naturally modeled by K-ary discrete distributions, where K is determined by the vocabulary size and can easily be in the hundred thousands. The conventional approach to training RBMs on word observations is limited because it requires sampling the states of K-way softmax visible units during block Gibbs updates, an operation that takes time linear in K. In this work, we address this issue by employing a more general class of Markov chain Monte Carlo operators on the visible units, yielding updates with computational complexity independent of K. We demonstrate the success of our approach by training RBMs on hundreds of millions of word n-grams using larger vocabularies than previously feasible with RBMs and using the learned features to improve p...

  19. Lattice-Boltzmann Simulation of Tablet Disintegration

    Science.gov (United States)

    Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

    Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.

  20. Ordinal Boltzmann Machines for Collaborative Filtering

    CERN Document Server

    Truyen, Tran The; Venkatesh, Svetha

    2012-01-01

    Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper explores and extends a probabilistic model known as Boltzmann Machine for collaborative filtering tasks. It seamlessly integrates both the similarity and co-occurrence in a principled manner. In particular, we study parameterisation options to deal with the ordinal nature of the preferences, and propose a joint modelling of both the user-based and item-based processes. Experiments on moderate and large-scale movie recomm...

  1. Autotagging music with conditional restricted Boltzmann machines

    CERN Document Server

    Mandel, Michael; Larochelle, Hugo; Bengio, Yoshua

    2011-01-01

    This paper describes two applications of conditional restricted Boltzmann machines (CRBMs) to the task of autotagging music. The first consists of training a CRBM to predict tags that a user would apply to a clip of a song based on tags already applied by other users. By learning the relationships between tags, this model is able to pre-process training data to significantly improve the performance of a support vector machine (SVM) autotagging. The second is the use of a discriminative RBM, a type of CRBM, to autotag music. By simultaneously exploiting the relationships among tags and between tags and audio-based features, this model is able to significantly outperform SVMs, logistic regression, and multi-layer perceptrons. In order to be applied to this problem, the discriminative RBM was generalized to the multi-label setting and four different learning algorithms for it were evaluated, the first such in-depth analysis of which we are aware.

  2. Boltzmann babies in the proper time measure

    Energy Technology Data Exchange (ETDEWEB)

    Bousso, Raphael; Bousso, Raphael; Freivogel, Ben; Yang, I-Sheng

    2007-12-20

    After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.

  3. 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.

  4. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics

    CERN Document Server

    Mohseni, F; Succi, S; Herrmann, H J

    2015-01-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...

  5. 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. PMID:26986435

  6. Lattice Boltzmann Model for Numerical Relativity

    CERN Document Server

    Ilseven, E

    2015-01-01

    In the Bona-Masso 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. Our model is validated with well-established tests, showing good agreement with analytical solutions. Furthermore, we show 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 improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  7. Scattering theory for the linearized Boltzmann equation

    International Nuclear Information System (INIS)

    Scattering theory for a cloud of mutually non-interacting particles that in its passage through R3 undergoes absorption and production in a region D is contained in R3 through interaction with the medium in D is investigated. The motion for such a model is given by the linearized Boltzmann equation. Let n(x,v,t) denote the particle density in phase space at time t. The dynamics is described by a 1-parameter semigroup, W(t), which is in general not isometric. The existence of the wave operators Ω/sub +/ = s - lim W0(-t)W(t) (t →+infinity) and Ω/sub -/ = s - lim W(-t)W0(t) (t →-infinity), where W0(t) is the free dynamics, is examined at length

  8. Thermal lattice Boltzmann method for complex microflows

    Science.gov (United States)

    Yasuoka, Haruka; Kaneda, Masayuki; Suga, Kazuhiko

    2016-07-01

    A methodology to simulate thermal fields in complex microflow geometries is proposed. For the flow fields, the regularized multiple-relaxation-time lattice Boltzmann method (LBM) is applied coupled with the diffusive-bounce-back boundary condition for wall boundaries. For the thermal fields, the regularized lattice Bhatnagar-Gross-Krook model is applied. For the thermal wall boundary condition, a newly developed boundary condition, which is a mixture of the diffuse scattering and constant temperature conditions, is applied. The proposed set of schemes is validated by reference data in the Fourier flows and square cylinder flows confined in a microchannel. The obtained results confirm that it is essential to apply the regularization to the thermal LBM for avoiding kinked temperature profiles in complex thermal flows. The proposed wall boundary condition is successful to obtain thermal jumps at the walls with good accuracy.

  9. Boltzmann-Gaussian transition under specific noise effect

    International Nuclear Information System (INIS)

    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.

  10. Fermion particle production in semiclassical Boltzmann-Vlasov transport theory

    International Nuclear Information System (INIS)

    We present numerical solutions of the semiclassical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and antiquarks on a second Casimir invariant of color SU(3).

  11. 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.

  12. Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project

    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...

  13. Second-order Boltzmann equation: gauge dependence and gauge invariance

    International Nuclear Information System (INIS)

    In the context of cosmological perturbation theory, we derive the second-order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: (i) the polarization of light is incorporated in this formalism by using a tensor-valued distribution function; (ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; (iii) we perform a separation between temperature and spectral distortion, both for the intensity and polarization for the first time; (iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gauge dependence for the observed temperature. (paper)

  14. Langevin theory of fluctuations in the discrete Boltzmann equation

    CERN Document Server

    Gross, M; Varnik, F; Adhikari, R

    2010-01-01

    The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, the fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.

  15. Second order Boltzmann equation : gauge dependence and gauge invariance

    CERN Document Server

    Naruko, Atsushi; Koyama, Kazuya; Sasaki, Misao

    2013-01-01

    In the context of cosmological perturbation theory, we derive the second order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: i) the polarisation of light is incorporated in this formalism by using a tensor-valued distribution function; ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; iii) we perform a separation between temperature and spectral distortion, both for the intensity and for polarisation for the first time; iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gaug...

  16. An extension of the Boltzmann relation to collisionless magnetized plasma

    International Nuclear Information System (INIS)

    The neutralization of positive space charge is studied for density perturbations of limited spatial extent in a collisionfree magnetized plasma. It is found that a local density maximum gets a positive potential which depends only on the ambient electron temperature Te and the relative increase in density ne/ne0. For small density increases, below 5%, the resulting relation between potential and plasma density agrees closely with the Boltzmann relation, which applies in the presence of collisions. For larger density increases, the difference from the Boltzmann relation rapidly becomes large, e.g. a factor 2 for a 50% density increase, and a factor 3 for a 100% density increase. The result constitutes (1) a justification for using the Boltzmann relation also in collisionless magnetized plasma, provided that the density perturbations are small, and (2) a general relation which replaces the Boltzmann relation for large-amplitude perturbations. (au)

  17. Poisson-Boltzmann-Nernst-Planck model

    International Nuclear Information System (INIS)

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  18. A Boltzmann model for rod alignment and schooling fish

    OpenAIRE

    Carlen, Eric A.; Carvalho, Maria C.; Degond, Pierre; Wennberg, Bernt

    2014-01-01

    We consider a Boltzmann model introduced by Bertin, Droz and Greegoire as a binary interaction model of the Vicsek alignment interaction. This model considers particles lying on the circle. Pairs of particles interact by trying to reach their mid-point (on the circle) up to some noise. We study the equilibria of this Boltzmann model and we rigorously show the existence of a pitchfork bifurcation when a parameter measuring the inverse of the noise intensity crosses a critical threshold. The an...

  19. Advanced Mean Field Theory of Restricted Boltzmann Machine

    OpenAIRE

    Huang, Haiping; Toyoizumi, Taro

    2015-01-01

    Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message passing based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those...

  20. Linearized Boltzmann Equation and Hydrodynamics for Granular Gases

    OpenAIRE

    Brey, J. Javier; Dufty, James W.; Ruiz-Montero, M. J.

    2003-01-01

    The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as the basis for a hydrodynamic description. Hydrodynamics is defined in terms of the spectrum of the generator for the dynamics of the linearized Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are calculated in the long wavelength limit....

  1. A new lattice Boltzmann model for incompressible magnetohydrodynamics

    Institute of Scientific and Technical Information of China (English)

    Chen Xing-Wang; Shi Bao-Chang

    2005-01-01

    Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.

  2. Analysis of Jeans instability from Boltzmann equation

    CERN Document Server

    Kremer, Gilberto M

    2015-01-01

    The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. The equilibrium distribution function takes into account the expansion of the Universe and a pressureless fluid in the matter dominated Universe. Without invoking Jeans "swindle" a dispersion relation is obtained by considering small perturbations of the equilibrium values of the distribution function and gravitational potential. The collapse criterion -- which happens in an unstable region where the solution grows exponentially with time -- is determined from the dispersion relation. The collapse criterion in a static Universe occurs when the wavenumber $k$ is smaller than the Jeans wavenumber $k_J$, which was the solution found by Jeans. For an expanding Universe it is shown that this criterion is $k\\leq\\sqrt{7/6}\\,k_J$. As a consequence the ratio of the mass contained in a sphere of diameter equal to the wavelength $\\lambda=2\\pi/k$ to t...

  3. Lattice Boltzmann algorithm for continuum multicomponent flow.

    Science.gov (United States)

    Halliday, I; Hollis, A P; Care, C M

    2007-08-01

    We present a multicomponent lattice Boltzmann simulation for continuum fluid mechanics, paying particular attention to the component segregation part of the underlying algorithm. In the principal result of this paper, the dynamics of a component index, or phase field, is obtained for a segregation method after U. D'Ortona [Phys. Rev. E 51, 3718 (1995)], due to Latva-Kokko and Rothman [Phys. Rev. E 71 056702 (2005)]. The said dynamics accord with a simulation designed to address multicomponent flow in the continuum approximation and underwrite improved simulation performance in two main ways: (i) by reducing the interfacial microcurrent activity considerably and (ii) by facilitating simulational access to regimes of flow with a low capillary number and drop Reynolds number [I. Halliday, R. Law, C. M. Care, and A. Hollis, Phys. Rev. E 73, 056708 (2006)]. The component segregation method studied, used in conjunction with Lishchuk's method [S. V. Lishchuk, C. M. Care, and I. Halliday, Phys. Rev. E 67, 036701 (2003)], produces an interface, which is distributed in terms of its component index; however, the hydrodynamic boundary conditions which emerge are shown to support the notion of a sharp, unstructured, continuum interface. PMID:17930175

  4. The relativistic linear Boltzmann transport equation

    International Nuclear Information System (INIS)

    In this thesis the relativistic linear Boltzmann transport equation is applied to an experiment in pion production by 740 MeV protons incident on a variety of nuclei. This equation is solved by the Monte Carlo method of generating a single particle intranuclear cascade. The transport equation is derived starting with the N-body equation of motion for quantum mechanics in phase in order to determine under what conditions it is a valid approximation. It is shown that it should be a valid semi-classical approximation provided that: (1) The kinetic energy of the transport particle is much greater than its energy of interaction with the mean nuclear potential field. (2) The two-body collision interactions which make up the single particle intranuclear cascade take place over space and time intervals which are small relative to the internucleon space and time intervals for interactions within the nucleus and also compared to the space and time scales over which the probability distribution undergoes variation. In the pion production calculation condition (2) is only approximately met but reasonable agreement with the experimental data is obtained similar to that obtained in other theoretical calculations compared to this experiment

  5. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.

    Science.gov (United States)

    Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J

    2015-08-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere. PMID:26382548

  6. Lattice Boltzmann method and its applications in engineering thermophysics

    Institute of Scientific and Technical Information of China (English)

    HE YaLing; LI Qing; WANG Yong; TANG GuiHua

    2009-01-01

    The lattice Boltzmann method (LBM),a mesoscopic method between the molecular dynamics method and the conventional numerical methods,has been developed into a very efficient numerical alternative in the past two decades.Unlike conventional numerical methods,the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function,and then accumulates the distribution to obtain macroscopic averaged properties.In this article we review some work on LBM applications in engineering thermophysics:(1) brief introduction to the development of the LBM; (2)fundamental theory of LBM including the Boltzmann equation,Maxwell distribution function,Boltzmann-BGK equation,and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows,bounce back-specular-reflection boundary scheme for microscale gaseous flows,the mass modified outlet boundary scheme for fully developed flows,and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow,compressible flow,porous media flow,non-equilibrium flow,and gas resonant oscillating flow.

  7. The Boltzmann equation theory of charged particle transport

    International Nuclear Information System (INIS)

    It is shown how a formally exact Kubo-like response theory equivalent to the Boltzmann equation theory of charged particle transport can be constructed. The response theory gives the general wavevector and time-dependent velocity distribution at any time in terms of an initial distribution function, to which is added the response induced by a generalized perturbation over the intervening time. The usual Kubo linear response result for the distribution function is recovered by choosing the initial velocity distribution to be Maxwellian. For completeness the response theory introduces an exponential convergence function into the response time integral. This is equivalent to using a modified Boltzmann equation but the general form of the transport theory is not changed. The modified transport theory can be used to advantage where possible convergence difficulties occur in numerical solutions of the Boltzmann equation. This paper gives a systematic development of the modified transport theory and shows how the response theory fits into the broader scheme of solving the Boltzmann equation. The discussion extends both the work of Kumar et al. (1980), where the distribution function is expanded out in terms of tensor functions, and the propagator description where the non-hydrodynamic time development of the distribution function is related to the wavevector dependent Green function of the Boltzmann equation

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

    International Nuclear Information System (INIS)

    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.)

  9. Lattice Boltzmann Large Eddy Simulation Model of MHD

    CERN Document Server

    Flint, Christopher

    2016-01-01

    The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...

  10. Lattice Boltzmann Model for Compressible Fluid on a Square Lattice

    Institute of Scientific and Technical Information of China (English)

    SUN Cheng-Hai

    2000-01-01

    A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated

  11. Systematic Study of the Boundary Composition in Poisson Boltzmann Calculations

    CERN Document Server

    Kar, P; Hansmann, U H E; Hoefinger, S

    2007-01-01

    We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but our results are also of interest to finite difference techniques of Poisson Boltzmann calculations. At first, we identify the critical size of the geometrical elements for discretizing the boundary, and thus the necessary resolution required to establish numerical convergence. In the following two steps we perform reference calculations on a set of dipeptides in different conformations using the Polarizable Continuum Model and a high-level Density Functional as well as a high-quality basis set. Afterwards, we propose a mechanism for defining appropriate boundary geometries. Finally, we compare the classic Poisson Boltzmann description with the Quantum Chemical description, and aim at finding appropriate fitting parameters to get a close match to the reference data. Surprisi...

  12. Linear and quadratic octahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    In this paper, two new wavelet bases are developed for discretising the angular term of the first-order Boltzmann transport equation. The wavelets proposed are based on Sweldens second generation wavelets [Sweldens, W., 1993. The lifting scheme: a construction of second generation wavelets. SIAM J. Math. 1, 54], which are constructed through the lifting procedure [Sweldens, W., 1995. The lifting scheme: a new philosophy in biorthogonal wavelet construction. Wavelet Applications in Signal and Image Processing III]. In this paper, the wavelets are built on an octahedral domain, Fig. 2, and the angular flux approximation takes the form of finite element linear and quadratic representations. Full details of the meshing over the octahedron and derivation of the wavelet functions are given. The wavelets discussed are similar to the wavelets developed in Buchan [Buchan, A., 2003 c. Angular discretisation of the first order Boltzmann transport equation. Part 2: linear spherical wavelets. Technical Report, Imperial College, London, Dep. Earth Sci. Eng.] and [Buchan, A., 2003b. Angular discretisation of the first order Boltzmann transport equation. Part 3: quadratic spherical wavelets. Technical Report, Imperial College, London, Dep. Earth Sci. Eng.], in this paper the bases use a new fundamental amendment for mitigating the inaccuracies observed with the earlier bases. The performance of the new angular discretisation techniques are demonstrated using 2 one-dimensional and 4 two-dimensional test problems. These problems demonstrate the accuracy and susceptibility to ray effects of the proposed methods. Comparisons of all calculations are made with the conventional S N and P N approximations. Benchmark solutions are provided by the established code EVENT

  13. 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.

  14. Axisymmetric multiphase Lattice Boltzmann method for generic equations of state

    CERN Document Server

    Reijers, Sten A; Toschi, Federico

    2015-01-01

    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 $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.

  15. Multiphase lattice Boltzmann simulations for porous media applications -- a review

    CERN Document Server

    Liu, Haihu; Leonardi, Christopher R; Jones, Bruce D; Schmieschek, Sebastian; Narváez, Ariel; Williams, John R; Valocchi, Albert J; Harting, Jens

    2014-01-01

    Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

  16. Asymptotic-preserving Boltzmann model equations for binary gas mixture

    Science.gov (United States)

    Liu, Sha; Liang, Yihua

    2016-02-01

    An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations.

  17. Jet propagation within a Linearized Boltzmann Transport Model

    CERN Document Server

    Luo, Tan; Wang, Xin-Nian; Zhu, Yan

    2015-01-01

    A Linear Boltzmann Transport (LBT) model has been developed for the study of jet propagation inside a quark-gluon plasma. Both leading and thermal recoiled partons are transported according to the Boltzmann equations to account for jet-induced medium excitations. In this talk, we present our study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate elastic energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons are found to have significant influences on the jet energy loss and transverse profile.

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

    CERN Document Server

    Wolf-Gladrow, Dieter A

    2000-01-01

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

  19. 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 ...... unsupervised adaptation of an image segmentation cellular network. The learning rule is applied to adaptive segmentation of satellite imagery......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 by...

  20. 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 Maxwell-Boltzman

  1. The Boltzmann-Hamel Equations for Optimal Control

    OpenAIRE

    Maruskin, Jared M.; Bloch, Anthony M.

    2007-01-01

    We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In particular, we will show the dynamic optimal control problem can be written as a minimal set of 4n-2m first order differential equations of motion.

  2. 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 the...

  3. Thermal creep problems by the discrete Boltzmann equation

    Directory of Open Access Journals (Sweden)

    L. Preziosi

    1991-05-01

    Full Text Available This paper deals with an initial-boundary value problem for the discrete Boltzmann equation confined between two moving walls at different temperature. A model suitable for the quantitative analysis of the initial boundary value problem and the relative existence theorem are given.

  4. Lattice Boltzmann simulations of attenuation-driven acoustic streaming

    International Nuclear Information System (INIS)

    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

  5. 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.)

  6. A path-integral approach to the collisional Boltzmann gas

    OpenAIRE

    Chen, C Y

    2000-01-01

    Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due to collisions, both the colliding molecules and the scattered molecules are allowed to have distributions; thus the calculation is done smoothly and no singularities arise.

  7. On the linearized relativistic Boltzmann equation. II. Existence of hydrodynamics

    International Nuclear Information System (INIS)

    Solutions are analyzed of the linearized relativistic Boltzmann equation for initial data from L2(r, p) in long-time and/or small-mean-free-path limits. In both limits solutions of this equation converge to approximate ones constructed with solutions of the set of differential equations called the equations of relativistic hydrodynamics

  8. Existence of the scattering operator for the linear Boltzmann equation

    International Nuclear Information System (INIS)

    Existence theorems are proven in a study of the scattering problem for the linear Boltzmann equation (transport equation), describing the motion of a cloud of nonself-interacting particles (neutrons) in phase space. Also Simon's weak coupling result is discussed, and a meaningful wave operator in the presence of trapped particles is defined and its existence proven. 7 references

  9. 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…

  10. Variably saturated flow described with the anisotropic Lattice Boltzmann methods

    OpenAIRE

    Ginzburg, I.

    2006-01-01

    This paper addresses the numerical solution of highly nonlinear parabolic equations with Lattice Boltzmann techniques. They are first developed for generic advection and anisotropic dispersion equations (AADE). Collision configurations handle the anisotropic diffusion forms by using either anisotropic eigenvalue sets or anisotropic equilibrium functions. The coordinate transformation from the orthorhombic (rectangular) discretization grid to the cuboid computational grid is equivalen...

  11. On Existence of $L^2$-solutions of Coupled Boltzmann Continuous Slowing Down Transport Equation System

    CERN Document Server

    Tervo, J; Frank, M; Herty, M

    2016-01-01

    The paper considers a coupled system of linear Boltzmann transport equation (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in radiation therapy. The evolution of charged particles (e.g. electrons and positrons) are in practice often modelled using the CSDA version of BTE because of the so-called forward peakedness of scattering events contributing to the particle fluencies (or particle densities), which causes severe problems for numerical methods. First, we prove the existence and uniqueness of solutions, under sufficient criteria and in appropriate $L^2$-based spaces, of a single (particle) CSDA-equation by using two complementary techniques, the Lions-Lax-Milgram Theorem (variational approach), and the theory evolution operators (semigroup approach). The necessary a priori estimates are shown. In addition, we prove the corresponding results and estimates for the system of coupled transport equat...

  12. Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel

    CERN Document Server

    Hohenegger, A

    2008-01-01

    With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.

  13. Solving the homogeneous Boltzmann equation with arbitrary scattering kernel

    International Nuclear Information System (INIS)

    With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space-homogeneous Boltzmann equation with an isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the scattering kernel in terms of two cosines of the 'scattering angles'. The scattering functions used by previous authors in particle physics for matrix elements in the Fermi approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.

  14. Boltzmann Samplers, P\\'olya Theory, and Cycle Pointing

    CERN Document Server

    Bodirsky, Manuel; Kang, Mihyun; Vigerske, Stefan

    2010-01-01

    We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n pointed structures. We extend Polya theory to the corresponding pointing operator, and present a random sampling framework based on both the principles of Boltzmann sampling and on P\\'olya operators. All previously known unlabeled construction principles for Boltzmann samplers are special cases of our new results. Our method is illustrated on several examples: in each case, we provide enumerative results and efficient random samplers. The approach applies to unlabeled families of plane and nonplane unrooted trees, and tree-like structures in general, but also to families of graphs (such as cacti graphs and outerplanar graphs) and families of planar maps.

  15. Quadrature-based Lattice Boltzmann Model for Relativistic Flows

    CERN Document Server

    Blaga, Robert

    2016-01-01

    A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

  16. Quantitative and qualitative Kac's chaos on the Boltzmann's sphere

    CERN Document Server

    Carrapatoso, Kleber

    2012-01-01

    We investigate the construction of chaotic probability measures on the Boltzmann's sphere, which is the state space of the stochastic process of a many-particle system undergoing a dynamics preserving energy and momentum. Firstly, based on a version of the local Central Limit Theorem (or Berry-Essenn theorem), we construct a sequence of probabilities that is Kac chaotic and we prove a quantitative rate of convergence. Then, we investigate a stronger notion of chaos, namely entropic chaos introduced in \\cite{CCLLV}, and we prove, with quantitative rate, that this same sequence is also entropically chaotic. Furthermore, we investigate more general class of probability measures on the Boltzmann's sphere. Using the HWI inequality we prove that a Kac chaotic probability with bounded Fisher's information is entropically chaotic and we give a quantitative rate. We also link different notions of chaos, proving that Fisher's information chaos, introduced in \\cite{HaurayMischler}, is stronger than entropic chaos, which...

  17. Simulation of ship airwakes using a lattice Boltzmann method

    International Nuclear Information System (INIS)

    The first step in analysing the fully-coupled helicopter/ship-airwake environment is to study the airwake of a frigate or frigate-like shape in isolation. This will give an understanding of the flow field that a helicopter pilot will encounter when operating from a maritime platform. The flow around a simplified frigate shape is simulated using a lattice Boltzmann algorithm and the results compared to experimentally obtained surface data. The mean flow field of the unsteady simulations captures all the flow features of the three ship yaw angles studied. The strength of these features as predicted by the numerical simulations decreases slightly in accuracy as the approaching wind angle is increased. The results presented demonstrate the ability of the lattice Boltzmann method to predict accurately the mean airwake of a frigate-like geometry. (author)

  18. Shock-wave structure using nonlinear model Boltzmann equations.

    Science.gov (United States)

    Segal, B. M.; Ferziger, J. H.

    1972-01-01

    The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.

  19. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

    CERN Document Server

    Li, Q; Kang, Q J; Chen, Q

    2014-01-01

    In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper, are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles, however, is unable to reproduce static contact angles close to 180 degrees. Meanwhile, it is found that the proposed modif...

  20. Modified Lattice Boltzmann method for compressible fluid simulations

    International Nuclear Information System (INIS)

    A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory

  1. Modified lattice Boltzmann method for compressible fluid simulations.

    Science.gov (United States)

    Hinton, F L; Rosenbluth, M N; Wong, S K; Lin-Liu, Y R; Miller, R L

    2001-06-01

    A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory. PMID:11415085

  2. Dynamics of annihilation. I. Linearized Boltzmann equation and hydrodynamics.

    Science.gov (United States)

    García de Soria, María Isabel; Maynar, Pablo; Schehr, Grégory; Barrat, Alain; Trizac, Emmanuel

    2008-05-01

    We study the nonequilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of ballistic annihilation therefore constantly loses particles. The dynamics of perturbations around the free decay regime is investigated using the spectral properties of the linearized Boltzmann operator, which characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of molecular dynamics simulations that validate the theoretical predictions. PMID:18643046

  3. Pointwise Description for the Linearized Fokker-Planck-Boltzmann Model

    Science.gov (United States)

    Wu, Kung-Chien

    2015-09-01

    In this paper, we study the pointwise (in the space variable) behavior of the linearized Fokker-Planck-Boltzmann model for nonsmooth initial perturbations. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as the long-wave expansion in the spectrum of the Fourier modes for the space variable, and it has polynomial time decay rate. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. The Mixture Lemma plays an important role in constructing the kinetic-like waves, this lemma was originally introduced by Liu-Yu (Commun Pure Appl Math 57:1543-1608, 2004) for Boltzmann equation, but the Fokker-Planck term in this paper creates some technical difficulties.

  4. Higher-order Boltzmann machines and entropy bounds

    Science.gov (United States)

    Apolloni, Bruno; Battistini, Egidio; de Falco, Diego

    1999-07-01

    We examine some aspects of the interface area between mathematical statistics and statistical physics relevant to the study of Boltzmann machines. The Boltzmann machine learning algorithm is based on a variational principle (Gibbs' lemma for relative entropy). This fact suggests the possibility of a scheme of successive approximations: here we consider successive approximations parametrized by the order of many-body interactions among individual units. We prove bounds on the gain in relative entropy in the crucial step of adding, and estimating by Hebb's rule, a new parameter. We address the problem of providing, on the basis of local observations, upper and lower bounds on the entropy. While upper bounds are easily obtained by subadditivity, lower bounds involve localization of Hirschman bounds on a dual quantum system.

  5. Big-Bang Nucleosynthesis verifies classical Maxwell-Boltzmann distribution

    CERN Document Server

    Hou, S Q; Parikh, A; Daid, K; Bertulani, C

    2014-01-01

    We provide the most stringent constraint to date on possible deviations from the usually-assumed Maxwell-Boltzmann (MB) velocity distribution for nuclei in the Big-Bang plasma. The impact of non-extensive Tsallis statistics on thermonuclear reaction rates involved in standard models of Big-Bang Nucleosynthesis (BBN) has been investigated. We find that the non-extensive parameter $q$ may deviate by, at most, $|\\delta q|$=6$\\times$10$^{-4}$ from unity for BBN predictions to be consistent with observed primordial abundances; $q$=1 represents the classical Boltzmann-Gibbs statistics. This constraint arises primarily from the {\\em super}sensitivity of endothermic rates on the value of $q$, which is found for the first time. As such, the implications of non-extensive statistics in other astrophysical environments should be explored. This may offer new insight into the nucleosynthesis of heavy elements.

  6. Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel

    OpenAIRE

    Hohenegger, A.

    2008-01-01

    With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. Th...

  7. Topological interactions in a Boltzmann-type framework

    OpenAIRE

    Blanchet, Adrien; Degond, Pierre

    2015-01-01

    We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader according to the proximity rank of the latter with respect to the former. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit equation is akin to the Boltzmann equation. However , it exhibits...

  8. Coupling Lattice Boltzmann and Molecular Dynamics models for dense fluids

    OpenAIRE

    Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.

    2006-01-01

    We propose a hybrid model, coupling Lattice Boltzmann and Molecular Dynamics models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with r...

  9. Weighted particle method for solving the Boltzmann equation

    International Nuclear Information System (INIS)

    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 12C. A comparison with usual stochastic methods is made. Advantages and disadvantages of the Weighted Particle Method are discussed

  10. Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

    OpenAIRE

    Molnar, E.; Niemi, H.; Rischke, D. H.

    2016-01-01

    Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break dow...

  11. Discrete Boltzmann model of shallow water equations with polynomial equilibria

    CERN Document Server

    Meng, Jianping; Emerson, David R; Peng, Yong; Zhang, Jianmin

    2016-01-01

    A hierarchy of discrete Boltzmann model is proposed for simulating shallow water flows. By using the Hermite expansion and Gauss-Hermite quadrature, the conservation laws are automatically satisfied without extra effort. Moreover, the expansion order and quadrature can be chosen flexibly according to the problem for striking the balance of accuracy and efficiency. The models are then tested using the classical one-dimensional dam-breaking problem, and successes are found for both supercritical and subcritical flows.

  12. Volume-Based Fabric Tensors through Lattice-Boltzmann Simulations

    OpenAIRE

    Moreno, Rodrigo; Smedby, Örjan

    2014-01-01

    This paper introduces a new methodology to compute fabric tensors from computational fluid dynamics simulations performed through the lattice-Boltzmann method. Trabecular bone is modeled as a pipeline where a synthetic viscous fluid can flow from a single source located at the center of a spherical region of interest toward its boundaries. Two fabric tensors are computed from local velocities at the steady state estimated from the simulations, a tortuosity and a normalized tortuosity tensor.T...

  13. Multi-component lattice-Boltzmann model with interparticle interaction

    OpenAIRE

    Shan, Xiaowen; Doolen, Gary

    1995-01-01

    A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two component...

  14. A Lattice Boltzmann model for diffusion of binary gas mixtures

    OpenAIRE

    Bennett, Sam

    2010-01-01

    This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the sca...

  15. Lattice Boltzmann Method for mixtures at variable Schmidt number

    OpenAIRE

    Monteferrante, Michele; Melchionna, Simone; Marconi, Umberto Marini Bettolo

    2015-01-01

    When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook (BGK) evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm ...

  16. Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics

    OpenAIRE

    de Soria, M. I. Garcia; Maynar, P.; Schehr, G.; Barrat, A.; Trizac, E.

    2008-01-01

    We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\\em ballistic annihilation} therefore constantly looses particles. The dynamics of perturbations around the free decay regime is investigated from the spectral properties of the linearized Boltzmann operator, that characterize linear excitations on all time scales. The linearized Boltzma...

  17. Average Contrastive Divergence for Training Restricted Boltzmann Machines

    OpenAIRE

    Xuesi Ma; Xiaojie Wang

    2016-01-01

    This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a new learning algorithm called average contrastive divergence (ACD) for training RBMs. It is an improved CD algorithm, and it is different from the traditional CD algorithm. Finally, we obtain some experimental resul...

  18. Learning Feature Hierarchies with Centered Deep Boltzmann Machines

    OpenAIRE

    Montavon, Grégoire; Müller, Klaus-Robert

    2012-01-01

    Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of the activation functions to zero. This modification leads to a better conditioned Hessian and thus makes learning easier. We test the algorithm on real data and demonstrate that ...

  19. Simulation of particle saltation using the lattice Boltzmann method

    Czech Academy of Sciences Publication Activity Database

    Dolanský, Jindřich; Chára, Zdeněk; Vlasák, Pavel; Kysela, Bohuš

    Delft : Delft University of Technology, 2015. ISBN 978-83-927084-8-3. ISSN 0867-7964. [17th International Conference on Transport and Sedimentation of Solid Particles. Delft (NL), 22.09.2015-25.09.2015] R&D Projects: GA ČR GA15-18870S Institutional support: RVO:67985874 Keywords : lattice Boltzmann method * entropic LBM * particle-laden turbulent flow * particle-fluid interaction * PIV Subject RIV: BK - Fluid Dynamics

  20. Simulation of particle saltation using the lattice Boltzmann method

    Czech Academy of Sciences Publication Activity Database

    Dolanský, Jindřich; Chára, Zdeněk; Vlasák, Pavel; Kysela, Bohuš

    Delft : Delft University of Technology, 2015, s. 53-60. ISBN 978-83-927084-8-3. ISSN 0867-7964. [17th International Conference on Transport and Sedimentation of Solid Particles. Delft (NL), 22.09.2015-25.09.2015] R&D Projects: GA ČR(CZ) GA15-18870S Institutional support: RVO:67985874 Keywords : lattice Boltzmann method * entropic LBM * particle-laden turbulent flow * particle-fluid interaction * PIV Subject RIV: BK - Fluid Dynamics

  1. Stochastic particle approximations for generalized Boltzmann models and convergence estimates

    OpenAIRE

    Graham, Carl; Méléard, Sylvie

    1997-01-01

    We specify the Markov process corresponding to a generalized mollified Boltzmann equation with general motion between collisions and nonlinear bounded jump (collision) operator, and give the nonlinear martingale problem it solves. We consider various linear interacting particle systems in order to approximate this nonlinear process. We prove propagation of chaos, in variation norm on path space with a precise rate of convergence, using coupling and interaction graph techniqu...

  2. 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.

  3. The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation

    CERN Document Server

    Vasques, Richard

    2015-01-01

    We show that, by correctly selecting the probability distribution function $p(s)$ for a particle's distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of $p(s)$ preserves the $true$ mean-squared free path of the system, which sheds new light on the results obtained in previous work.

  4. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

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

  5. On half-space problems for the discrete Boltzmann equation

    International Nuclear Information System (INIS)

    We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for the discrete Boltzmann equation (a general discrete velocity model, DVM, with an arbitrary finite number of velocities). Then the discrete Boltzmann equation reduces to a system of Odes. The data for the outgoing particles at the boundary are assigned, possibly linearly depending on the data for the incoming particles. A classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete Boltzmann equation is made. In the non-linear case the solutions are assumed to tend to an assigned Maxwellian at infinity. The conditions on the data at the boundary needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated. In the non-degenerate case (corresponding, in the continuous case, to the case when the Mach number at the Maxwellian at infinity is different of (1, 0 and 1) implicit conditions are found. Furthermore, under certain assumptions explicit conditions are found, both in the non-degenerate and degenerate cases. An application to axially symmetric models is also studied.

  6. Capillary filling and Haines jump dynamics using free energy Lattice Boltzmann simulations

    Science.gov (United States)

    Zacharoudiou, Ioannis; Boek, Edo S.

    2016-06-01

    We investigate numerically the dynamics of capillary filling and Haines jump events using free energy Lattice Boltzmann (LB) simulations. Both processes are potentially important multi-phase pore-scale flow processes for geological CO2 sequestration and oil recovery. We first focus on capillary filling and demonstrate that the numerical method can capture the correct dynamics in the limit of long times for both high and low viscosity ratios, i.e. the method gives the correct scaling for the length of the penetrating fluid column as a function of time. Examining further the early times of capillary filling, three consecutive length vs. time regimes have been observed, in agreement with available experimental work in the literature. In addition, we carry out simulations of Haines jump events in idealised and realistic rock pore geometries. We observe that the Haines jump events are cooperative, non-local and associated with both drainage and imbibition dynamics. Our observations show that the pore filling dynamics is controlled by the Ohnesorge number, associated with the balance between viscous forces and inertial / surface tension forces. Using this concept, we are able to identify the type of pore filling dynamics that will occur.

  7. Cauchy Annealing Schedule: An Annealing Schedule for Boltzmann Selection Scheme in Evolutionary Algorithms

    OpenAIRE

    Dukkipati, Ambedkar; Murty, Narasimha M; Bhatnagar, Shalabh

    2004-01-01

    Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the `inverse temperature' parameter is lacking. In this paper we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two sel...

  8. Numerical and analytic solutions of the Boltzmann equation for cosmic ray transport

    International Nuclear Information System (INIS)

    A method for accurately determining the longitudinal transport of cosmic rays in a disordered, diverging magnetic field is described. Eigenfunctions of the operator in the Boltzmann equation which describes the effects of adiabatic focusing and pitch angle scattering are defined and numerically evaluated. When the particle distribution function is expressed as a series of these focusing eigenfunctions, the Boltzmann equation is transformed into a matrix equation. A computer program was written which uses this matrix representation to calculate the distribution function as a function of distance, time, and pitch angle. In addition, an analytic expression for pseudodiffusion, which replaces classical diffusion when the guiding magnetic field is not rectilinear, is derived. It is shown that the theory of focused transport predicts many of the observed features of solar cosmic ray events. Application of the theory to extragalactic radio sources is also considered. To enable other investigators to apply this method, documented listings of the requisite computer programs are included. In a separate analysis, the effect that energy loss due to synchrotron radiation has on electron propagation in a rectilinear magnetic field is considered. It is shown that a synchrotron radiation region, defined as the region in which the density of electrons of a specific energy is nonzero, has a double-lobed structure even when the electrons are injected into the field isotropically. It is also shown that, because the electrons decay to a given energy almost simultaneously over a large area, a synchrotron radiation region can expand with a superluminal velocity. Application of the theory to radio galaxies and quasars is considered

  9. Lattice Boltzmann method for the fractional advection-diffusion equation

    Science.gov (United States)

    Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  10. Appendix: Chapman-Enskog Expansion in the Lattice Boltzmann Method

    CERN Document Server

    Li, Jun

    2015-01-01

    The Chapman-Enskog expansion was used in the lattice Boltzmann method (LBM) to derive a Navier-Stokes-like equation and a formula was obtained to correlate the LBM model parameters to the kinematic viscosity implicitly implemented in LBM simulations. The obtained correlation formula usually works as long as the model parameters are carefully selected to make the Mach number and Knudsen number small although the validity of Chapman-Enskog expansion that has a formal definition of time derivative without tangible mathematical sense is not recognized by many mathematicians.

  11. El suicidio de Ludwig Boltzmann: el misterio persiste

    OpenAIRE

    Sierra Cuartas, Carlos Eduardo de Jesus

    1994-01-01

    En este año de 1994 se cumple 150 años del nacimiento del muy ilustre, y malogrado según veremos, físico austriaco Ludwig Boltzmann. Tal circunstancia ha motivado la publicación de escritos diversos acerca de su vida y obra, máxime si se tiene en cuenta su indiscutible aporte al inicio del esclarecimiento del misterio de la fecha del tiempo, merced a su trabajo sobre entropía, una medida del cambio que siempre aumenta con el tiempo en un sistema termodinámico aislado, en tanto se alcanza el ...

  12. LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD

    Institute of Scientific and Technical Information of China (English)

    FENG SHI-DE; MAO JIANG-YU; ZHANG QIONG

    2001-01-01

    In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.

  13. Hydrodynamic limit with geometric correction of stationary Boltzmann equation

    Science.gov (United States)

    Wu, Lei

    2016-05-01

    We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in L∞ both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with geometric correction.

  14. Entropy inequality and hydrodynamic limits for the Boltzmann equation.

    Science.gov (United States)

    Saint-Raymond, Laure

    2013-12-28

    Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as huge systems of identical and indistinguishable elementary particles. The state of a gas can therefore be described in a statistical way. The evolution, which introduces couplings, loses part of the information, which is expressed by the decay of the so-called mathematical entropy (the opposite of physical entropy!). PMID:24249776

  15. Boltzmann Machines and Denoising Autoencoders for Image Denoising

    OpenAIRE

    Cho, Kyunghyun

    2013-01-01

    Image denoising based on a probabilistic model of local image patches has been employed by various researchers, and recently a deep (denoising) autoencoder has been proposed by Burger et al. [2012] and Xie et al. [2012] as a good model for this. In this paper, we propose that another popular family of models in the field of deep learning, called Boltzmann machines, can perform image denoising as well as, or in certain cases of high level of noise, better than denoising autoencoders. We empiri...

  16. Lattice Boltzmann method and its application in engineering

    CERN Document Server

    Guo, Zhaoli

    2013-01-01

    Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.This book will cover the fundamental and practical application of LBM. The first part of the book consists of

  17. An alternative method for simulating particle suspensions using lattice Boltzmann

    CERN Document Server

    Santos, Luís Orlando Emerich dos

    2011-01-01

    In this study, we propose an alternative way to simulate particle suspensions using the lattice Boltzmann method. The main idea is to impose the non-slip boundary condition in the lattice sites located on the particle boundaries. The focus on the lattice sites, instead of the links between them, as done in the more used methods, represents a great simplification in the algorithm. A fully description of the method will be presented, in addition to simulations comparing the proposed method with other methods and, also, with experimental results.

  18. Multi-component lattice-Boltzmann model with interparticle interaction

    CERN Document Server

    Shan, X; Shan, Xiaowen; Doolen, Gary

    1995-01-01

    Abstract: A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.

  19. Existence of the scattering matrix for the linearized Boltzmann equation

    International Nuclear Information System (INIS)

    Following Hejtmanek, we consider neutrons in infinite space obeying a linearized Boltzmann equation describing their interaction with matter in some compact set D. We prove existence of the S-matrix and subcriticality of the dynamics in the (weak-coupling) case where the mean free path is larger than the diameter of D uniform in the velocity. We prove existence of the S-matrix also for the case where D is convex and filled with uniformly absorbent material. In an appendix, we present an explicit example where the dynamics is not invertible on L+1, the cone of positive elements in L1. (orig.)

  20. Pointwise Behavior of the Linearized Boltzmann Equation on Torus

    OpenAIRE

    Wu, Kung-Chien

    2013-01-01

    We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbation. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which ...

  1. Jet propagation within a Linearized Boltzmann Transport model

    International Nuclear Information System (INIS)

    A Linearized Boltzmann Transport (LBT) model has been developed for the study of parton propagation inside quark–gluon plasma. Both leading and thermal recoiled partons are tracked in order to include the effect of jet-induced medium excitation. In this talk, we present a study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons and jet-induced medium excitations are found to have significant influences on the jet energy loss and transverse profile

  2. Jet propagation within a Linearized Boltzmann Transport model

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Tan; He, Yayun [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); Zhu, Yan [Departamento de Física de Partículas and IGFAE, Universidade de Santiago de Compostela, E-15706 Santiago de Compostela, Galicia (Spain)

    2014-12-15

    A Linearized Boltzmann Transport (LBT) model has been developed for the study of parton propagation inside quark–gluon plasma. Both leading and thermal recoiled partons are tracked in order to include the effect of jet-induced medium excitation. In this talk, we present a study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons and jet-induced medium excitations are found to have significant influences on the jet energy loss and transverse profile.

  3. Lattice-Boltzmann Method for Geophysical Plastic Flows

    CERN Document Server

    Leonardi, Alessandro; Mendoza, Miller; Herrmann, Hans J

    2015-01-01

    We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.

  4. An implicit Lagrangian lattice Boltzmann method for the compressible flows

    Science.gov (United States)

    Yan, Guangwu; Dong, Yinfeng; Liu, Yanhong

    2006-08-01

    In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results.

  5. Relativistic Rotating Boltzmann Gas Using the Tetrad Formalism

    Directory of Open Access Journals (Sweden)

    Ambrus Victor E.

    2015-12-01

    Full Text Available We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to rel- ativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle ow four-vector and of the equilibrium stress-energy tensor.

  6. Linearized Boltzmann collision integral with the correct cutoff

    Science.gov (United States)

    Chang, Yongbin; White, R. D.

    2014-07-01

    In the calculation of the linearized Boltzmann collision operator for an inverse-square force law interaction (Coulomb interaction) F(r)=κ /r2, we found the widely used scattering angle cutoff θ ≥θmin is a wrong practise since the divergence still exists after the cutoff has been made. When the correct velocity change cutoff |v '-v|≥δmin is employed, the scattering angle can be integrated. A unified linearized Boltzmann collision operator for both inverse-square force law and rigid-sphere interactions is obtained. Like many other unified quantities such as transition moments, Fokker-Planck expansion coefficients and energy exchange rates obtained recently [Y. B. Chang and L. A. Viehland, AIP Adv. 1, 032128 (2011)], the difference between the two kinds of interactions is characterized by a parameter, γ, which is 1 for rigid-sphere interactions and -3 for inverse-square force law interactions. When the cutoff is removed by setting δmin=0, Hilbert's well known kernel for rigid-sphere interactions is recovered for γ = 1.

  7. Linearized Boltzmann collision integral with the correct cutoff

    International Nuclear Information System (INIS)

    In the calculation of the linearized Boltzmann collision operator for an inverse-square force law interaction (Coulomb interaction) F(r)=κ/r2, we found the widely used scattering angle cutoff θ≥θmin is a wrong practise since the divergence still exists after the cutoff has been made. When the correct velocity change cutoff |v′−v|≥δmin is employed, the scattering angle can be integrated. A unified linearized Boltzmann collision operator for both inverse-square force law and rigid-sphere interactions is obtained. Like many other unified quantities such as transition moments, Fokker-Planck expansion coefficients and energy exchange rates obtained recently [Y. B. Chang and L. A. Viehland, AIP Adv. 1, 032128 (2011)], the difference between the two kinds of interactions is characterized by a parameter, γ, which is 1 for rigid-sphere interactions and −3 for inverse-square force law interactions. When the cutoff is removed by setting δmin=0, Hilbert's well known kernel for rigid-sphere interactions is recovered for γ = 1

  8. Lattice Boltzmann simulation of flow around a confined circular cyclinder

    International Nuclear Information System (INIS)

    A two dimensional lattice Boltzmann model (LBM) based on a single time relaxation BGK model has been developed. Several benchmark problems including the Poiseuille flow, the lid driven cavity flow and the flow around a circular cylinder have been performed employing a d2q9 lattice. The laminar flow around a circular cylinder within a channel has been extensively investigated using the present lattice Boltzmann model. Both symmetric and asymmetric placement configurations of the circular cylinder within the channel have been considered. A new treatment for the outlet velocity and pressure (density) boundary conditions has been proposed and validated. The present LBM results are in excellent agreement with those of the other existing CFD results. Careful examination of the LBM results and an appropriate calculation of the lift coefficient based on the rectangular lattice representation of the circular cylinder reveals that the periodic oscillation of the lift coefficient has a second harmonic when the cylinder is placed asymmetrically within the channel. The second harmonic could be associated with an asymmetrical shedding pattern of the vortices behind the cylinder from the upper and lower sides of the cylinder. (author)

  9. Reciprocal relations based on the non-stationary Boltzmann equation

    Science.gov (United States)

    Sharipov, Felix

    2012-03-01

    The reciprocal relations for open gaseous systems are obtained on the basis of main properties of the non-stationary Boltzmann equation and gas-surface interaction law. It is shown that the main principles to derive the kinetic coefficients satisfying the reciprocal relations remain the same as those used for time-independent gaseous systems [F. Sharipov, Onsager-Casimir reciprocal relations based on the Boltzmann equation and gas-surface interaction law single gas, Phys. Rev. 73 (2006) 026110]. First, the kinetic coefficients are obtained from the entropy production expression; then it is proved that the coefficient matrix calculated for time reversed source functions is symmetric. The proof is based on the reversibility of the gas-gas and gas-surface interactions. Three examples of applications of the present theory are given. None of these examples can be treated in the frame of the classical Onsager-Casimir reciprocal relations, which are valid only in a particular case, when the kinetic coefficients are odd or even with respect to the time reversion. The approach is generalized for gaseous mixtures.

  10. Fault diagnosis via neural networks: The Boltzmann machine

    International Nuclear Information System (INIS)

    The Boltzmann machine is a general-purpose artificial neural network that can be used as an associative memory as well as a mapping tool. The usual information entropy is introduced, and a network energy function is suitably defined. The network's training procedure is based on the simulated annealing during which a combination of energy minimization and entropy maximization is achieved. An application in the nuclear reactor field is presented in which the Boltzmann input-output machine is used to detect and diagnose a pipe break in a simulated auxiliary feedwater system feeding two coupled steam generators. The break may occur on either the hot or the cold leg of any of the two steam generators. The binary input data to the network encode only the trends of the thermohydraulic signals so that the network is actually a polarity device. The results indicate that the trained neural network is actually capable of performing its task. The method appears to be robust enough so that it may also be applied with success in the presence of substantial amounts of noise that cause the network to be fed with wrong signals

  11. Polyelectrolyte Microcapsules: Ion Distributions from a Poisson-Boltzmann Model

    Science.gov (United States)

    Tang, Qiyun; Denton, Alan R.; Rozairo, Damith; Croll, Andrew B.

    2014-03-01

    Recent experiments have shown that polystyrene-polyacrylic-acid-polystyrene (PS-PAA-PS) triblock copolymers in a solvent mixture of water and toluene can self-assemble into spherical microcapsules. Suspended in water, the microcapsules have a toluene core surrounded by an elastomer triblock shell. The longer, hydrophilic PAA blocks remain near the outer surface of the shell, becoming charged through dissociation of OH functional groups in water, while the shorter, hydrophobic PS blocks form a networked (glass or gel) structure. Within a mean-field Poisson-Boltzmann theory, we model these polyelectrolyte microcapsules as spherical charged shells, assuming different dielectric constants inside and outside the capsule. By numerically solving the nonlinear Poisson-Boltzmann equation, we calculate the radial distribution of anions and cations and the osmotic pressure within the shell as a function of salt concentration. Our predictions, which can be tested by comparison with experiments, may guide the design of microcapsules for practical applications, such as drug delivery. This work was supported by the National Science Foundation under Grant No. DMR-1106331.

  12. Avoiding Boltzmann Brain domination in holographic dark energy models

    Directory of Open Access Journals (Sweden)

    R. Horvat

    2015-11-01

    Full Text Available In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB. It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a dimensionless model parameter c, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural c=1 line, the theory is rendered BB-safe. In the latter case, the bound on c is exponentially stronger, and seemingly at odds with those bounds on c obtained from various observational tests.

  13. Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

    Science.gov (United States)

    Molnár, Etele; Niemi, Harri; Rischke, Dirk H.

    2016-06-01

    Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function, f^0 k, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from f^0 k. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

  14. A hybrid method for the solution of linear Boltzmann equation

    International Nuclear Information System (INIS)

    Highlights: • The paper presents a novel method for the solution of linear Boltzmann equation. • The hybrid method, based on multiple collisions, combines transport with diffusion. • The physical basis of the method is discussed together with the mathematical model. • Results show its performance in terms of accuracy and computational time. • The extension of the method to more general configurations is discussed. - Abstract: This paper presents a novel approach devised to solve the transport of neutral particles in scattering and absorbing media. The solution to the linear Boltzmann equation is sought starting from a multi-collision approach of the integro-differential equation which is combined with an approximate model for the description of the residue after truncation of the Neumann series. In the paper, the theoretical basis of such hybrid method is discussed together with the physical intuition at the basis of the methodology. Results for both steady-state and transient problems are presented and an extension to general multi-dimensional, anisotropic problem is reported

  15. Wall Orientation and Shear Stress in the Lattice Boltzmann Model

    CERN Document Server

    Matyka, Maciej; Mirosław, Łukasz

    2013-01-01

    The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near ...

  16. Lattice Boltzmann Method for 3-D Flows with Curved Boundary

    Science.gov (United States)

    Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi

    2002-01-01

    In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.

  17. Avoiding Boltzmann Brain domination in holographic dark energy models

    CERN Document Server

    Horvat, R

    2015-01-01

    In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter) regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB). It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a parameter $c$, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural $c = 1$ line, the theory is rendered BB-safe. In the later case, the bound on $c$ is exponentially stronger, and seemingly at odds with those bounds on $c$ obtained from various observational tests.

  18. Lattice Boltzmann Simulation for Complex Flow in a Solar Wall

    Institute of Scientific and Technical Information of China (English)

    CHEN Rou; Shao Jiu-Gu; ZHENG You-Qu; YU Hui-Dan; XU You-Sheng

    2013-01-01

    In this letter,we present a lattice Boltzmann simulation for complex flow in a solar wall system which includes porous media flow and heat transfer,specifically for solar energy utilization through an unglazed transpired solar air collector (UTC).Besides the lattice Boltzmann equation (LBE) for time evolution of particle distribution function for fluid field,we introduce an analogy,LBE for time evolution of distribution function for temperature.Both temperature fields of fluid (air) and solid (porous media) are modeled.We study the effects of fan velocity,solar radiation intensity,porosity,etc.on the thermal performance of the UTC.In general,our simulation results are in good agreement with what in literature.With the current system setting,both fan velocity and solar radiation intensity have significant effect on the thermal performance of the UTC.However,it is shown that the porosity has negligible effect on the heat collector indicating the current system setting might not be realistic.Further examinations of thermal performance in different UTC systems are ongoing.The results are expected to present in near future.

  19. 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)

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

    International Nuclear Information System (INIS)

    We present a L2-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 L2-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 L2-stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L2-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 L2-stability estimate. This is the first result on the L2-stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

  1. Boltzmann-Gibbs Entropy Versus Tsallis Entropy: Recent Contributions to Resolving the Argument of Einstein Concerning "Neither Herr Boltzmann nor Herr Planck has given a definition of W"?

    CERN Document Server

    Haubold, H J; Saxena, R K

    2004-01-01

    Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intense investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technology 2003'to Professor Constantino Tsallis from the Brazilian Center for Research in Physics.

  2. EVENT MARKETING

    OpenAIRE

    Cajnko, Katja

    2014-01-01

    In a highly developed consumer society saturated with advertisements, events are getting more and more popular as a marketing communication element. In literature events are mentioned in connection with tourism and event management, but recent research shows an increase in using events as an element of the marketing communication mix. Two of the most important advantages of events are: it is the consumer's own decision to attend the events and they can offer to the consumer a positive experie...

  3. Event management

    OpenAIRE

    Urban, Zdeněk

    2013-01-01

    The thesis deals with event management and is formally divided into three sections. The first section provides the theoretical basis for the practical part. It primarily defines the terms event, event management and event marketing. The theoretical part proceeds from the general introduction to more detailed examination of the issue, which includes the classification of event marketing within the marketing and communication mix of the company, the typology of events and explanation of various...

  4. Event management

    OpenAIRE

    Jandová, Dita

    2011-01-01

    The thesis deal with event management. For better insight into this field event management is described on case of management of conference. The thesis has three main parts. In the theoretical part there are definitions of terms like event management, conference and other related terms. Further chapters are concerned with the position of event management in the communication mix, typologies of events and mostly with the crucial aspects of event management. In the second part of the thesis the...

  5. Event management

    OpenAIRE

    Šubrtová, Veronika

    2013-01-01

    This bachelor thesis on the topic event management develops this concept, focuses mainly on the creation of the event and its application in practice. Management, event and event management are described in the theoretical section. The importace of event management in the marketing communications mix is shown subsequently and especially the creation of the event is more detailed described. This is then reflected in the practical part of the thesis, in which the awards gala is planed and orga...

  6. Event management

    OpenAIRE

    Grebíková, Kristýna

    2014-01-01

    The thesis in theoretical part focuses on the concepts of event management and their interaction. The theoretical part focuses on the creation of event planning and marketing strategies, typology of events, and provides a situational analysis, objectives events, defines the target group, plan the resources, establish a budget and will focus on event controlling. The practical part carries theory into practice and deals with the organization of the event in the company TON in Chile. Based on a...

  7. Boltzmann and Einstein: Statistics and dynamics –An unsolved problem

    Indian Academy of Sciences (India)

    E G D Cohen

    2005-05-01

    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, arguing that a statistical description of a system should be based on the dynamics of the system. This opened the way, especially for complex systems, for other than Boltzmann statistics. The first non-Boltzmann statistics, not based on dynamics though, was proposed by Tsallis. A generalization of Tsallis' statistics as a special case of a new class of superstatistics, based on Einstein's criticism of Boltzmann, is discussed. It seems that perhaps a combination of dynamics and statistics is necessary to describe systems with complicated dynamics.

  8. Lattice-Boltzmann scheme for computer simulation of two-phase flows; Gitter-Boltzmann-Verfahren zur Simulation von Zweiphasenstroemungen

    Energy Technology Data Exchange (ETDEWEB)

    Toelke, J.

    2001-07-01

    The first part of this work is concerned with the development of methodological foundations for the computer simulation of two-phase flows like gas-liquid-mixtures in complex, three-dimensional structures. The basic numerical approach is the Lattice-Boltzmann scheme which is very suitable for this class of problems. After the approach is verified using standard test cases, the method is applied to complex engineering problems. The most important application is the simulation of the two-phase flow (air/water) in a laboratory-scale biofilm reactor for wastewater treatment. The second part of the work deals with the development of efficient numerical methods for the stationary discrete Boltzmann equations. They are discretized by finite differences on uniform and non-uniform grids and fast solvers are applied to the resulting algebraic system of equations. Also a multigrid approach is developed and examined. For typical problems like boundary-layer and driven cavity flow a considerable gain in computing time is achieved. (orig.)

  9. Event marketing

    OpenAIRE

    Pham, Quynh Trang

    2008-01-01

    This study aims to analyze event-marketing activities of the small firm and propose new events. At first the theoretical part describes marketing and communication mix and then especially planning and development of event marketing campaign. Research data were collected by the method of survey to propose the new events. Randomly selected customers were asked to fill the questionnaire. Its results were integrated into the proposal of the new events. The interview was realized with the owner of...

  10. Event management

    OpenAIRE

    Pavléková, Markéta

    2013-01-01

    The main theme of the work is event management, which deals with the social events of various types. Event as a mean of communication is a common part of business strategy today and the organization became a separate industry. Procedures how to implement successful event are the essential part of the work. Organizationally demanding activity of event managers, which includes planning, organizing, staffing, leadership and control is supported by marketing activities, which are described in the...

  11. Event management

    OpenAIRE

    Michňa, Michal

    2011-01-01

    The theoretical part of this thesis deals with event management in general. The stress of its theoretical part is put on relation between event management and the other communication channels usually used by marketing experts in a firm. There is also described a confrontation of event management with processes which are basically used in project management. The theoretical part is mainly concerned with event management and organisation of events. There is a deep description of its prepara...

  12. Event management

    OpenAIRE

    Vomáčková, Kateřina

    2013-01-01

    This thesis deals with event management from theory to practice. First part of the thesis consists of literature review of this topic – from definition of basic terms, through event management’s classification in marketing of a company, to description of different stages of event management process. The second part of the thesis is based on practice – an agency that organized for the third year an event focusing on children and sport, is presented here. Last year of this event including...

  13. Approximate Message Passing with Restricted Boltzmann Machine Priors

    CERN Document Server

    Tramel, Eric W; Krzakala, Florent

    2015-01-01

    Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.

  14. Gauss Quadratures - the Keystone of Lattice Boltzmann Models

    Science.gov (United States)

    Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor

    2014-01-01

    In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.

  15. Beyond Poisson-Boltzmann: Numerical Sampling of Charge Density Fluctuations.

    Science.gov (United States)

    Poitevin, Frédéric; Delarue, Marc; Orland, Henri

    2016-07-01

    We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin-like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counterions. PMID:27075231

  16. Simulation of a Microfluidic Gradient Generator using Lattice Boltzmann Methods

    CERN Document Server

    Simon, Tanaka

    2013-01-01

    Microfluidics provides a powerful and versatile technology to accurately control spatial and temporal conditions for cell culturing and can therefore be used to study cellular responses to gradients. Here we use Lattice Boltzmann methods (LBM) to solve both the Navier-Stokes equation (NSE) for the fluid and the coupled convection-diffusion equation (CDE) for the compounds that form the diffusion-based gradient. The design of a microfluidic chamber for diffusion-based gradients must avoid flow through the cell chamber. This can be achieved by alternately opening the source and the sink channels. The fast toggling of microfluidic valves requires switching between different boundary conditions. We demonstrate that the LBM is a powerful method for handling complex geometries, high Peclet number conditions, discontinuities in the boundary conditions, and multiphysics coupling.

  17. Lattice-Boltzmann hydrodynamics of anisotropic active matter

    Science.gov (United States)

    de Graaf, Joost; Menke, Henri; Mathijssen, Arnold J. T. M.; Fabritius, Marc; Holm, Christian; Shendruk, Tyler N.

    2016-04-01

    A plethora of active matter models exist that describe the behavior of self-propelled particles (or swimmers), both with and without hydrodynamics. However, there are few studies that consider shape-anisotropic swimmers and include hydrodynamic interactions. Here, we introduce a simple method to simulate self-propelled colloids interacting hydrodynamically in a viscous medium using the lattice-Boltzmann technique. Our model is based on raspberry-type viscous coupling and a force/counter-force formalism, which ensures that the system is force free. We consider several anisotropic shapes and characterize their hydrodynamic multipolar flow field. We demonstrate that shape-anisotropy can lead to the presence of a strong quadrupole and octupole moments, in addition to the principle dipole moment. The ability to simulate and characterize these higher-order moments will prove crucial for understanding the behavior of model swimmers in confining geometries.

  18. Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid.

    Science.gov (United States)

    Papenkort, S; Voigtmann, Th

    2015-07-28

    We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation. PMID:26233150

  19. Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations

    CERN Document Server

    Riotto, Antonio

    1998-01-01

    The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...

  20. Free Surface Lattice Boltzmann with Enhanced Bubble Model

    CERN Document Server

    Anderl, Daniela; Rauh, Cornelia; Rüde, Ulrich; Delgado, Antonio

    2016-01-01

    This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid-gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes.

  1. Comparison of different Propagation Steps for the Lattice Boltzmann Method

    CERN Document Server

    Wittmann, Markus; Hager, Georg; Wellein, Gerhard

    2011-01-01

    Several possibilities exist to implement the propagation step of the lattice Boltzmann method. This paper describes common implementations which are compared according to the number of memory transfer operations they require per lattice node update. A memory bandwidth based performance model is then used to obtain an estimation of the maximal reachable performance on different machines. A subset of the discussed implementations of the propagation step were benchmarked on different Intel and AMD-based compute nodes using the framework of an existing flow solver which is specially adapted to simulate flow in porous media. Finally the estimated performance is compared to the measured one. As expected, the number of memory transfers has a significant impact on performance. Advanced approaches for the propagation step like "AA pattern" or "Esoteric Twist" require more implementation effort but sustain significantly better performance than non-naive straight forward implementations.

  2. 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 of...... an objective function for which the gradient is not available. The algorithm samples function values from a search distribution and adapts the parameters of the distribution during the optimization process. In the thesis, new update schemes for the covariance matrix used by the CMA-ES are...... second part of the thesis is concerned with RBMs that are fitted to a dataset using maximum log-likelihood. As the computation of the distribution's normalization constant is intractable, Markov Chain Monte Carlo methods are required to estimate and follow the log-likelihood gradient. The thesis...

  3. Electric Conductivity from the solution of the Relativistic Boltzmann Equation

    CERN Document Server

    Puglisi, A; Greco, V

    2014-01-01

    We present numerical results of electric conductivity $\\sigma_{el}$ of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute $\\sigma_{el}$ using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for $\\sigma_{el}$ is determined by the transport cross section $\\sigma_{tr}$, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably $\\sigma_{el}$; for example at screening masses $...

  4. Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid

    Science.gov (United States)

    Papenkort, S.; Voigtmann, Th.

    2015-07-01

    We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation.

  5. Modeling of urban traffic networks with lattice Boltzmann model

    Science.gov (United States)

    Meng, Jian-ping; Qian, Yue-hong; Dai, Shi-qiang

    2008-02-01

    It is of great importance to uncover the characteristics of traffic networks. However, there have been few researches concerning kinetics models for urban traffic networks. In this work, a lattice Boltzmann model (LBM) for urban traffic networks is proposed by incorporating the ideas of the Biham-Middleton-Levine (BML) model into the LBM for road traffic. In the present model, situations at intersections with the red and green traffic signals are treated as a kind of boundary conditions varying with time. Thus, the urban traffic network could be described in the mesoscopic level. By performing numerical simulations under the periodic boundary conditions, the behavior of average velocity is investigated in detail. The numerical results agree quite well with those given by the Chowdhury-Schadschneider (ChSch) model (Chowdhury D. and Schadschneider A., Phys. Rev. E, 59 (1999) R1311). Furthermore, the statistical noise is reduced in this discrete kinetics model, thus, the present model has considerably high computational efficiency.

  6. Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium

    CERN Document Server

    Birrell, Jeremiah

    2014-01-01

    We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature $T(t)$ and phase space occupation factor $\\Upsilon(t)$. In this first paper we address (effectively) massless fermions and derive dynamical equations for $T(t)$ and $\\Upsilon(t)$ such that the zeroth order term of the basis alone captures the number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component ($e^\\pm$-annihilation).

  7. Determination of the Boltzmann Constant Using the Differential - Cylindrical Procedure

    CERN Document Server

    Feng, X J; Lin, H; Gillis, K A; Moldover, M R

    2015-01-01

    We report in this paper the progresses on the determination of the Boltzmann constant using the acoustic gas thermometer (AGT) of fixed-length cylindrical cavities. First, we present the comparison of the molar masses of pure argon gases through comparing speeds of sound of gases. The procedure is independent from the methodology by Gas Chromatography-Mass Spectrometry (GC-MS). The experimental results show good agreement between both methods. The comparison offers an independent inspection of the analytical results by GC-MS. Second, we present the principle of the novel differential-cylindrical procedure based on the AGT of two fixed-length cavities. The deletion mechanism for some major perturbations is analyzed for the new procedure. The experimental results of the differential-cylindrical procedure demonstrate some major improvements on the first, second acoustic and third virial coefficients, and the excess half-widths. The three acoustic virial coefficients agree well with the stated-of-the-art experime...

  8. Lattice Boltzmann method for mixtures at variable Schmidt number

    Science.gov (United States)

    Monteferrante, Michele; Melchionna, Simone; Marconi, Umberto Marini Bettolo

    2014-07-01

    When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.

  9. Lattice Boltzmann Equation On a 2D Rectangular Grid

    Science.gov (United States)

    Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

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

    International Nuclear Information System (INIS)

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

  11. On the Three-dimensional Central Moment Lattice Boltzmann Method

    CERN Document Server

    Premnath, Kannan N; 10.1007/s10955-011-0208-9

    2012-01-01

    A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-...

  12. Lattice Boltzmann model for melting with natural convection

    Energy Technology Data Exchange (ETDEWEB)

    Huber, Christian [Department of Earth and Planetary Science, University of California - Berkeley, 307 McCone Hall 4767, Berkeley, CA 94720-4767 (United States)], E-mail: chuber@seismo.berkeley.edu; Parmigiani, Andrea [Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211 Geneva 4 (Switzerland)], E-mail: andrea.parmigiani@terre.unige.ch; Chopard, Bastien [Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211 Geneva 4 (Switzerland)], E-mail: Bastien.Chopard@cui.unige.ch; Manga, Michael [Department of Earth and Planetary Science, University of California - Berkeley, 177 McCone Hall 4767, Berkeley, CA 94720-4767 (United States)], E-mail: manga@seismo.berkeley.edu; Bachmann, Olivier [Department of Earth and Space Science, University of Washington, Johnson Hall 070, Seattle WA 98195-1310 (United States)], E-mail: bachmano@u.washington.edu

    2008-10-15

    We develop a lattice Boltzmann method to couple thermal convection and pure-substance melting. The transition from conduction-dominated heat transfer to fully-developed convection is analyzed and scaling laws and previous numerical results are reproduced by our numerical method. We also investigate the limit in which thermal inertia (high Stefan number) cannot be neglected. We use our results to extend the scaling relations obtained at low Stefan number and establish the correlation between the melting front propagation and the Stefan number for fully-developed convection. We conclude by showing that the model presented here is particularly well-suited to study convection melting in geometrically complex media with many applications in geosciences.

  13. Ab initio molecular dynamics on the electronic Boltzmann equilibrium distribution

    Energy Technology Data Exchange (ETDEWEB)

    Alonso, J L; Echenique, P [Departamento de Fisica Teorica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Castro, A; Polo, V [Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza (Spain); Rubio, A [Nano-Bio Spectroscopy group and ETSF Scientific Development Centre, Departamento de Fisica de Materiales, Universidad del PaIs Vasco, Centro de Fisica de Materiales, CSIC-UPV/EHU-MPC and DIPC, E-20018 San Sebastian (Spain); Zueco, D, E-mail: dzueco@unizar.e [Instituto de Ciencia de Materiales de Aragon and Departamento de Fisica de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza (Spain)

    2010-08-15

    We prove that for a combined system of classical and quantum particles, it is possible to describe a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics (MD) do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach) and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings). A practical application of this MD to the study of the effect of temperature on molecular systems presenting (nearly) degenerate states-such as the avoided crossing in the ring-closure process of ozone-is presented.

  14. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

    International Nuclear Information System (INIS)

    Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials

  15. Full Eulerian lattice Boltzmann model for conjugate heat transfer.

    Science.gov (United States)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2015-12-01

    In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results. PMID:26764851

  16. The peeling process of infinite Boltzmann planar maps

    CERN Document Server

    Budd, Timothy

    2015-01-01

    We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a biased random walk, in terms of which the admissibility 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 be obtained from the peeling process of finite random maps by conditioning the perimeter process to stay positive. The simplicity of the resulting description of the peeling process allows us to obtain the scaling limit of the associated perimeter and volume process for arbitrary regular critical weight sequences.

  17. Thermal Correction to the Molar Polarizability of a Boltzmann Gas

    CERN Document Server

    Jentschura, U D; Mohr, P J

    2013-01-01

    Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI) for which an accurate value of the Boltzmann constant is needed. Here, we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorenz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation.

  18. Thermal correction to the molar polarizability of a Boltzmann gas

    Science.gov (United States)

    Jentschura, U. D.; Puchalski, M.; Mohr, P. J.

    2011-12-01

    Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI), for which an accurate value of the Boltzmann constant is needed. Here we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorentz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation.

  19. Sedimentation analysis of small ice crystals by Lattice Boltzmann Method

    CERN Document Server

    Giovacchini, Juan P

    2016-01-01

    Lattice Boltzmann Method (LBM) is used to simulate and analyze the sedimentation of small ($16-80 \\,\\mu m$) ice particles in the atmosphere. We are specially interested in evaluating the terminal falling velocity for two ice particle shapes: columnar ice crystals and six bullet-rosettes ice policrystal. The main objective in this paper is to investigate the LBM suitability to solve ice crystal sedimentation problems, as well as to evaluate these numerical methods as a powerful numerical tool to solve these problems for arbitrary ice crystal shapes and sizes. LBM results are presented in comparison with laboratory experimental results and theoretical proposals well known in the literature. The numerical results show good agreement with experimental and theoretical results for both geometrical configurations.

  20. Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics

    CERN Document Server

    Kuron, Michael; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-01-01

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann (LB) algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions, which are needed to simulate moving colloids, into the Capuani scheme has been lacking. In this paper, we detail how to introduce such moving boundaries, based on an analogue to the moving boundary method for the pure LB solver. The key ingredients in our method are mass and charge conservation for the solute spec...

  1. Towards Full Aircraft Airframe Noise Prediction: Lattice Boltzmann Simulations

    Science.gov (United States)

    Khorrami, Mehdi R.; Fares, Ehab; Casalino, Damiano

    2014-01-01

    Computational results for an 18%-scale, semi-span Gulfstream aircraft model are presented. Exa Corporation's lattice Boltzmann PowerFLOW(trademark) solver was used to perform time-dependent simulations of the flow field associated with this high-fidelity aircraft model. The simulations were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg (landing configuration). We focused on accurately predicting the prominent noise sources at the flap tips and main landing gear for the two baseline configurations, namely, landing flap setting without and with gear deployed. Capitalizing on the inherently transient nature of the lattice Boltzmann formulation, the complex time-dependent flow features associated with the flap were resolved very accurately and efficiently. To properly simulate the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips. Extensive comparison of the computed time-averaged and unsteady surface pressures with wind tunnel measurements showed excellent agreement for the global aerodynamic characteristics and the local flow field at the flap inboard and outboard tips and the main landing gear. In particular, the computed fluctuating surface pressure field for the flap agreed well with the measurements in both amplitude and frequency content, indicating that the prominent airframe noise sources at the tips were captured successfully. Gear-flap interaction effects were remarkably well predicted and were shown to affect only the inboard flap tip, altering the steady and unsteady pressure fields in that region. The simulated farfield noise spectra for both baseline configurations, obtained using a Ffowcs-Williams and Hawkings acoustic analogy approach, were shown to be in close agreement with measured values.

  2. Generalizing the Boltzmann equation in complex phase space.

    Science.gov (United States)

    Zadehgol, Abed

    2016-08-01

    In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)JCTPAH0021-999110.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015)PLEEE81539-375510.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others. PMID:27627421

  3. Polarizable atomic multipole solutes in a Poisson-Boltzmann continuum

    Science.gov (United States)

    Schnieders, Michael J.; Baker, Nathan A.; Ren, Pengyu; Ponder, Jay W.

    2007-03-01

    Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc. 58, 1486 (1936)] used vacuum properties of small molecules, including polarizability, dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pKa prediction. Introduction of 150mM salt lowered the electrostatic solvation energy between 2 and 13kcal /mole, depending on

  4. Kapitza conductance, temperature gradients, and solutions to the Boltzmann equation

    International Nuclear Information System (INIS)

    In the belief that the study of heat transport requires the study of the transport equation, we present an approach to the problem of the Kapitza conductance h/subK/ between two materials which involves the solutions of the Boltzmann equation. One of our purposes is to investigate the origin of the apparent temperature discontinuity ΔT that is associated with this phenomenon. The hydrodynamic solutions of the Boltzmann equation, which (by definition) are describable in terms of local thermohydrodynamic variables, can transfer heat but are not at all responsible for ΔT; whereas the nonhydrodynamic solutions are completely responsible for ΔT but do not transfer heat. An effective temperature T tilde is defined which approaches the thermodynamic temperature T far from the interface, and which is assumed to be continuous across the interface. With this assumption, formal expressions for ΔT and h/subK/ are derived. In the limit as the properties of the two materials become identical, R/subK/ (=h/subK//sup -1/) approaches zero, as should be the case. Further, this approach has a natural generalization to finite frequencies and includes lifetime effects. It is pointed out that thermometers do not measure T tilde but rather T/subR/ which reflects, in a complicated fashion, the presence of the nonhydrodynamic modes, whose amplitudes fall off exponentially as one moves from the interface. In He II, determination of the exponential damping lengths (as a function of temperature and pressure) would provide information about phonon dispersion and phonon interactions which is at least as detailed as could be obtained by other means

  5. Boltzmann electron PIC simulation of the E-sail effect

    Science.gov (United States)

    Janhunen, P.

    2015-12-01

    The solar wind electric sail (E-sail) is a planned in-space propulsion device that uses the natural solar wind momentum flux for spacecraft propulsion with the help of long, charged, centrifugally stretched tethers. The problem of accurately predicting the E-sail thrust is still somewhat open, however, due to a possible electron population trapped by the tether. Here we develop a new type of particle-in-cell (PIC) simulation for predicting E-sail thrust. In the new simulation, electrons are modelled as a fluid, hence resembling hybrid simulation, but in contrast to normal hybrid simulation, the Poisson equation is used as in normal PIC to calculate the self-consistent electrostatic field. For electron-repulsive parts of the potential, the Boltzmann relation is used. For electron-attractive parts of the potential we employ a power law which contains a parameter that can be used to control the number of trapped electrons. We perform a set of runs varying the parameter and select the one with the smallest number of trapped electrons which still behaves in a physically meaningful way in the sense of producing not more than one solar wind ion deflection shock upstream of the tether. By this prescription we obtain thrust per tether length values that are in line with earlier estimates, although somewhat smaller. We conclude that the Boltzmann PIC simulation is a new tool for simulating the E-sail thrust. This tool enables us to calculate solutions rapidly and allows to easily study different scenarios for trapped electrons.

  6. A simple lattice Boltzmann scheme for low Mach number reactive flows

    Institute of Scientific and Technical Information of China (English)

    CHEN; Sheng; LIU; Zhaohui; ZHANG; Chao; HE; Zhu; TIAN; Zhiwei; SHI; Baochang

    2006-01-01

    For simulating low Mach number reactive flows, a simple and coupled lattice Boltzmann (CLB) scheme is proposed, by which the fluid density can bear significant changes. Different from the existing hybrid lattice Boltzmann (HLB) scheme and non-coupled lattice Boltzmann (NCLB) scheme, this scheme is strictly lattice Boltzmann style and the fluid density couples directly with the temperature. Because it has got rid of the constraint of traditional thought in lattice Boltzmann scheme,on the basis of the equality among the particle speed c, the time step △t and the lattice grid spacing △x held, both c and △t can be adjusted in this scheme according to a "characteristic temperature" instead of the local temperature. The whole algorithm becomes more stable and efficient besides inheriting the intrinsically outstanding strong points of conventional lattice Boltzmann scheme. In this scheme, we also take into account different molecular weights of species, so it is more suitable for simulating actual low Mach number reactive flows than previous work. In this paper, we simulated a so-called "counter-flow" premixed propane-air flame, and the results got by our scheme are much better than that obtained by NCLB. And the more important thing is that the exploration in this work has offered a kind of brand-new train of thought for building other novel lattice Boltzmann scheme in the future.

  7. Event management

    OpenAIRE

    Palkosková, Barbora

    2011-01-01

    The diploma thesis deals with a term of event management and its connection to the event marketing. First part of the work focuses on terms that are superior to event management and those are marketing and marketing mix of 4P´s. Communication mix is than separated into smaller parts, defining the position of event marketing and management among them. Accent is put on the current possibilities of typology and separation of event and its practical use. Issue of events is connected to the...

  8. First-principles particle simulation and Boltzmann equation analysis of Negative Differential Conductivity and Transient Negative Mobility effects in xenon

    CERN Document Server

    Donko, Zoltan

    2015-01-01

    The Negative Differential Conductivity and Transient Negative Mobility effects in xenon gas are analyzed by a first-principles particle simulation technique and via an approximate solution of the Boltzmann transport equation (BE). The particle simulation method is devoid of the approximations that are traditionally adopted in the BE solutions in which (i) the distribution function is searched for in a two-term form, (ii) the Coulomb part of the collision integral for the anisotropic part of the distribution function is neglected, (iii) Coulomb collisions are treated as binary events, and (iv) the range of the electron-electron interaction is limited to a cutoff distance. The results obtained from the two methods are, for both effects, in good qualitative agreement, small differences are attributed to the approximations listed above.

  9. Event management

    OpenAIRE

    Štefl, Petr

    2011-01-01

    This bachelor thesis on the topic of event management deals with planning, organizing, managing, monitoring and implementation of special social events, termed event. It explains what they mean by this term we can imagine and as you can in terms of typology to distinguish events. Literature review consists of the acquired theoretical knowledge in management, project management and marketing. It describes the principles and procedure in place, we should keep the successful organization of ...

  10. Event management

    OpenAIRE

    Strýhalová, Veronika

    2013-01-01

    The Diploma thesis is focused on the Event management company, which organizes a big family minded sport day and describes its activity plan. The thesis consists three main parts, the first – the teoretic part specifices proffesional terms about an event management. This part also describes different event forms which are focused on the right selection and final strategy, the following control of financial situation and event overall what is in general a part of marketing mixture. The second ...

  11. Event management

    OpenAIRE

    Stružková, Tereza

    2014-01-01

    The main objective of this thesis is based on theoretical knowledge and analysis of the actual implementation event action in congress centre of 4*hotel. Asesment of importance, correctnesand effectivess of the vatious procedures of organizin events and create new complete schematic principle of organizin events Implementation actions will be considered from two sides – from side of the company organizer and from the side of event managment coordinator. All the outputs of these two aspect ...

  12. On Exact Solutions to the Cylindrical Poisson-Boltzmann Equation with Applications to Polyelectrolytes

    OpenAIRE

    Tracy, C. A.; Widom, H.

    1997-01-01

    Using exact results from the theory of completely integrable systems of the Painleve/Toda type, we examine the consequences for the theory of polyelectrolytes in the (nonlinear) Poisson-Boltzmann approximation.

  13. A Stability Notion for the viscous Shallow Water Lattice Boltzmann Equations

    CERN Document Server

    Banda, Mapundi K

    2015-01-01

    The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in Banda, M. K., Yong, W.- A. and Klar, A: A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. {\\bf 27(6)}, 2098-2111 (2006). It is found that to maintain stability a careful choice of the value of the reduced gravity must be made. The stability notion is employed to investigate different shallow water lattice Boltzmann Equations. The effect of the reduced gravity on the mechanism of instability is investigated. Results are tested using the Lattice Boltzmann Method for various values of the governing parameters of the flow. It is observed that even for the discrete model the reduced gravity has a significant effect on the stability.

  14. Corrected Stefan—Boltzmann Law and Lifespan of Schwarzschild-de-sitter Black Hole

    Science.gov (United States)

    Shi, Yan; Tang-Mei, He; Jing-Yi, Zhang

    2016-06-01

    In this paper, we correct the Stefan—Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan—Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan—Boltzmann law contains two terms, the T4 term and the T6 term. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan—Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small. Supported by the National Natural Science Foundation of China under Grant Nos. 11273009 and 11303006

  15. An Entropy Stable Discontinuous Galerkin Finite-Element Moment Method for the Boltzmann Equation

    CERN Document Server

    Abdelmalik, M R A

    2016-01-01

    This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the moment systems derives from minimization of a suitable {\\phi}-divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic moment systems that retain the fundamental structural properties of the Boltzmann equation. The resulting combined discontinuous Galerkin moment method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. We present a new class of numerical flux functions, based on the underlying renormalized Boltzmann equation, that ensure entropy dissipation of the approximation scheme. Numerical results are presented for a one-dimensional test case.

  16. Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

    Indian Academy of Sciences (India)

    Tao Jiang; Qiwei Gong; Ruofan Qiu; Anlin Wang

    2014-10-01

    An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce `spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.

  17. A generalized linear Boltzmann equation for non-classical particle transport

    International Nuclear Information System (INIS)

    This paper presents a derivation and initial study of a new generalized linear Boltzmann equation (GLBE), which describes particle transport for random statistically homogeneous systems in which the distribution function for chord lengths between scattering centers is non-exponential. Such problems have recently been proposed for the description of photon transport in atmospheric clouds; this paper is a first attempt to develop a Boltzmann-like equation for these and other related applications.

  18. 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.

  19. Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

    OpenAIRE

    Degond, Pierre; Liu, Hailiang; Savelief, Dominique; Vignal, Marie-Hélène

    2012-01-01

    International audience This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare...

  20. On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions

    OpenAIRE

    Punshon-Smith, Samuel; Smith, Scott

    2016-01-01

    This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kin...

  1. From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries

    CERN Document Server

    Golse, François

    2011-01-01

    The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of the Navier-Stokes equations. The present paper slightly extends recent results from [C. Bardos, F. Golse, L. Paillard, Comm. Math. Sci., 10 (2012), 159--190] to the case of boundary conditions for the Boltzmann equation more general than Maxwell's accomodation condition.

  2. Global stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system

    OpenAIRE

    Duan, Renjun; Liu, Shuangqian

    2014-01-01

    This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann relation. We allows that the electric potential may take distinct constant states at both far-fields. The rarefaction wave whose strength is not necessarily small is constructed through the quasineutral Euler equations coming from the zero-order fluid dynamic app...

  3. Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons

    OpenAIRE

    Nguyen, Toan T.; Tran, Minh-Binh

    2016-01-01

    We consider the quantum Boltzmann equation, which describes the growth of the condensate, or in other words, models the interaction between excited atoms and a condensate. In this work, the full form of Bogoliubov dispersion law is considered, which leads to a detailed study of surface integrals inside the collision operator on energy manifolds. We prove that positive radial solutions of the quantum Boltzmann equation are bounded from below by a Gaussian, uniformly in time.

  4. Anwendung des Lattice-Boltzmann-Verfahrens zur Berechnung strömungsakustischer Probleme

    OpenAIRE

    Wilde, Andreas

    2007-01-01

    The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) an...

  5. The Boltzmann-Langevin approach and its application to nuclear multifragmentation

    International Nuclear Information System (INIS)

    We present the Boltzmann-Langevin approach which provides a description of the strongly out of equilibrium dynamics encountered in the course of violent heavy-ion collisions. After having introduced the Boltzmann-Langevin model we present some applications to a situation where fluctuations are expected to play an important role: the production of Intermediate Mass Fragments in heavy-ion collisions at beam energies of a few tens of MeV/u. (authors)

  6. From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries

    OpenAIRE

    Golse, François

    2011-01-01

    The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of the Navier-Stokes equations. The present paper slightly extends recent results from [C. Bardos, F. Golse, L. Paillard, Comm. Math. Sci., 10 (2012), 159--190] to the case of boundary conditions for the Boltzmann equation more general than Maxwell's accomoda...

  7. Corrections to the Boltzmann mean free path in disordered systems with finite size scatterers

    OpenAIRE

    Correia, S

    2001-01-01

    The mean free path is an essential characteristic length in disordered systems. In microscopic calculations, it is usually approximated by the classical value of the elastic mean free path. It corresponds to the Boltzmann mean free path when only isotropic scattering is considered, but it is different for anisotropic scattering. In this paper, we work out the corrections to the so called Boltzmann mean free path due to multiple scattering effects on finite size scatterers, in the s-wave appro...

  8. MULTI-FLUX FORMULATION OF THE BOLTZMANN EQUATION FOR CARRIER TRANSPORT IN SEMICONDUCTORS

    OpenAIRE

    Banoo, Kausar; Lundstrom, Mark

    1998-01-01

    This report describes how the Boltzmann Transport Equation for carrier transport in s~~miconductocrasn be formulated in a manner suit able for numerical simulation. It arose from an effort to generalise earlier work which used pre-computed scattering matrices to solve the Boltzmann Transport Equation. It also generalises the formulation used to treat neutron transport so that energy band-structure, scattering in semiconductors and electric fields can be treated. We present two different, but ...

  9. Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion

    OpenAIRE

    Baldovin, Fulvio; Moyano, Luis G.; Tsallis, Constantino

    2004-01-01

    We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\\Gamma$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $\\beta$-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (${\\mathbf F}=m{\\mathbf a}$). At higher energies we discuss partia...

  10. Simulation of a Natural Convection by the Hybrid Thermal Lattice Boltzmann Equation

    Energy Technology Data Exchange (ETDEWEB)

    Ryu, Seungyeob; Kang, Hanok; Seo, Jaekwang; Yun, Juhyeon; Zee, Sung-Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    2006-07-01

    Recently, the lattice Boltzmann method(LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over 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. In spite of its success in solving various challenging problems involving athermal fluids, the LBM has not been able to handle realistic thermal fluids with a satisfaction. The difficulty encountered in the thermal LBM seems to be the numerical instabilities. The existing thermal lattice Boltzmann models may be classified into three categories based on their approach in solving the Boltzmann equation, namely, the multispeed, the passive scalar and the thermal energy distribution approach. For more details see Ref. In the present work, the hybrid thermal lattice Boltzmann scheme proposed by Lallemand and Luo is used for simulating a natural convection in a square cavity. They proposed a hybrid thermal lattice Boltzmann equation(HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time(MRT) model, whereas the diffusion-advection equations for the temperature are solved separately by using finite-difference technique. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of temperature fields at high Rayleigh numbers.

  11. 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.

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

    International Nuclear Information System (INIS)

    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)

  13. Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model

    Science.gov (United States)

    Velasco, Ali Mauricio; Muñoz, José Daniel

    2015-10-01

    Rayleigh-Taylor and Kelvin-Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil-water one. The model, proposed by He, Chen and Zhang (1999) [1] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [2]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation γ ∝√{ A} between the growing rate γ of the Rayleigh-Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.

  14. Lattice Boltzmann Modeling of Micro-fluidic Devices

    Energy Technology Data Exchange (ETDEWEB)

    Clague, D S

    2002-01-28

    The results to date do indeed show that the lattice Boltzmann method accurately solves relevant, non-trivial flow problems. The parallelization of both the fluid and the mobile species in flow has enhanced this capability such that it is useful for solving relevant problems in a timely fashion. The initial studies of stationary or capture species revealed evidence of hydrodynamic screening between upstream and downstream particles. Numerical studies reveal that the critical length for which the test particle is hydrodynamically decoupled from upstream and downstream particles is on the order of 30 sphere radii. For mobile species, the LB capability was shown to be naturally suited for predicting the hydrodynamic lift phenomenon (inertial lift). A conversion factor was developed based on scaling arguments to include relevant forces generated by external fields. Using this conversion, an analytic solution for the Dielectrophoretic force was included into the LB capability which enabled the study of Dielectrophoretic particle capture. The Non-Newtonian enhancements have expanded the applicability of the LB capability to more physical systems. Specifically, with the bead-n-spring representation of macromolecules researchers will be able to study chain dynamics in micro-, physiological and Bio-MEMS environments. Furthermore, the ability to capture the shear thinning behavior, without any increase in computational time, positions this capability to be applied to a whole host of new problems involving biofluids.

  15. Multiblock approach for the passive scalar thermal lattice Boltzmann method

    Science.gov (United States)

    Huang, Rongzong; Wu, Huiying

    2014-04-01

    A multiblock approach for the passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time collision scheme is proposed based on the Chapman-Enskog analysis. The interaction between blocks is executed in the moment space directly and an external force term is considered. Theoretical analysis shows that all the nonequilibrium parts of the nonconserved moments should be rescaled, while the nonequilibrium parts of the conserved moments can be calculated directly. Moreover, a local scheme based on the pseudoparticles for computing heat flux is proposed with no need to calculate temperature gradient based on the finite-difference scheme. In order to validate the multiblock approach and local scheme for computing heat flux, thermal Couette flow with wall injection is simulated and good results are obtained, which show that the adoption of the multiblock approach does not deteriorate the convergence rate of TLBM and the local scheme for computing heat flux has second-order convergence rate. Further application of the present approach is the simulation of natural convection in a square cavity with the Rayleigh number up to 109.

  16. Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes

    Science.gov (United States)

    Ginzburg, Irina

    2013-01-01

    This paper develops a symmetrized framework for the analysis of the anisotropic advection-diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.

  17. Consistent lattice Boltzmann methods for incompressible axisymmetric flows

    Science.gov (United States)

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

    2016-08-01

    In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

  18. Lattice Boltzmann modeling of three-phase incompressible flows

    Science.gov (United States)

    Liang, H.; Shi, B. C.; Chai, Z. H.

    2016-01-01

    In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.

  19. 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.

  20. One-dimensional transient radiative transfer by lattice Boltzmann method.

    Science.gov (United States)

    Zhang, Yong; Yi, Hongliang; Tan, Heping

    2013-10-21

    The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed. PMID:24150298

  1. Lattice Boltzmann modeling of three-phase incompressible flows.

    Science.gov (United States)

    Liang, H; Shi, B C; Chai, Z H

    2016-01-01

    In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems. PMID:26871191

  2. Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

    CERN Document Server

    Molnar, E; Rischke, D H

    2016-01-01

    Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. To zeroth order this expansion yields ideal fluid dynamics, to first order Navier-Stokes theory, and to second order transient theories of dissipative fluid dynamics. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, so-called anisotropic fluid dynamics, in terms of an expansion around a single-particle distribution function which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. In this paper we derive, up to terms of second order in this expansion, the equations of mo...

  3. Transition flow ion transport via integral Boltzmann equation

    International Nuclear Information System (INIS)

    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

  4. Boltzmann electron PIC simulation of the E-sail effect

    CERN Document Server

    Janhunen, Pekka

    2015-01-01

    The solar wind electric sail (E-sail) is a planned in-space propulsion device that uses the natural solar wind momentum flux for spacecraft propulsion with the help of long, charged, centrifugally stretched tethers. The problem of accurately predicting the E-sail thrust is still somewhat open, however, due to a possible electron population trapped by the tether. Here we develop a new type of particle-in-cell (PIC) simulation for predicting E-sail thrust. In the new simulation, electrons are modelled as a fluid, hence resembling hydrid simulation, but in contrast to normal hybrid simulation, the Poisson equation is used as in normal PIC to calculate the self-consistent electrostatic field. For electron-repulsive parts of the potential, the Boltzmann relation is used. For electron-attractive parts of the potential we employ a power law which contains a parameter that can be used to control the number of trapped electrons. We perform a set of runs varying the parameter and select the one with the smallest number...

  5. Lattice Boltzmann Modeling of Micro-fluidic Devices

    International Nuclear Information System (INIS)

    The results to date do indeed show that the lattice Boltzmann method accurately solves relevant, non-trivial flow problems. The parallelization of both the fluid and the mobile species in flow has enhanced this capability such that it is useful for solving relevant problems in a timely fashion. The initial studies of stationary or capture species revealed evidence of hydrodynamic screening between upstream and downstream particles. Numerical studies reveal that the critical length for which the test particle is hydrodynamically decoupled from upstream and downstream particles is on the order of 30 sphere radii. For mobile species, the LB capability was shown to be naturally suited for predicting the hydrodynamic lift phenomenon (inertial lift). A conversion factor was developed based on scaling arguments to include relevant forces generated by external fields. Using this conversion, an analytic solution for the Dielectrophoretic force was included into the LB capability which enabled the study of Dielectrophoretic particle capture. The Non-Newtonian enhancements have expanded the applicability of the LB capability to more physical systems. Specifically, with the bead-n-spring representation of macromolecules researchers will be able to study chain dynamics in micro-, physiological and Bio-MEMS environments. Furthermore, the ability to capture the shear thinning behavior, without any increase in computational time, positions this capability to be applied to a whole host of new problems involving biofluids

  6. Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles

    Science.gov (United States)

    Zhang, Pei; Galindo-Torres, S. A.; Tang, Hongwu; Jin, Guangqiu; Scheuermann, A.; Li, Ling

    2016-06-01

    We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100 . The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

  7. Lattice-Boltzmann Simulations of Microswimmer-Tracer Interactions

    CERN Document Server

    de Graaf, Joost

    2016-01-01

    Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\\textit{et al.}, J. Chem. Phys.~\\textbf{144}, 134106 (2016)], in order to validate its applicability to study large-scale microswimmer suspensions. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The LB algorithm has an inherent near-field renormalization of the flow field, due to the force interpolation between the swimmers and the lattice. This strongly pe...

  8. Treatment of moving boundaries in lattice-Boltzmann simulations.

    Science.gov (United States)

    Indireshkumar, K.; Pal, A.; Brasseur, J. G.

    2000-11-01

    We consider the treatment of moving boundaries with the lattice-Boltzmann (LB) technique, where the treatment of the boundary often does not precisely conserve mass and spurious fluctuations in density/pressure result from boundary motion through fixed grids. First, we applied the extrapolation method proposed by Chen et. al.(S. Y. Chen, D. Martinez, and R Mei, Phys. Fluids) 8, 2527 (1996) to incompressible flow induced by the movement of a piston in a 2D ``cylinder'' with mass flow out of or into the cylinder. In these simulations, the velocity of the boundary nodes is set equal to the (known) velocity of the boundary (piston) in the equilibrium distribution function (Method I). In a second set of simulations, the boundary node velocities are obtained by interpolating between interior nodes and the boundary, thus including the effect of boundary position more precisely (Method II). Comparison of LB predictions with simulations using FIDAP show pressure agreement to witnin 2 %. The total mass is conserved to within 0.1% with Method I and improves to within 0.02 % using method II. Spurious fluctuations in density/pressure due to boundary movement is about 0.9% with Method I, which improves significantly to about 0.3% with Method II. The application of these simple techniques to more complex geometries and wall (and fluid) motions in a stomach during gastric emptying will be presented.

  9. Lattice Boltzmann method for one-dimensional vector radiative transfer.

    Science.gov (United States)

    Zhang, Yong; Yi, Hongliang; Tan, Heping

    2016-02-01

    A one-dimensional vector radiative transfer (VRT) model based on lattice Boltzmann method (LBM) that considers polarization using four Stokes parameters is developed. The angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by LBM. LBM has such attractive properties as simple calculation procedure, straightforward and efficient handing of boundary conditions, and capability of stable and accurate simulation. To validate the performance of LBM for vector radiative transfer, four various test problems are examined. The first case investigates the non-scattering thermal-emitting atmosphere with no external collimated solar. For the other three cases, the external collimated solar and three different scattering types are considered. Particularly, the LBM is extended to solve VRT in the atmospheric aerosol system where the scattering function contains singularities and the hemisphere space distributions for the Stokes vector are presented and discussed. The accuracy and computational efficiency of this algorithm are discussed. Numerical results show that the LBM is accurate, flexible and effective to solve one-dimensional polarized radiative transfer problems. PMID:26906779

  10. Event Modeling

    DEFF Research Database (Denmark)

    Bækgaard, Lars

    2001-01-01

    The purpose of this chapter is to discuss conceptual event modeling within a context of information modeling. Traditionally, information modeling has been concerned with the modeling of a universe of discourse in terms of information structures. However, most interesting universes of discourse...... are dynamic and we present a modeling approach that can be used to model such dynamics.We characterize events as both information objects and change agents (Bækgaard 1997). When viewed as information objects events are phenomena that can be observed and described. For example, borrow events in a library can...... temporarily from bookcases to borrowers. When we characterize events as change agents we focus on concepts like transactions, entity processes, and workflow processes....

  11. Event Modeling

    DEFF Research Database (Denmark)

    Bækgaard, Lars

    2001-01-01

    The purpose of this chapter is to discuss conceptual event modeling within a context of information modeling. Traditionally, information modeling has been concerned with the modeling of a universe of discourse in terms of information structures. However, most interesting universes of discourse...... are dynamic and we present a modeling approach that can be used to model such dynamics. We characterize events as both information objects and change agents (Bækgaard 1997). When viewed as information objects events are phenomena that can be observed and described. For example, borrow events in a library can...... temporarily from bookcases to borrowers. When we characterize events as change agents we focus on concepts like transactions, entity processes, and workflow processes....

  12. A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio

    OpenAIRE

    Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

    2016-01-01

    A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice ...

  13. How do ants make sense of gravity? A Boltzmann Walker analysis of Lasius niger trajectories on various inclines.

    Directory of Open Access Journals (Sweden)

    Anaïs Khuong

    Full Text Available The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by [Formula: see text] rad ([Formula: see text] data points. At the population scale, support inclination favors dispersal along uphill and downhill directions. An ant's decision making process is modeled using a version of the Boltzmann Walker model, which describes an ant's random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ([Formula: see text] segments, this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the [Formula: see text] incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines.

  14. Implementing the lattice Boltzmann model on commodity graphics hardware

    International Nuclear Information System (INIS)

    Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications. The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM). We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor. Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the

  15. Expected energy-based restricted Boltzmann machine for classification.

    Science.gov (United States)

    Elfwing, S; Uchibe, E; Doya, K

    2015-04-01

    In classification tasks, restricted Boltzmann machines (RBMs) have predominantly been used in the first stage, either as feature extractors or to provide initialization of neural networks. In this study, we propose a discriminative learning approach to provide a self-contained RBM method for classification, inspired by free-energy based function approximation (FE-RBM), originally proposed for reinforcement learning. For classification, the FE-RBM method computes the output for an input vector and a class vector by the negative free energy of an RBM. Learning is achieved by stochastic gradient-descent using a mean-squared error training objective. In an earlier study, we demonstrated that the performance and the robustness of FE-RBM function approximation can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that the learning performance of RBM function approximation can be further improved by computing the output by the negative expected energy (EE-RBM), instead of the negative free energy. To create a deep learning architecture, we stack several RBMs on top of each other. We also connect the class nodes to all hidden layers to try to improve the performance even further. We validate the classification performance of EE-RBM using the MNIST data set and the NORB data set, achieving competitive performance compared with other classifiers such as standard neural networks, deep belief networks, classification RBMs, and support vector machines. The purpose of using the NORB data set is to demonstrate that EE-RBM with binary input nodes can achieve high performance in the continuous input domain. PMID:25318375

  16. Peristaltic particle transport using the Lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Connington, Kevin William [Los Alamos National Laboratory; Kang, Qinjun [Los Alamos National Laboratory; Viswanathan, Hari S [Los Alamos National Laboratory; Abdel-fattah, Amr [Los Alamos National Laboratory; Chen, Shiyi [JOHNS HOPKINS UNIV.

    2009-01-01

    Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.

  17. Podolsky electromagnetism and a modification in Stefan-Boltzmann law

    Energy Technology Data Exchange (ETDEWEB)

    Bonin, Carlos Alberto; Bufalo, Rodrigo Santos; Escobar, Bruto Max Pimentel; Zambrano, German Enrique Ramos [Instituto de Fisica Teorica (IFT/UNESP), Sao Paulo, SP (Brazil)

    2009-07-01

    Full text. As it is well-known, gauge fields that emerge from the gauge principle are massless vector fields. Considering the photon as a Proca particle, experience sets an upper limit on its mass. This limit is m{sub Proca} < 6X10{sup -17}eV (PDG 2006). However, a mass term, regardless how small, breaks the gauge symmetry. Nevertheless, there exists a theory in which is possible to introduce a mass term preserving all symmetries of Maxwell electromagnetism, including the gauge one: such theory is known as Podolsky Electromagnetism. Podolsky theory is a second- order-derivative theory and has some remarkable properties, despite those already mentioned: the theory has two sectors, a massive one and massless one, it depends on a free parameter (which happens to be the mass of the massive sector) that, like all other elementary particles's masses of the Standard Model, must be fixed through experiences, and the fact that the electrostatic potential is finite everywhere, including over a punctual charge. Just like Maxwell electromagnetism, Podolsky's is a constrained theory and, since it is of second order in the derivatives, it consists in a much richer theoretical structure. Therefore, from both, theoretical and experimental points of view, Podolsky electromagnetism is a very attractive theory. In this work we study a gas of Podolsky photons at finite temperature through path integration. We show that the massless sector leads to the famous Planck's law for black-body radiation and, therefore, to the Stefan-Boltzmann law. We also show that the massive sector of the Podolsky theory induces a modification in both these laws. It is possible to set limits on the Podolsky parameter through comparison of our results with data from cosmic microwave background radiation. (author)

  18. Podolsky electromagnetism and a modification in Stefan-Boltzmann law

    International Nuclear Information System (INIS)

    Full text. As it is well-known, gauge fields that emerge from the gauge principle are massless vector fields. Considering the photon as a Proca particle, experience sets an upper limit on its mass. This limit is mProca -17eV (PDG 2006). However, a mass term, regardless how small, breaks the gauge symmetry. Nevertheless, there exists a theory in which is possible to introduce a mass term preserving all symmetries of Maxwell electromagnetism, including the gauge one: such theory is known as Podolsky Electromagnetism. Podolsky theory is a second- order-derivative theory and has some remarkable properties, despite those already mentioned: the theory has two sectors, a massive one and massless one, it depends on a free parameter (which happens to be the mass of the massive sector) that, like all other elementary particles's masses of the Standard Model, must be fixed through experiences, and the fact that the electrostatic potential is finite everywhere, including over a punctual charge. Just like Maxwell electromagnetism, Podolsky's is a constrained theory and, since it is of second order in the derivatives, it consists in a much richer theoretical structure. Therefore, from both, theoretical and experimental points of view, Podolsky electromagnetism is a very attractive theory. In this work we study a gas of Podolsky photons at finite temperature through path integration. We show that the massless sector leads to the famous Planck's law for black-body radiation and, therefore, to the Stefan-Boltzmann law. We also show that the massive sector of the Podolsky theory induces a modification in both these laws. It is possible to set limits on the Podolsky parameter through comparison of our results with data from cosmic microwave background radiation. (author)

  19. Thermostatistically approaching living systems: Boltzmann Gibbs or nonextensive statistical mechanics?

    Science.gov (United States)

    Tsallis, Constantino

    2006-03-01

    Boltzmann-Gibbs ( BG) statistical mechanics is, since well over one century, successfully used for many nonlinear dynamical systems which, in one way or another, exhibit strong chaos. A typical case is a classical many-body short-range-interacting Hamiltonian system (e.g., the Lennard-Jones model for a real gas at moderately high temperature). Its Lyapunov spectrum (which characterizes the sensitivity to initial conditions) includes positive values. This leads to ergodicity, the stationary state being thermal equilibrium, hence standard applicability of the BG theory is verified. The situation appears to be of a different nature for various phenomena occurring in living organisms. Indeed, such systems exhibit a complexity which does not really accommodate with this standard dynamical behavior. Life appears to emerge and evolve in a kind of delicate situation, at the frontier between large order (low adaptability and long memory; typically characterized by regular dynamics, hence only nonpositive Lyapunov exponents) and large disorder (high adaptability and short memory; typically characterized by strong chaos, hence at least one positive Lyapunov exponent). Along this frontier, the maximal relevant Lyapunov exponents are either zero or close to that, characterizing what is currently referred to as weak chaos. This type of situation is shared by a great variety of similar complex phenomena in economics, linguistics, to cite but a few. BG statistical mechanics is built upon the entropy S=-k∑plnp. A generalization of this form, S=k(1-∑piq)/(q-1) (with S=S), has been proposed in 1988 as a basis for formulating what is nowadays currently called nonextensive statistical mechanics. This theory appears to be particularly adapted for nonlinear dynamical systems exhibiting, precisely, weak chaos. Here, we briefly review the theory, its dynamical foundation, its applications in a variety of disciplines (with special emphasis to living systems), and its connections with

  20. A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio

    CERN Document Server

    Hu, Kainan; Geng, Shaojuan

    2016-01-01

    A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice Boltzmann models are applied to simulating the shock tube of one dimension. Good agreement between the numerical results and the analytical solutions are obtained.

  1. Simulations of the fusion of necklace-ring pattern in the complex Ginzburg-Landau equation by lattice Boltzmann method

    Science.gov (United States)

    Zhang, Jianying; Yan, Guangwu

    2016-04-01

    A lattice Boltzmann model for solving the (2+1) dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a two-dimensional space, and the evolution of the model is about a spatial axis rather than time. The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Numerical results reproduce the phenomena of the fusion of necklace-ring pattern and the effect of non-linearity on the soliton in the CQCGLE.

  2. Lattice Boltzmann simulation to study reaction-diffusion processes in geological media

    International Nuclear Information System (INIS)

    A reaction-diffusion process of 135Cs diffusion through a sand column has been simulated using lattice Boltzmann simulation technique. Mathematical formulation of the reaction-diffusion process has been carried out where interaction of 135Cs with soil has been modeled as linear isotherm. The linear isotherm model converts reaction diffusion problem to a diffusion problem with apparent diffusion coefficient instead of effective diffusion coefficient. Values of apparent diffusion coefficient for a particular Trombay soil has been taken from published literature data. A lattice Boltzmann diffusion model is used to simulate the process. Lattice Boltzmann solution is compared with analytical solution and a good agreement between the two is obtained. It has been shown that lattice Boltzmann simulation gives more accurate results as compared to finite difference method based solutions for the same time step value. Accuracy here is shown to be the closest to the analytical solution. Other superiorities of lattice Boltzmann method over convention numerical technique are highlighted with proper reasoning. (author)

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

    International Nuclear Information System (INIS)

    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)

  4. EVENT SEGMENTATION

    OpenAIRE

    Zacks, Jeffrey M.; Swallow, Khena M.

    2007-01-01

    One way to understand something is to break it up into parts. New research indicates that segmenting ongoing activity into meaningful events is a core component of ongoing perception, with consequences for memory and learning. Behavioral and neuroimaging data suggest that event segmentation is automatic and that people spontaneously segment activity into hierarchically organized parts and sub-parts. This segmentation depends on the bottom-up processing of sensory features such as movement, an...

  5. Event management

    OpenAIRE

    Plechatý, Josef

    2012-01-01

    This theses focused on Event management is divided into two parts. First part includes theoretical knowledge while the second part is strictly practical. The first part is focused on marketing, its importance and basic terms. The chapter about marketing is followed by marketing mix, which is shortly characterized and divided into advertisement, sales promotion, public relations and other elements of the communication mix. The last part is a detailed study of Event marketing which includes th...

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

    International Nuclear Information System (INIS)

    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 v2 values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from Elab=2-160 A GeV. The HBT correlation of the negatively charged pion source created in central

  7. 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

  8. Investigation of the Boltzmann relation in plasmas with non-Maxwellian electron distribution

    International Nuclear Information System (INIS)

    An experimental investigation of the Boltzmann relation at various radio frequency (RF) powers was performed in a low pressure RF inductively coupled plasma (ICP). The measured electron energy probability functions (EEPFs) show a high population of low energy electrons at low RF powers, while the population of high energy electrons is high at high RF powers. In these bi-Maxwellian EEPFs, radial variations of the electron density and the plasma potential from the center to the edge of the discharge chamber were plotted according to the Boltzmann relation with the effective temperature Teff and the screening temperature Ts, and it was found that the Boltzmann relation with the screening temperature, rather than with the effective temperature, describes the relation between the electron density and the plasma potential

  9. Comment on ‘A low-uncertainty measurement of the Boltzmann constant’

    Science.gov (United States)

    Macnaughton, Donald B.

    2016-02-01

    The International Committee for Weights and Measures has projected a major revision of the International System of Units in which all the base units will be defined by fixing the values of certain fundamental constants of nature. To assist, de Podesta et al recently experimentally obtained a precise new estimate of the Boltzmann constant. This estimate is proposed as a basis for the redefinition of the unit of temperature, the kelvin. The present paper reports a reanalysis of de Podesta et al’s data that reveals systematic non-random patterns in the residuals of the key fitted model equation. These patterns violate the assumptions underlying the analysis and thus they raise questions about the validity of de Podesta et al’s estimate of the Boltzmann constant. An approach is discussed to address these issues, which should lead to an accurate estimate of the Boltzmann constant with a lower uncertainty.

  10. The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics

    Science.gov (United States)

    Tirnakli, Ugur; Borges, Ernesto P.

    2016-03-01

    As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results.

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

    International Nuclear Information System (INIS)

    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

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

    International Nuclear Information System (INIS)

    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

  13. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lema\\^itre-Robertson-Walker spacetime

    CERN Document Server

    Bazow, D; Heinz, U; Martinez, M; Noronha, J

    2016-01-01

    The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lema\\^itre-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation...

  14. Development of a coarse-grained water forcefield via multistate iterative Boltzmann inversion

    CERN Document Server

    Moore, Timothy C; McCabe, Clare

    2015-01-01

    A coarse-grained water model is developed using multistate iterative Boltzmann inversion. Following previous work, the k-means algorithm is used to dynamically map multiple water molecules to a single coarse-grained bead, allowing the use of structure-based coarse-graining methods. The model is derived to match the bulk and interfacial properties of liquid water and improves upon previous work that used single state iterative Boltzmann inversion. The model accurately reproduces the density and structural correlations of water at 305 K and 1.0 atm, stability of a liquid droplet at 305 K, and shows little tendency to crystallize at physiological conditions. This work also illustrates several advantages of using multistate iterative Boltzmann inversion for deriving generally applicable coarse-grained forcefields.

  15. The non-linear Boltzmann equation and its application to time and space dependent problems

    International Nuclear Information System (INIS)

    This thesis is divided into two parts which both involve finding solutions of the Boltzmann Equation. The motivation behind Part 1 is laser fusion where energy transport is by electrons but the temperature gradients are so large in relation to their mean free paths that classical conduction theory breaks down. In this treatment the electron distribution function is found from an appropriate space-dependent Boltzmann Equation and thus physical quantities (in particular heat flux) are calculated for typical parameters from laser fusion. In part 2, an analytic solution of a certain non-linear one-dimensional Boltzmann Equation is obtained which describes the temporal relaxation to equilibrium of a system of particles. Solutions to the corresponding linearised equation and two E.G.K models (with energy-dependent and ''averaged'' collision times) are also derived and compared with that of the non-linear equation. (author)

  16. Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions

    CERN Document Server

    Dorschner, B; Karlin, I V

    2016-01-01

    Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil at a Reynolds number of Re = 40000 an...

  17. A Characteristic Non-Reflecting Boundary Treatment in Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    KIM Dehee; KIM Hyung Min; JHON Myung S.; VINAY Ⅲ Stephen J.; BUCHANAN John

    2008-01-01

    In lattice Boltzmann methods, disturbances develop at the initial stages of the simulation, the decay characteristics depend mainly on boundary treatment methods; open boundary conditions such as equilibrium and bounce-back schemes potentially generate uncontrollable disturbances. Excessive disturbances originate from non-physical reflecting waves at boundaries. Characteristic boundary conditions utilizing the signs of waves at boundaries which suppress these reflecting waves, as well as their implementation in the lattice Boltzmann method, are introduced herein. The performance of our novel boundary treatment method to effectively suppress excessive disturbances is verified by three different numerical experiments.

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

    CERN Document Server

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

    2013-01-01

    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 until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al 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 until fourth order in the Hermite polynomials.

  19. Thermodynamics of noncommutative geometry inspired black holes based on Maxwell-Boltzmann smeared mass distribution

    Science.gov (United States)

    Liang, Jun; Liu, Yan-Chun; Zhu, Qiao

    2014-02-01

    In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole.

  20. Thermodynamics of noncommutative geometry inspired black holes based on Maxwell-Boltzmann smeared mass distribution

    International Nuclear Information System (INIS)

    In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole. (authors)

  1. A revised uncertainty budget for measuring the Boltzmann constant using the Doppler Broadening Technique on ammonia

    CERN Document Server

    Lemarchand, Cyril; Sow, Papa Lat Tabara; Triki, Meriam; Tokunaga, Sean K; Briaudeau, Stephan; Chardonnet, Christian; Darquié, Benoît; Daussy, Christophe

    2013-01-01

    We report on our on-going effort to measure the Boltzmann constant, kB, using the Doppler Broadening Technique. The main systematic effects affecting the measurement are discussed. A revised error budget is presented in which the global uncertainty on systematic effects is reduced to 2.3 ppm. This corresponds to a reduction of more than one order of magnitude compared to our previous Boltzmann constant measurement. Means to reach a determination of kB at the part per million accuracy level are outlined.

  2. From Newton's law to the linear Boltzmann equation without cut-off

    OpenAIRE

    Ayi, Nathalie

    2016-01-01

    We provide a rigorous derivation of the linear Boltzmann equation without cutoff starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combin...

  3. Solution of the nonlinear Poisson–Boltzmann equation: Application to ionic diffusion in cementitious materials

    International Nuclear Information System (INIS)

    A robust numerical solution of the nonlinear Poisson–Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson–Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

  4. Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation

    Science.gov (United States)

    Lu, Jianfeng; Mendl, Christian B.

    2015-06-01

    We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 × 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as a special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.

  5. Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation

    CERN Document Server

    Lu, Jianfeng

    2014-01-01

    We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 x 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.

  6. Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

    CERN Document Server

    Zhang, Jingfeng; Ouyang, Jie

    2014-01-01

    A numerical method, based on discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.

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

    CERN Document Server

    Hammond, L A; 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 sup 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.

  8. Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

    CERN Document Server

    Degond, Pierre; Savelief, Dominique; Vignal, Marie-Hélène

    2010-01-01

    This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately.

  9. Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation

    OpenAIRE

    Arkeryd, Leif; Nouri, Anne

    2015-01-01

    A fully non-linear kinetic Boltzmann equation for anyons is studied in a periodic 1d setting with large initial data. Strong L 1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness and stabililty. We use the Bony functional, the two-dimensional velocity frame specific for anyons, and an initial layer analysis that moves the solution away from a critical value. 1 Anyons and the Boltzmann equation. Let us first recall the definition of anyon. Con...

  10. A Fokker-Planck model of the Boltzmann equation with correct Prandtl number

    CERN Document Server

    Mathiaud, J

    2015-01-01

    We propose an extension of the Fokker-Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier-Stokes asymptotics. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model (ES) is obtained from the Bathnagar-Gross-Krook model (BGK) of the Boltzmann equation. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman-Enskog analysis and two numerical tests show that a correct Prandtl number of 2/3 can be obtained.

  11. Contributions to the spectral theory of the linear Boltzmann operator for various geometries

    International Nuclear Information System (INIS)

    The linear monoenergetic Boltzmann operator with isotropic scattering is studied for various geometries and boundary conditions as the infinitesimal generator of a positivity preserving contractive semigroup in an appropriate Hilbert space. General results about the existence and the uniqueness of the solutions of the corresponding evolution problems are reviewed. The spectrum of the Boltzmann operator is analyzed for semi-infinite, slab and parallelepipedic geometries with vacuum, periodic, perfectly reflecting, generalized and diffusely reflecting boundary condition respectively. The main features of these spectra, their importance for determining the asymptotic evolution and possible generalizations to more realistic models are put together in a final section. (author)

  12. A Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids

    OpenAIRE

    Horbach, Juergen; Frenkel, Daan

    2001-01-01

    We present a new simulation scheme based on the Lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U_0 for a cubic array of charged spheres...

  13. Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids

    OpenAIRE

    Horbach, J.; Frenkel, D

    2001-01-01

    We present a simulation scheme based on the lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U0 for a cubic array of charged spheres in a...

  14. Variational formulation of the steady Boltzmann equation for semiconductors and applications

    International Nuclear Information System (INIS)

    We present a variational formulation of the steady Boltzmann equation for semiconductors. In this formulation, the distribution function is replaced by a weighted distribution function, and the symmetry of the drift operator is obtained by using the parity operator. We show that the solutions of the Boltzmann equation for the weighted distribution function are stationary functions of a suitable functional, which takes into account realistic boundary conditions. After introducing a general numerical framework, the approach proposed is tested in the bulk case, by computing an approximate expression for carrier mobility in silicon.

  15. Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids

    Science.gov (United States)

    Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

    2016-02-01

    In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.

  16. Event management

    OpenAIRE

    Myslivcová, Hana Bc.

    2007-01-01

    V práci je popsán teoretický postup při pořádání eventů, který vychází ze zásad projektového řízení. Tyto postupy jsou také aplikovány v praktické realizaci eventu. Následuje výzkum aktuálních trendů v event managementu a výzkum cílových skupin s pomocí dat MML/TGI.

  17. Topography's event

    DEFF Research Database (Denmark)

    Munck Petersen, Rikke

    The aim of the paper is first to discuss how horizon and scale can be understood, secondly how they differ and what they might have in common? If topography can be seen as a way of working with these relations experiences, creations and latencies? Thirdly if diagrams and diagrammatology can bring...... space formation - to stimulate and elaborate the event of conception and topological thinking....

  18. Lattice Boltzmann Hydrodynamic and Transport Modeling of Everglades Mangrove Estuaries

    Science.gov (United States)

    Sukop, M. C.; Engel, V.

    2010-12-01

    Lattice Boltzmann methods are being developed and applied to simulate groundwater and surface water flows, and heat, solute, and particle transport. Their ability to solve Navier-Stokes, St. Venant, or Darcy equations with closely coupled solute transport and density-dependent flow effects in geometrically complex domains is attractive for inverse modeling of tracer release data and forward modeling of carbon transport in mangrove estuaries under various future conditions. Key physical processes to be simulated include tidal cycles, storm surge, sea level change, variable upstream stage, subsurface groundwater inputs, and precipitation/recharge and their effects on estuary salinity and carbon transport in the estuaries and groundwater beneath the mangroves. Carbon sources and storage in the aquifer and exchanges at the mangrove-estuary interface and carbon transformations in the water column also need to be simulated. Everglades tidal mangrove estuaries are characterized by relatively high velocity (approaching 1 m s-1) tidal flows. The channels are generally less than 2 m in depth. Tidal fluctuations approach 2 m leading to significant areas of periodic inundation and emergence of oyster beds, shell beaches, mangrove root masses, and sandy beaches. Initial models are two-dimensional, although a three-dimensional model explicitly incorporating bathymetry, density-dependent flow, and wind-driven circulation could be developed. Preliminary work highlights some of the abilities of early models. A satellite image of a 64-km2 area surrounding a CO2 flux tower is used to provide the model geometry. Model resolution is 15 m per grid node. A sinusoidal tidal stage variation and constant, high salinity are applied to the Gulf side of the model while a constant stage (corresponding to mean tide), zero salinity boundary is applied on the inland side. The Navier-Stokes equations coupled with the advection-diffusion equation are solved in the open channels. The mangrove areas

  19. An alternative approach to the Boltzmann distribution through the chemical potential

    Science.gov (United States)

    D'Anna, Michele; Job, Georg

    2016-05-01

    The Boltzmann distribution is one of the most significant results of classical physics. Despite its importance and its wide range of application, at high school level it is mostly presented without any derivation or link to some basic ideas. In this contribution we present an approach based on the chemical potential that allows to derive it directly from the basic idea of thermodynamical equilibrium.

  20. Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow

    Science.gov (United States)

    Fazio, Claudio; Battaglia, Onofrio R.; Guastella, Ivan

    2012-01-01

    In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms…

  1. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    NARCIS (Netherlands)

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

  2. Aerodynamic simulation of high-speed trains based on the Lattice Boltzmann Method (LBM)

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Aerodynamic simulation of high-speed trains has been carried out by using Lattice Boltzmann Method (LBM). Non-simplified train model was used and the number of space grids reached tens of millions. All results under different working conditions reflected the actual situation.

  3. Comparing Entropic and Multiple Relaxation Times Lattice Boltzmann Methods for blood flow simulations

    NARCIS (Netherlands)

    J.B.W. Geerdink; A.G. Hoekstra

    2009-01-01

    We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predicta

  4. 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.

  5. Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure

    Science.gov (United States)

    Shi, Wei; Lu, Wei-Zhen; Xue, Yu; He, Hong-Di

    2016-02-01

    A revised lattice Boltzmann model concerning the equilibrium traffic pressure is proposed in this study to tackle the phase transition phenomena of traffic flow system. The traditional lattice Boltzmann model has limitation to investigate the complex traffic phase transitions due to its difficulty for modeling the equilibrium velocity distribution. Concerning this drawback, the equilibrium traffic pressure is taken into account to derive the equilibrium velocity distribution in the revised lattice Boltzmann model. In the proposed model, a three-dimensional velocity-space is assumed to determine the equilibrium velocity distribution functions and an alternative, new derivative approach is introduced to deduct the macroscopic equations with the first-order accuracy level from the lattice Boltzmann model. Based on the linear stability theory, the stability conditions of the corresponding macroscopic equations can be obtained. The outputs indicate that the stability curve is divided into three regions, i.e., the stable region, the neutral stability region, and the unstable region. In the stable region, small disturbance appears in the initial uniform flow and will vanish after long term evolution, while in the unstable region, the disturbance will be enlarged and finally leads to the traffic system entering the congested state. In the neutral stability region, small disturbance does not vanish with time and maintains its amplitude in the traffic system. Conclusively, the stability of traffic system is found to be enhanced as the equilibrium traffic pressure increases. Finally, the numerical outputs of the proposed model are found to be consistent with the recognized, theoretical results.

  6. 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. PMID:27413369

  7. Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

    Science.gov (United States)

    Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen

    1995-01-01

    A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

  8. Preliminary Results in the Use of Energy-Dependent Octagonal Lattices for Thermal Lattice Boltzmann Simulations

    Czech Academy of Sciences Publication Activity Database

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

    2002-01-01

    Roč. 107, 1/2 (2002), s. 499-519. ISSN 0022-4715 R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : thermal lattice Boltzmann simulations Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.537, year: 2002

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

    Science.gov (United States)

    Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J. Javier; González-Flores, Carlos

    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. PMID:27413369

  10. The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform

    Science.gov (United States)

    Machida, Manabu

    2016-04-01

    The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this paper, we show that the three-dimensional Green's function can be computed with the Fourier transform even in the case of arbitrary anisotropic scattering.

  11. A Revisiting of the -Stability Theory of the Boltzmann Equation Near Global Maxwellians

    Science.gov (United States)

    Ha, Seung-Yeal; Xiao, Qinghua

    2015-07-01

    We study the -stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the -distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in -topology. Our local-in-time -stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657-688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the -stability theory for the Boltzmann equation near a global Maxwellian. For this -stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform -stability of the Boltzmann equation.

  12. Podolsky Electromagnetism at Finite Temperature: Implications on Stefan-Boltzmann Law

    OpenAIRE

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

    2009-01-01

    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.

  13. Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation

    Science.gov (United States)

    Nagaev, K. E.

    2016-08-01

    We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.

  14. Calculation of electronic transport coefficients by a variational method for the linearized Boltzmann equation

    International Nuclear Information System (INIS)

    A variational procedure is applied to a linearized Boltzmann equation to calculate electric conductivity, thermal conductivity and Seebeck coefficient. Interaction of electrons with vacancies and impurities as well as with magnetic ions and phonons are taken into consideration. As an example these three transport coefficients are evaluated for GdAl2 in the temperature range 0-300 0K. (G.Q.)

  15. A Nonlinera Krylov Accelerator for the Boltzmann k-Eigenvalue Problem

    CERN Document Server

    Calef, Matthew T; Warsa, James S; Berndt, Markus; Carlson, Neil N

    2011-01-01

    We compare variants of Anderson Mixing with the Jacobian-Free Newton-Krylov and Broyden methods applied to the k-eigenvalue formulation of the linear Boltzmann transport equation. We present evidence that one variant of Anderson Mixing finds solutions in the fewest number of iterations. We examine and strengthen theoretical results of Anderson Mixing applied to linear problems.

  16. Pseudospectral Methods of Solution of the Linear and Linearized Boltzmann Equations; Transport and Relaxation

    Science.gov (United States)

    Shizgal, Bernie D.

    2011-05-01

    The study of the solution of the linearized Boltzmann equation has a very long history arising from the classic work by Chapman and Cowling. For small departures from a Maxwellian, the nonlinear Boltzmann equation can be linearized and the transport coefficients calculated with the Chapman-Enskog approach. This procedure leads to a set of linear integral equations which are generally solved with the expansion of the departure from Maxwellian in Sonine polynomials. The method has been used successfully for many decades to compare experimental transport data in atomic gases with theory generally carried out for realistic atom-atom differential cross sections. There are alternate pseudospectral methods which involve the discretization of the distribution function on a discrete grid. This paper considers a pseudospectral method of solution of the linearized hard sphere Boltzmann equation for the viscosity in a simple gas. The relaxation of a small departure from a Maxwellian is also considered for the linear test particle problem with unit mass ratio which is compared with the relaxation for the linearized one component Boltzmann equation.

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

    International Nuclear Information System (INIS)

    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.

  18. 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...

  19. Calibration of modified parallel-plate rheometer through calibrated oil and lattice Boltzmann simulation

    DEFF Research Database (Denmark)

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

    2007-01-01

    inapplicable here. This paper presents the analysis of a modified parallel plate rheometer for measuring cement mortar and propose a methodology for 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...... rheological data should be extracted from the experimental results....

  20. Uniform Polynomial Equations Providing Higher-order Multi-dimensional Models in Lattice Boltzmann Theory

    International Nuclear Information System (INIS)

    We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models applicable to describe thermal compressible flows of the level of the Navier-Stokes equations.

  1. 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...

  2. Derivation of the Second Law of Thermodynamics from Boltzmann's Distribution Law.

    Science.gov (United States)

    Nelson, P. G.

    1988-01-01

    Shows how the thermodynamic condition for equilibrium in an isolated system can be derived by the application of Boltzmann's law to a simple physical system. States that this derivation could be included in an introductory course on chemical equilibrium to help prepare students for a statistical mechanical treatment presented in the curriculum.…

  3. Models, Their Application, and Scientific Anticipation: Ludwig Boltzmann's Work as Tacit Knowing

    Science.gov (United States)

    Schmitt, Richard Henry

    2011-01-01

    Ludwig Boltzmann's work in theoretical physics exhibits an approach to the construction of theory that he transmitted to the succeeding generation by example. It involved the construction of clear models, allowed more than one, and was not based solely on the existing facts, with the intent of examining and criticizing the assumptions that made…

  4. A Pedagogical Approach to the Boltzmann Factor through Experiments and Simulations

    Science.gov (United States)

    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…

  5. Developing extensible lattice-Boltzmann simulators for general-purpose graphics-processing units

    Energy Technology Data Exchange (ETDEWEB)

    Walsh, S C; Saar, M O

    2011-12-21

    Lattice-Boltzmann methods are versatile numerical modeling techniques capable of reproducing a wide variety of fluid-mechanical behavior. These methods are well suited to parallel implementation, particularly on the single-instruction multiple data (SIMD) parallel processing environments found in computer graphics processing units (GPUs). Although more recent programming tools dramatically improve the ease with which GPU programs can be written, the programming environment still lacks the flexibility available to more traditional CPU programs. In particular, it may be difficult to develop modular and extensible programs that require variable on-device functionality with current GPU architectures. This paper describes a process of automatic code generation that overcomes these difficulties for lattice-Boltzmann simulations. It details the development of GPU-based modules for an extensible lattice-Boltzmann simulation package - LBHydra. The performance of the automatically generated code is compared to equivalent purpose written codes for both single-phase, multiple-phase, and multiple-component flows. The flexibility of the new method is demonstrated by simulating a rising, dissolving droplet in a porous medium with user generated lattice-Boltzmann models and subroutines.

  6. Developing extensible lattice-Boltzmann simulationsfor general-purpose graphics-programming units

    Energy Technology Data Exchange (ETDEWEB)

    Walsh, S C; Saar, M O

    2011-10-27

    Lattice-Boltzmann methods are versatile numerical modeling techniques capable of reproducing a wide variety of fluid-mechanical behavior. These methods are well suited to parallel implementation, particularly on the single-instruction multiple data (SIMD) parallel processing environments found in computer graphics processing units (GPUs). Although more recent programming tools dramatically improve the ease with which GPU programs can be written, the programming environment still lacks the flexibility available to more traditional CPU programs. In particular, it may be difficult to develop modular and extensible programs that require variable on-device functionality with current GPU architectures. This paper describes a process of automatic code generation that overcomes these difficulties for lattice-Boltzmann simulations. It details the development of GPU-based modules for an extensible lattice-Boltzmann simulation package - LBHydra. The performance of the automatically generated code is compared to equivalent purpose written codes for both single-phase, multiple-phase, and multiple-component flows. The flexibility of the new method is demonstrated by simulating a rising, dissolving droplet in a porous medium with user generated lattice-Boltzmann models and subroutines.

  7. Learning features for tissue classification with the classification restricted Boltzmann machine

    DEFF Research Database (Denmark)

    van Tulder, Gijs; de Bruijne, Marleen

    Performance of automated tissue classification in medical imaging depends on the choice of descriptive features. In this paper, we show how restricted Boltzmann machines (RBMs) can be used to learn features that are especially suited for texture-based tissue classification. We introduce the...

  8. Bistable solutions for the electron energy distribution function in electron swarms in xenon: a comparison between the results of first-principles particle simulations and conventional Boltzmann equation analysis

    Science.gov (United States)

    Dyatko, Nikolay; Donkó, Zoltán

    2015-08-01

    At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This ‘bistability effect’—in which electron-electron (Coulomb) collisions play an essential role—is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms (‘two-term approximation’), (ii) neglecting the Coulomb part of the collision integral for the anisotropic part of the distribution function, (iii) treating Coulomb collisions as binary events, and (iv) truncating the range of the electron-electron interaction beyond a characteristic distance. The particle-based simulation method avoids these approximations: the many-body interactions within the electron gas with a true (un-truncated) Coulomb potential are described by a molecular dynamics algorithm, while the collisions between electrons and the background gas atoms are treated with Monte Carlo simulation. We find a good general agreement between the results of the two techniques, which confirms, to a certain extent, the approximations used in the solution of the Boltzmann equation. The differences observed between the results are believed to originate from these approximations and from the presence of statistical noise in the particle simulations.

  9. Event Index - a LHCb Event Search System

    CERN Document Server

    Ustyuzhanin, Andrey; Kazeev, Nikita; Redkin, Artem

    2015-01-01

    LHC experiments generate up to $10^{12}$ events per year. This paper describes Event Index - an event search system. Event Index's primary function is quickly selecting subsets of events from a combination of conditions, such as the estimated decay channel or stripping lines output. Event Index is essentially Apache Lucene optimized for read-only indexes distributed over independent shards on independent nodes.

  10. Simulating events

    Energy Technology Data Exchange (ETDEWEB)

    Ferretti, C.; Bruzzone, L. [Techint Italimpianti, Milan (Italy)

    2000-06-01

    The Petacalco Marine terminal on the Pacific coast in the harbour of Lazaro Carclenas (Michoacan) in Mexico, provides coal to the thermoelectric power plant at Pdte Plutarco Elias Calles in the port area. The plant is being converted from oil to burn coal to generate 2100 MW of power. The article describes the layout of the terminal and equipment employed in the unloading, coal stacking, coal handling areas and the receiving area at the power plant. The contractor Techint Italimpianti has developed a software system, MHATIS, for marine terminal management which is nearly complete. The discrete event simulator with its graphic interface provides a real-type decision support system for simulating changes to the terminal operations and evaluating impacts. The article describes how MHATIS is used. 7 figs.

  11. On the Self-Consistent Event Biasing Schemes for Monte Carlo Simulations of Nanoscale MOSFETs

    CERN Document Server

    Islam, Sharnali; Ahmed, Shaikh

    2009-01-01

    Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the calculation of terminal current. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. After presenting a brief overview on the Monte Carlo technique for solving the Boltzmann transport equation, the basic steps of deriving the approach in presence of both the initial and the boundary conditions have been discussed. In the derivation, the linearity of the transport problem has been utilized first, where Coulomb forces between the carriers are initially neglected. The generalization of the approach for Hartree carriers has been established in the iterative procedure of coupling with the Poisson equation. It is shown that the weight of the particles, as obtained by biasing of the Boltzmann equation, survive...

  12. Events diary

    Science.gov (United States)

    2000-01-01

    as Imperial College, the Royal Albert Hall, the Royal College of Art, the Natural History and Science Museums and the Royal Geographical Society. Under the heading `Shaping the future together' BA2000 will explore science, engineering and technology in their wider cultural context. Further information about this event on 6 - 12 September may be obtained from Sandra Koura, BA2000 Festival Manager, British Association for the Advancement of Science, 23 Savile Row, London W1X 2NB (tel: 0171 973 3075, e-mail: sandra.koura@britassoc.org.uk ). Details of the creating SPARKS events may be obtained from creating.sparks@britassoc.org.uk or from the website www.britassoc.org.uk . Other events 3 - 7 July, Porto Alegre, Brazil VII Interamerican conference on physics education: The preparation of physicists and physics teachers in contemporary society. Info: IACPE7@if.ufrgs.br or cabbat1.cnea.gov.ar/iacpe/iacpei.htm 27 August - 1 September, Barcelona, Spain GIREP conference: Physics teacher education beyond 2000. Info: www.blues.uab.es/phyteb/index.html

  13. 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)

  14. Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows

    CERN Document Server

    Matin, Rastin; Hernandez-Garcia, Anier; Mathiesen, Joachim

    2016-01-01

    In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.

  15. Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

    International Nuclear Information System (INIS)

    In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques. (paper)

  16. Drag correlation for dilute and moderately dense fluid-particle systems using the lattice Boltzmann method

    CERN Document Server

    Bogner, Simon; Rüde, Ulrich

    2014-01-01

    This paper presents a numerical study of flow through static random assemblies of monodisperse, spherical particles. A lattice Boltzmann approach based on a two relaxation time collision operator is used to obtain reliable predictions of the particle drag by direct numerical simulation. From these predictions a closure law $F(Re, {\\phi})$ of the drag force relationship to the bed density ${\\phi}$ and the particle Reynolds number $Re$ is derived. The present study includes densities ${\\phi}$ ranging from $0.01$ to $0.35$ with Re ranging up to $300$, that is compiled into a single drag correlation valid for the whole range. The corelation has a more compact expression compared to others previously reported in literature. At low particle densities, the new correlation is close to the widely used Wen & Yu - correlation. Recently, there has been reported a discrepancy between results obtained using different numerical methods, namely the comprehensive lattice Boltzmann study of Beetstra et al. (2007) and the p...

  17. 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...

  18. Why Boltzmann Brains Don't Fluctuate Into Existence From the De Sitter Vacuum

    CERN Document Server

    Boddy, Kimberly K; Pollack, Jason

    2015-01-01

    Many modern cosmological scenarios feature large volumes of spacetime in a de Sitter vacuum phase. Such models are said to be faced with a "Boltzmann Brain problem" - the overwhelming majority of observers with fixed local conditions are random fluctuations in the de Sitter vacuum, rather than arising via thermodynamically sensible evolution from a low-entropy past. We argue that this worry can be straightforwardly avoided in the Many-Worlds (Everett) approach to quantum mechanics, as long as the underlying Hilbert space is infinite-dimensional. In that case, de Sitter settles into a truly stationary quantum vacuum state. While there would be a nonzero probability for observing Boltzmann-Brain-like fluctuations in such a state, "observation" refers to a specific kind of dynamical process that does not occur in the vacuum (which is, after all, time-independent). Observers are necessarily out-of-equilibrium physical systems, which are absent in the vacuum. Hence, the fact that projection operators corresponding...

  19. Investigation of Resistivity of Saturated Porous Media with Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    YUE Wen-Zheng; TAO Guo; ZHU Ke-Qin

    2004-01-01

    The lattice Boltzmann method is employed to study the electrical transport properties of saturated porous media.Electrical current flow through the porous media is simulated and the relationship between resistivity index and water saturation is derived. It is found that this kind of relation is not a straight line as described by the Archie equation with the parameter n being a constant in a log-log scale. A new equation is thus developed to formulate this relation with n being a function of porosity and water saturation. The comparisons between the results by lattice Boltzmann and by the laboratory experiments on rock samples demonstrate that this numerical method can provide an alternative way for the expensive laboratory experiments to investigate the electrical transport properties of saturated porous media and can be used to explore micro mechanisms more conveniently.

  20. Beyond Poisson–Boltzmann: fluctuations and fluid structure in a self-consistent theory

    Science.gov (United States)

    Buyukdagli, S.; Blossey, R.

    2016-09-01

    Poisson–Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson–Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent—a dipolar Coulomb fluid—including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations.

  1. Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory.

    Science.gov (United States)

    Buyukdagli, S; Blossey, R

    2016-09-01

    Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent-a dipolar Coulomb fluid-including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations. PMID:27357125

  2. Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example

    Science.gov (United States)

    Treumann, Rudolf; Baumjohann, Wolfgang

    2014-08-01

    We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative T" claim.

  3. SIMULATION OF TURBULENT FLOW OVER A BACKWARD FACING STEP USING LATTICE BOLTZMANN METHOD

    Directory of Open Access Journals (Sweden)

    NOR AZWADI C. SIDIK

    2013-12-01

    Full Text Available The lattice Boltzmann scheme for solving the equations governing the flow of fluids has become increasingly popular in recent years. In this method, a probability distribution function for the velocity of fluid elements is computed at each grid point, which contrasts with more established computational fluid dynamics methods, which solve for an average velocity. In this paper the effectiveness of the lattice Boltzmann equation (LBE as a computational tool for performing large-eddy simulations (LES of turbulent flows was assessed. Three- dimensional turbulent flow over backward facing step was considered for this investigation. LBE-LES and Navier Stokes Direct Numerical Simulation (NS-DNS results for this case has been compared and it was observed that the LBE-LES simulation is in good agreement with other computational simulations.

  4. Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

    CERN Document Server

    Freguglia, Paolo

    2015-01-01

    This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.

  5. Simulating Anomalous Dispersion and Multiphase Segregation in Porous Media with the Lattice Boltzmann Method

    Science.gov (United States)

    Matin, Rastin; Misztal, Marek K.; Hernandez-Garcia, Anier; Mathiesen, Joachim

    2015-11-01

    Many hydrodynamic phenomena such as flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated numerically using the lattice Boltzmann method. By solving the Lattice Boltzmann Equation on three-dimensional unstructured meshes, we efficiently model single-phase fluid flow in real rock samples. We use the flow field to estimate the permeability and further investigate the anomalous dispersion of passive tracers in porous media. By extending our single-phase model with a free-energy based method, we are able to simulate binary systems with moderate density ratios in a thermodynamically consistent way. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.

  6. Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation

    CERN Document Server

    Holst, Michael; Yu, Zeyun; Zhou, Yongcheng; Zhu, Yunrong

    2010-01-01

    We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a priori pointwise estimates and the first complete solution and approximation theory for the Poisson-Boltzmann equation. It also made possible the first provably convergent discretization of the PBE, and allowed for the development of a provably convergent AFEM for the PBE. However, in practice the regularization turns out to be numerically ill-conditioned. In this article, we examine a second regularization, and establish a number of basic results to ensure that the new approach produces the same mathematical advantages of the original regularization, without the ill-conditioning property. We then design an AFEM scheme based on the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This res...

  7. Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production

    CERN Document Server

    Gressman, Philip T

    2010-01-01

    This article provides sharp constructive upper and lower bound estimates for the non-linear Boltzmann collision operator with the full range of physical non cut-off collision kernels ($\\gamma > -n$ and $s\\in (0,1)$) in the trilinear $L^2(\\R^n)$ energy $\\langle \\mathcal{Q}(g,f),f\\rangle$. These new estimates prove that, for a very general class of $g(v)$, the global diffusive behavior (on $f$) in the energy space is that of the geometric fractional derivative semi-norm identified in the linearized context in our earlier works [2009 arXiv:0912.0888v1, 2010, 2010 arXiv:1002.3639v1]. We further prove new global entropy production estimates with the same anisotropic semi-norm. This resolves the longstanding, widespread heuristic conjecture about the sharp diffusive nature of the non cut-off Boltzmann collision operator in the energy space $L^2(\\R^n)$.

  8. A Stochastic Sharpening Method for the Propagation of Phase Boundaries in Multiphase Lattice Boltzmann Simulations

    KAUST Repository

    Reis, T.

    2010-09-06

    Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting.

  9. Stability of Global Solution to Boltzmann-Enskog Equation with External Force

    Institute of Scientific and Technical Information of China (English)

    JIANG ZHENG-LU; MA LI-JUN; YAO ZHENG-AN

    2012-01-01

    In the presence of external forces depending only on the time and space variables,the Boltzmann-Enskog equation formally conserves only the mass of the system,and its entropy functional is also nonincreasing.Corresponding to this type of equation,we first give some hypotheses of its bicharacteristic equations and then get some results about the stablity of its global solution with the help of two new Lyapunov functionals:one is to describe interactions between particles with different velocities and the other is to measure the L1 distance between two mild solutions.The former Lyapunov functional yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the verification of the L1 stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.

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

    KAUST Repository

    El-Amin, M.F.

    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.

  11. Evaluation of the Performance of the Hybrid Lattice Boltzmann Based Numerical Flux

    Science.gov (United States)

    Zheng, H. W.; Shu, C.

    2016-06-01

    It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.

  12. Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study

    CERN Document Server

    Neuville, Amélie; Toussaint, Renaud

    2013-01-01

    The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier-Stokes and advection-diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three-dimensional (3D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two-dimensional (integrated over the thickness) advection-diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic ...

  13. Lattice Boltzmann simulation of flow around two, three and four circular cylinders in close proximity

    Science.gov (United States)

    Kang, XiuYing; Su, YanPing

    2012-10-01

    Cross-flows around two, three and four circular cylinders in tandem, side-by-side, isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5 D, where D is the identical circular cylinder diameter. The wake patterns, pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases. The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures, which are interesting, complex and useful for practical applications. This study provides a useful database to validate the simplicity, accuracy and robustness of the Lattice Boltzmann method.

  14. 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.

  15. Pore-scale lattice Boltzmann simulation of laminar and turbulent flow through a sphere pack

    CERN Document Server

    Fattahia, Ehsan; Wohlmuth, Barbara; Rüde, Ulrich; Manhart, Michael; Helmig, Rainer

    2015-01-01

    The lattice Boltzmann method can be used to simulate flow through porous media with full geometrical resolution. With such a direct numerical simulation, it becomes possible to study fundamental effects which are difficult to assess either by developing macroscopic mathematical models or experiments. We first evaluate the lattice Boltzmann method with various boundary handling of the solid-wall and various collision operators to assess their suitability for large scale direct numerical simulation of porous media flow. A periodic pressure drop boundary condition is used to mimic the pressure driven flow through the simple sphere pack in a periodic domain. The evaluation of the method is done in the Darcy regime and the results are compared to a semi-analytic solution. Taking into account computational cost and accuracy, we choose the most efficient combination of the solid boundary condition and collision operator. We apply this method to perform simulations for a wide range of Reynolds numbers from Stokes flo...

  16. U.S. stock market interaction network as learned by the Boltzmann machine

    Science.gov (United States)

    Borysov, Stanislav S.; Roudi, Yasser; Balatsky, Alexander V.

    2015-12-01

    We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model's parameters might be used as a precursor of financial instabilities.

  17. Numerical modeling of microchannel gas flows in the transition flow regime via cascaded lattice Boltzmann method

    CERN Document Server

    Liu, Qing

    2016-01-01

    As a numerically accurate and computationally efficient mesoscopic numerical method, the lattice Boltzmann (LB) method has achieved great success in simulating microscale rarefied gas flows. In this paper, an LB method based on the cascaded collision operator is presented to simulate microchannel gas flows in the transition flow regime. The Bosanquet-type effective viscosity is incorporated into the cascaded lattice Boltzmann (CLB) method to account for the rarefaction effects. In order to gain accurate simulations and match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection scheme with a modified second-order slip boundary condition is employed in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel with pressure boundary condition over a wide range of Knudsen numbers. The predicted results, including the velocity profile, the mass flow rate, and the non-linear pressure deviatio...

  18. Regularized lattice Boltzmann model for a class of convection-diffusion equations.

    Science.gov (United States)

    Wang, Lei; Shi, Baochang; Chai, Zhenhua

    2015-10-01

    In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. PMID:26565368

  19. Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory

    CERN Document Server

    Markovich, Tomer; Podgornik, Rudi

    2016-01-01

    We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.

  20. Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

    Energy Technology Data Exchange (ETDEWEB)

    Guzik, Stephen M. [Colorado State Univ., Fort Collins, CO (United States). Dept. of Mechanical Engineering; Weisgraber, Todd H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Alder, Berni J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2013-12-10

    A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examples highlighting the mesh adaptivity of this method are also provided.

  1. Lattice Boltzmann model for collisionless electrostatic drift wave turbulence obeying Charney-Hasegawa-Mima dynamics

    CERN Document Server

    Held, M

    2015-01-01

    A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas, is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occuring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.

  2. Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids.

    Science.gov (United States)

    Horbach, J; Frenkel, D

    2001-12-01

    We present a simulation scheme based on the lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U(0) for a cubic array of charged spheres in an electrolyte. We show that we recover the analytical solution first derived by Booth [F. Booth, J. Chem. Phys. 22, 1956 (1954)] for a weakly charged, isolated sphere in an unbounded electrolyte. The present method makes it possible to go beyond the Booth theory, and we discuss the dependence of the sedimentation velocity on the charge of the spheres. Finally we compare our results to experimental data. PMID:11736191

  3. Radiative or neutron transport modeling using a lattice Boltzmann equation framework

    Science.gov (United States)

    Bindra, H.; Patil, D. V.

    2012-07-01

    In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

  4. Simulation of Rarefied Gas Flow in Slip and Transitional Regimes by the Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    S Abdullah

    2010-07-01

    Full Text Available In this paper, a lattice Boltzmann method (LBM based simulation of microscale flow has been carried out, for various values of Knudsen number. The details in determining the parameters critical for LBM applications in microscale flow are provided. Pressure distributions in the slip flow regime are compared with the analytical solution based on the Navier-Stokes equationwith slip-velocity boundary condition. Satisfactory agreements have been achieved. Simulations are then extended to transition regime (Kn = 0.15 and compared with the same analytical solution. The results show some deviation from the analytical solution due to the breakdown of continuum assumption. From this study, we may conclude that the lattice Boltzmann method is an efficient approach for simulation of microscale flow.

  5. 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

    describing the training data and for classification. We present experiments with feature learning for lung texture classification and airway detection in CT images. In both applications, a combination of learning objectives outperformed purely discriminative or generative learning, increasing, for instance......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...

  6. Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer

    CERN Document Server

    Guo, Zhaoli

    2016-01-01

    Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.

  7. Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains?

    CERN Document Server

    Boddy, Kimberly K

    2013-01-01

    The standard $\\Lambda$CDM model provides an excellent fit to current cosmological observations but suffers from a potentially serious Boltzmann Brain problem. If the universe enters a de Sitter vacuum phase that is truly eternal, there will be a finite temperature in empty space and corresponding thermal fluctuations. Among these fluctuations will be intelligent observers, as well as configurations that reproduce any local region of the current universe to arbitrary precision. We discuss the possibility that the escape from this unacceptable situation may be found in known physics: vacuum instability induced by the Higgs field. Avoiding Boltzmann Brains in a measure-independent way requires a decay timescale of order the current age of the universe, which can be achieved if the top quark pole mass is approximately 178 GeV. Otherwise we must invoke new physics or a particular cosmological measure before we can consider $\\Lambda$CDM to be an empirical success.

  8. 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.

  9. Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation

    CERN Document Server

    Aksoylu, Burak; Cyr, Eric; Holst, Michael

    2011-01-01

    In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goal-oriented indicators are not sufficient on their own to lead to a superior refinement algorithm. To remedy this, we propose a problem-specific marking strategy using the solvation free energy computed from the solution of the linear regularized Poisson-Boltzmann equation. The convergence of the solvation free energy using this marking strategy, combined with goal-oriented refinement, compares favorably to adaptive methods using an energy-based error indicator. Due to the use of adaptive mesh refinement, it is critical to use multilevel preconditioning in order to maintain optimal computational complexity. We use variants of the classical multigrid method, which can be viewed as generalizations of the hierarchical basis multigrid and Bramble-Pasciak-Xu (BPX) preconditioners.

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

    CERN Document Server

    Jakovác, A

    2002-01-01

    A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium 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 smearing out of the non-analytic threshold behaviour of the spectral function. Possible consequences for the dilepton production are discussed.

  11. 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 of...... generalized geometry optimization formulation and derive the corresponding sensitivity analysis for the single relaxation LBM for both topology and shape optimization applications. Using numerical examples, we verify the accuracy of the analytical sensitivity analysis through a comparison with finite...... differences. In addition, we show that for fluidic topology optimization a scaled volume constraint should be used to obtain the desired "0-1" optimal solutions. (C) 2008 Elsevier Ltd. All rights reserved....

  12. Pseudopotential MRT lattice Boltzmann model for cavitation bubble collapse with high density ratio

    CERN Document Server

    Shan, Ming-Lei; 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 present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q. et al. 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. The independence between the kinematic viscosity and the thermodynamic consistency, surface tension is founded. By homogeneous and heterogeneous cavitation simulation, the capability 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 collapsing bubble is consistent with the results from experiments and simulations by other numerical method. It is demonstrated that the present pseudopotential...

  13. Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term

    OpenAIRE

    Suriyawichitseranee, A.; Grigoriev, Yu. N.; Meleshko, S. V.

    2014-01-01

    The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Using a particular class of solutions, the determining equation for the admitted Lie group is reduced to a partial differential equation for the source function. The latter equation is analyzed by an algebraic method. A complete group classification of the...

  14. Bistable solutions for the electron energy distribution function in electron swarms in xenon via Boltzmann equation analysis and particle simulations

    OpenAIRE

    Dyatko, Nikolay; Donko, Zoltan

    2015-01-01

    At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This "bistability effect" - in which electron-electron (Coulomb) collisions play an essential role - is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms ("two-term app...

  15. Causality, realism and the two strands of Boltzmann's legacy (1896 - 1936)

    OpenAIRE

    Stöltzner, Michael

    2003-01-01

    My thesis investigates a debate between Vienna and Berlin about the view that the basic laws of nature are genuinely indeterministic that started long before the advent of quantum mechanics. It involved two different readings of Ludwig Boltzmann's legacy statistical mechanics and two different answers to how causality and ontology ought to be combined. Having adopted Ernst Mach's weak notion of causality, the local Viennese tradition could more easily contemplate ontologies for irreducibly st...

  16. 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.

  17. Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension

    OpenAIRE

    d'Eon, Eugene

    2013-01-01

    We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing medium with isotropic scattering. We consider both classical transport theory with exponentially-distributed free paths in arbitrary dimensions as well as a number of non-classical transport theories (non-exponential random flights) that describe a broader clas...

  18. Finite-difference lattice Boltzmann simulation on acoustics-induced particle deposition

    Science.gov (United States)

    Fu, Sau-Chung; Yuen, Wai-Tung; Wu, Chili; Chao, Christopher Yu-Hang

    2015-10-01

    Particle manipulation by acoustics has been investigated for many years. By a proper design, particle deposition can be induced by the same principle. The use of acoustics can potentially be developed into an energy-efficient technique for particle removal or filtration system as the pressure drop due to acoustic effects is low and the flow velocity is not necessary to be high. Two nonlinear acoustic effects, acoustic streaming and acoustic radiation pressure, are important. Acoustic streaming introduces vortices and stagnation points on the surface of an air duct and removes the particles by deposition. Acoustic radiation pressure causes particles to form agglomerates and enhances inertial impaction and/or gravitational sedimentation. The objective of this paper is to develop a numerical model to investigate the particle deposition induced by acoustic effects. A three-step approach is adopted and lattice Boltzamnn technique is employed as the numerical method. This is because the lattice Boltzmann equation is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. In the first step, the acoustic field and its mean square fluctuation values are calculated. Due to the advantage of the lattice Boltzmann technique, a simple, stable and fast lattice Boltzmann method is proposed and verified. The result of the first step is input into the second step to solve for acoustic streaming. Another finite difference lattice Boltzmann method, which has been validated by a number of flows and benchmark cases in the literature, is used. The third step consists in tracking the particle's motion by a Lagrangian approach where the acoustic radiation pressure is considered. The influence of the acoustics effects on particle deposition is explained. The numerical result matches with an experiment. The model is a useful tool for optimizing the design and helps to further develop the technique.

  19. Galilean Invariant Fluid-Solid Interfacial Dynamics in Lattice Boltzmann Simulations

    CERN Document Server

    Wen, Binghai; Tu, Yusong; Wang, Chunlei; Fang, Haiping

    2013-01-01

    Galilean invariance is a fundamental property; however, although the lattice Boltzmann equation itself is Galilean invariant, this property is usually not taken into account in the treatment of the fluid-solid interface. Here, we show that consideration of Galilean invariance in fluid-solid interfacial dynamics can greatly enhance the computational accuracy and robustness in a numerical simulation. Surprisingly, simulations are so vastly improved that the force fluctuation is very small and a time average becomes unnecessary.

  20. A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation

    OpenAIRE

    Crouseilles, Nicolas; Degond, Pierre; Lemou, Mohammed

    2004-01-01

    International audience Our purpose s toderive a hybrid model for particles systems which combines a kinetic description of the fast particles with a fluid description of the thermal ones. Fats particles will be described through a collisional kinetic equation of Boltzmann-BGK type while thermal particles will be modeled by means of a system of a Euler type equations. A conservative numerical scheme is constructed and enables us to validate the approach on various numerical tests.

  1. Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo

    OpenAIRE

    Degond, Pierre; Dimarco, Giacomo

    2010-01-01

    In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations. Recently we presented in [14],[16],[17] different methodologies which permit to solve fluid dynamics problems with localized regions of departure from thermodynamical equilibrium. The methods rely on the introduction of buffer zones which realize a smooth transi...

  2. Incompressible Navier–Stokes equations from Boltzmann equations for reacting mixtures

    International Nuclear Information System (INIS)

    Incompressible Navier–Stokes equations for gas mixtures are derived from Boltzmann kinetic models in a suitable fluid dynamic limit. We consider polyatomic gases, each one endowed with a discrete set of internal energy levels. Specifically, we deal with a mixture of four polyatomic gases also undergoing chemical reactions. In the Maxwell molecule case, diffusion coefficients and contributions due to inelastic scattering and to chemical reactions may be explicitly computed. (paper)

  3. The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

    OpenAIRE

    Golse, François; Saint-Raymond, Laure

    2008-01-01

    The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161 (2004)] for Maxwell molecules.

  4. Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models

    OpenAIRE

    Lods, Bertrand; Mouhot, Clément; Toscani, Giuseppe

    2008-01-01

    We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional fo...

  5. Sliding periodic boundary conditions for lattice Boltzmann and lattice kinetic equations

    OpenAIRE

    Adhikari, R.; Desplat, J. -C.; Stratford, K.

    2005-01-01

    We present a method to impose linear shear flow in discrete-velocity kinetic models of hydrodynamics through the use of sliding periodic boundary conditions. Our method is derived by an explicit coarse-graining of the Lees-Edwards boundary conditions for Couette flow in molecular dynamics, followed by a projection of the resulting equations onto the subspace spanned by the discrete velocities of the lattice Boltzmann method. The boundary conditions are obtained without resort to perturbative ...

  6. A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles

    Science.gov (United States)

    Ramachandran, S.; Kumar, P. B. Sunil; Pagonabarraga, I.

    2006-06-01

    We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.

  7. A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles

    OpenAIRE

    Ramachandran, Sanoop; Kumar, P. B. Sunil; Pagonabarraga, I.

    2006-01-01

    We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the e...

  8. Measuring the Boltzmann constant by mid-infrared laser spectroscopy of ammonia

    OpenAIRE

    Mejri, S.; Sow, Papa,; Kozlova, O; Ayari, C.; Tokunaga, Sean,; Chardonnet, C.; Briaudeau, S.; Darquié, B; Rohart, F.; Daussy, C

    2015-01-01

    We report on our ongoing effort to measure the Boltzmann constant, $k_B,$ using the Doppler broadening technique on ammonia. This paper presents some of the improvements made to the mid-infrared spectrometer including the use of a phase-stabilized quantum cascade laser, a lineshape analysis based on a refined physical model and an improved fitting program 2 increasing the confidence in our estimates of the relevant molecular parameters, and a first evaluation of the saturation parameter and i...

  9. Steady detonation waves via the Boltzmann equation for a reacting mixture

    International Nuclear Information System (INIS)

    Based on the Boltzmann equation, the detonation problem is dealt with on a mesoscopic level. The model is based on the assumption that ahead of a shock an explosive gas mixture is in meta stable equilibrium. Starting from the Von Neumann point the chemical reaction, initiated by the pressure jump, proceeds until the chemical equilibrium is reached. Numerical solutions of the derived macroscopic equations as well as the corresponding Hugoniot diagrams which reveal the physical relevance of the mathematical model are provided

  10. Sailfish: a flexible multi-GPU implementation of the lattice Boltzmann method

    OpenAIRE

    Januszewski, Michal; Kostur, Marcin

    2013-01-01

    We present Sailfish, an open source fluid simulation package implementing the lattice Boltzmann method (LBM) on modern Graphics Processing Units (GPUs) using CUDA/OpenCL. We take a novel approach to GPU code implementation and use run-time code generation techniques and a high level programming language (Python) to achieve state of the art performance, while allowing easy experimentation with different LBM models and tuning for various types of hardware. We discuss the general design principl...

  11. Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

    OpenAIRE

    Premnath, Kannan N.; Abraham, John

    2006-01-01

    In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show th...

  12. An Algorithm of Quantum Restricted Boltzmann Machine Network Based on Quantum Gates and Its Application

    Directory of Open Access Journals (Sweden)

    Peilin Zhang

    2015-01-01

    Full Text Available We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.

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

    International Nuclear Information System (INIS)

    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.

  14. Online Semi-Supervised Learning with Deep Hybrid Boltzmann Machines and Denoising Autoencoders

    OpenAIRE

    Ororbia II, Alexander G.; Giles, C. Lee; Reitter, David

    2015-01-01

    Two novel deep hybrid architectures, the Deep Hybrid Boltzmann Machine and the Deep Hybrid Denoising Auto-encoder, are proposed for handling semi-supervised learning problems. The models combine experts that model relevant distributions at different levels of abstraction to improve overall predictive performance on discriminative tasks. Theoretical motivations and algorithms for joint learning for each are presented. We apply the new models to the domain of data-streams in work towards life-l...

  15. Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies

    OpenAIRE

    Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2011-01-01

    Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is follow...

  16. A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation

    OpenAIRE

    José Colmenares; Antonella Galizia; Jesús Ortiz; Andrea Clematis; Walter Rocchia

    2014-01-01

    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 ...

  17. Poisson-Boltzmann Calculations of Nonspecific Salt Effects on Protein-Protein Binding Free Energies

    OpenAIRE

    Bertonati, Claudia; Honig, Barry; Alexov, Emil

    2007-01-01

    The salt dependence of the binding free energy of five protein-protein hetero-dimers and two homo-dimers/tetramers was calculated from numerical solutions to the Poisson-Boltzmann equation. Overall, the agreement with experimental values is very good. In all cases except one involving the highly charged lactoglobulin homo-dimer, increasing the salt concentration is found both experimentally and theoretically to decrease the binding affinity. To clarify the source of salt effects, the salt-dep...

  18. Spherical-harmonic type expansion for the Boltzmann equation in semiconductor devices

    Directory of Open Access Journals (Sweden)

    Armando Majorana

    1998-10-01

    Full Text Available The Boltzmann equation for an electron gas in a semiconductor is considered. The electron energy is assumed to have a very general form, so that, for instance, parabolic or non parabolic band approximations can be treated. A technique, which recalls the classical moment method due to Grad, to deduce an approximate quasi-hydrodynamical model is shown and compared with the spherical harmonic expansion. Some characteristics of the model, as entropy inequality, are explicitly presented.

  19. NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA

    Institute of Scientific and Technical Information of China (English)

    许友生; 刘慈群; 俞慧丹

    2002-01-01

    By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fiuctuation on boundary surface and takes no average measure.

  20. Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow

    OpenAIRE

    Lamura, A.; Gonnella, G.

    2000-01-01

    We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier-Stokes and convection-diffusion equations. We propose a new scheme for imposing the shear flow which has the advantage of preserving mass and momentum conservation on the boundary walls without introducing slip velocities. Our main results concern the presence of two typical lenght scales in the phase separation pro...

  1. Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear

    OpenAIRE

    Xu, Aiguo; Gonnella, G.

    2003-01-01

    We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required to obtain a triangular profile is inversely proportional to the viscosity and proportional to the square of the size of the system. We find that the same behaviour also occurs for binary mixtures, for any component ratio in the mixture and independently fr...

  2. Relativistic Causal Hydrodynamics Derived from Boltzmann Equation: a novel reduction theoretical approach

    OpenAIRE

    Tsumura, Kyosuke; Kikuchi, Yuta; Kunihiro, Teiji

    2015-01-01

    We derive the second-order hydrodynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel development of the renormalization-group method, a powerful reduction theory of dynamical systems, which has been applied successfully to derive the non-relativistic second-order hydrodynamic equation Our theory nicely gives a compact expression of the deviation of...

  3. ab initio Electronic Transport Model with Explicit Solution to the Linearized Boltzmann Transport Equation

    OpenAIRE

    Faghaninia, Alireza; Ager III, Joel W.; Lo, Cynthia S.

    2015-01-01

    Accurate models of carrier transport are essential for describing the electronic properties of semiconductor materials. To the best of our knowledge, the current models following the framework of the Boltzmann transport equation (BTE) either rely heavily on experimental data (i.e., semi-empirical), or utilize simplifying assumptions, such as the constant relaxation time approximation (BTE-cRTA). While these models offer valuable physical insights and accurate calculations of transport propert...

  4. A Spectral Study of the Linearized Boltzmann Equation for Diffusively Excited Granular Media

    OpenAIRE

    Rey, Thomas

    2013-01-01

    In this work, we are interested in the spectrum of the diffusively excited granular gases equation, in a space inhomogeneous setting, linearized around an homogeneous equilibrium. We perform a study which generalizes to a non-hilbertian setting and to the inelastic case the seminal work of Ellis and Pinsky about the spectrum of the linearized Boltzmann operator. We first give a precise localization of the spectrum, which consists in an essential part lying on the left of the imaginary axis an...

  5. Derivation of relativistic hydrodynamic equations consistent with relativistic Boltzmann equation by renormalization-group method

    OpenAIRE

    Tsumura, Kyosuke; Kunihiro, Teiji

    2012-01-01

    We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., ...

  6. Estimates of solutions of linear Boltzmann equation at large time and spectral singularities

    CERN Document Server

    Romanov, Roman

    2010-01-01

    The spectral analysis of the dissipative linear transport (Boltzmann) operator with polynomial collision integral by the Szokefalvi-Nagy - Foias functional model is given. An exact estimate for the reminder in the asymptotic of the corresponding evolution semigroup is proved in the isotropic case. In the general case, it is shown that the operator has finitely many eigenvalues and spectral singularities and an absolutely continuous essential spectrum, and an upper estimate for the reminder is established.

  7. Application of Boltzmann equation to electron transmission and seconary electron emission

    International Nuclear Information System (INIS)

    A method is presented for numerical treatment of integro-differential equation, based upon finite difference techniques. This method allows to formulate in a satisfactory manner the Boltzmann's equation applied to backscattering, transmission and secondary emission of metallic targets, avoiding must of the restrictive hypothesis, used until now in these models. For aluminium, the calculated energy spectra, angular distribution, transmission and backscattering coefficients, and secondary emission yield, are found to be in good agreement with experiment

  8. On the asymptotic behavior of a boltzmann-type price formation model

    KAUST Repository

    Burger, Martin

    2014-01-01

    In this paper we study the asymptotic behavior of a Boltzmann-type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transaction costs. This observation motivates the study of the limit as the number of transactions k tends to infinity, the transaction cost a to zero and ka=const. Furthermore we illustrate the price dynamics with numerical simulations © 2014 International Press.

  9. 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.

  10. Interaction of multiple flapping filaments for cylinder wake modification using the Lattice Boltzmann Method

    OpenAIRE

    Revell, A; Favier, J.; Pinelli, Alfredo

    2012-01-01

    This paper introduces the recent work undertaken on the development of a code based on the combination of the Lattice Boltzmann Method (LBM) with a recent version of the Immersed Boundary Method (IBM). The code is first validated against existing results, before being applied to investigate the different modes of flapping behaviour for single and multiple filaments at various separation distances. The work proceeds to investigate the cylinder wake modification for moderate Reynolds number wh...

  11. Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances

    CERN Document Server

    Lahanas, A B; Nanopoulos, Dimitri V

    2006-01-01

    In this work we derive the modifications to the Boltzmann equation governing the cosmic evolution of relic abundances induced by dilaton dissipative-source and non-critical-string terms in dilaton-driven non-equilibrium string Cosmologies. We also discuss briefly the most important phenomenological consequences, including modifications of the constraints on the available parameter space of cosmologically appealing particle physics models, imposed by recent precision data of astrophysical measurements.

  12. Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances

    Science.gov (United States)

    Lahanas, Ab; Mavromatos, Ne; Nanopoulos, Dv

    In this work we derive the modifications to the Boltzmann equation governing the cosmic evolution of relic abundances induced by dilaton dissipative-source and non-critical-string terms in dilaton-driven non-equilibrium string Cosmologies. We also discuss briefly the most important phenomenological consequences, including modifications of the constraints on the available parameter space of cosmologically appealing particle physics models, imposed by recent precision data of astrophysical measurements.

  13. Steady detonation waves via the Boltzmann equation for a reacting mixture

    CERN Document Server

    Conforto, F; Schürrer, F; Ziegler, I

    2003-01-01

    Based on the Boltzmann equation, the detonation problem is dealt with on a mesoscopic level. The model is based on the assumption that ahead of a shock an explosive gas mixture is in meta stable equilibrium. Starting from the Von Neumann point the chemical reaction, initiated by the pressure jump, proceeds until the chemical equilibrium is reached. Numerical solutions of the derived macroscopic equations as well as the corresponding Hugoniot diagrams which reveal the physical relevance of the mathematical model are provided.

  14. Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

    OpenAIRE

    Javier A. Dottori; Boroni, Gustavo A.; Alejandro Clausse

    2015-01-01

    A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM) based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that th...

  15. PDB2PQR: an automated pipeline for the setup of Poisson–Boltzmann electrostatics calculations

    OpenAIRE

    Dolinsky, Todd J.; Nielsen, Jens E.; McCammon, J. Andrew; Baker, Nathan A.

    2004-01-01

    Continuum solvation models, such as Poisson–Boltzmann and Generalized Born methods, have become increasingly popular tools for investigating the influence of electrostatics on biomolecular structure, energetics and dynamics. However, the use of such methods requires accurate and complete structural data as well as force field parameters such as atomic charges and radii. Unfortunately, the limiting step in continuum electrostatics calculations is often the addition of missing atomic coordinate...

  16. Nonlinear Boltzmann equation for the homogeneous isotropic case: Some improvements to deterministic methods and applications to relaxation towards local equilibrium

    Science.gov (United States)

    Asinari, P.

    2011-03-01

    Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).

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

    Science.gov (United States)

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

    2016-01-01

    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.

  18. Analysis of transport of collimated radiation in a participating media using the lattice Boltzmann method

    International Nuclear Information System (INIS)

    Application of the lattice Boltzmann method (LBM) recently proposed by Asinari et al. [Asinari P, Mishra SC, Borchiellini R. A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium. Numer Heat Transfer B 2010; 57:126–146] is extended to the analysis of transport of collimated radiation in a planar participating medium. To deal with azimuthally symmetric radiation in planar medium, a new lattice structure for the LBM is used. The transport of the collimated component in the medium is analysed by two different, viz., flux splitting and direct approaches. For different angles of incidence of the collimated radiation, the LBM formulation is tested for the effects of the extinction coefficient, the anisotropy factor, and the boundary emissivities on heat flux and emissive power distributions. Results are compared with the benchmark results obtained using the finite volume method. Both the approaches in LBM provide accurate results. -- Highlights: ► Transport of collimated radiation in participating media is studied. ► Usage of Lattice Boltzmann method (LBM) is extended in this study. ► In LBM, flux splitting and direct approaches are proposed. ► Effects of various parameters are studied on heat flux and temperature profiles. ► In all cases, LBM provides correct results.

  19. A general multiple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection-diffusion equations

    CERN Document Server

    Chai, Zhenhua; Guo, Zhaoli

    2016-01-01

    In this paper, based on the previous work [B. Shi, Z. Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E 79 (2009) 016701], we develop a general multiple-relaxation-time (MRT) lattice Boltzmann model for nonlinear anisotropic convection-diffusion equation (NACDE), and show that the NACDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the MRT model through some classic CDEs, and find that the numerical results are in good agreement with analytical solutions or some available results. Besides, the numerical results also show that similar to the single-relaxation-time (SRT) lattice Boltzmann model or so-called BGK model, the present MRT model also has a second-order convergence rate in space. Finally, we also perform a comparative study on the accuracy and stability of the MRT model and BGK model by using two examples. In terms of the accuracy, both the theoretical analysis and numerical results show that a \\emph{numerical}...

  20. Entropic Lattice Boltzmann Methods for Fluid Mechanics: Thermal, Multi-phase and Turbulence

    Science.gov (United States)

    Chikatamarla, Shyam; Boesch, F.; Frapolli, N.; Mazloomi, A.; Karlin, I.

    2014-11-01

    With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques. Major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence. In this talk, we shall review recent advances in ELBM as a practical, modeling-free tool for simulation of complex flow phenomenon. We shall present recent simulations of fluid turbulence including turbulent channel flow, flow past a circular cylinder, creation and dynamics of vortex tubes, and flow past a surface mounted cube. Apart from its achievements in turbulent flow simulations, ELBM has also presented us the opportunity to extend lattice Boltzmann method to higher order lattices which shall be employed for turbulent, multi-phase and thermal flow simulations. A new class of entropy functions are proposed to handle non-ideal equation of state and surface tension terms in multi-phase flows. It is shown the entropy principle brings unconditional stability and thermodynamic consistency to all the three flow regimes considered here. Acknowledgements: ERC Advanced Grant ``ELBM'' and CSCS grant s437 are deeply acknowledged. References:

  1. An exact energy conservation property of the quantum lattice Boltzmann algorithm

    International Nuclear Information System (INIS)

    The quantum lattice Boltzmann algorithm offers a unitary and readily parallelisable discretisation of the Dirac equation that is free of the fermion-doubling problem. The expectation of the discrete time-advance operator is an exact invariant of the algorithm. Its imaginary part determines the expectation of the Hamiltonian operator, the energy of the solution, with an accuracy that is consistent with the overall accuracy of the algorithm. In the one-dimensional case, this accuracy may be increased from first to second order using a variable transformation. The three-dimensional quantum lattice Boltzmann algorithm uses operator splitting to approximate evolution under the three-dimensional Dirac equation by a sequence of solutions of one-dimensional Dirac equations. The three-dimensional algorithm thus inherits the energy conservation property of the one-dimensional algorithm, although the implementation shown remains only first-order accurate due to the splitting error. -- Highlights: ► The quantum lattice Boltzmann algorithm approximates the Dirac equation. ► It has an exact invariant: the expectation of the discrete time-advance operator. ► The invariant consistently approximates the energy of the continuous system. ► We achieve second-order accuracy through a variable transformation.

  2. 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.

  3. Backward mapping solutions of the Boltzmann equation in cylindrically symmetric, uniformly charged auroral ionosphere

    Science.gov (United States)

    Ma, John Z. G.; St.-Maurice, J.-P.

    2015-06-01

    By applying a backward mapping technique, we solve the Boltzmann equation to investigate the effects of ion-neutral collisions on the ion velocity distribution and related transport properties in cylindrically symmetric, uniformly charged auroral ionosphere. Such a charge geometry introduces a radial electric field which increases linearly with distance from the axis of symmetry. In order to obtain complete analytical solutions for gaining physical insights into more complicated problems, we have substituted a relaxation collision model for the Boltzmann collision integral in the Boltzmann equation. Our calculations show that collisions drive the velocity distribution to a "horseshoe" shape after a few collision times. This feature extends to all radial positions as long as the electric field keeps increasing linearly versus radius. If the electric field is introduced suddenly, there is a transition from the collision-free pulsating Maxwellian distributions obtained in previous work (Ma and St.-Maurice, J. Geophys. Res., 113:A05312, 2008) to the "horseshoe" shapes on a time scale of within the few collision times. We also show how the transport properties evolve in a similar fashion, from oscillating to a non-oscillating features over the same time interval.

  4. Chebyshev spectral hexahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    This paper describes a new second generation spherical wavelet method for discretising the angular dimension of the Boltzmann transport equation. The approximation scheme provides a spectrally accurate expansion of the angular domain using Chebyshev collocation polynomials mapped into a wavelet space. Our method extends the work in Buchan et al. [Buchan, A., Pain, C.C., Eaton, M.D., Smedley-Stevenson, R., Goddard, A., Oliveira, C.D., submitted for publication. Linear and quadratic hexahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation. Nucl. Sci. Eng.; Buchan, A., Pain, C.C., Eaton, M.D., Smedley-Stevenson, R., Goddard, A., Oliveira, C.D., 2005. Linear and quadratic octahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation. Ann. Nucl. Energy 32, 1224-1273] of using low order finite element based wavelets. Here we show the spectral wavelets can improve on these techniques by providing more accurate representation of the angular fluxes. This also implies the method can provide improved solutions to those of the established methods SN and PN by reducing ray-effects and possibly Gibbs oscillations. We demonstrate this using a set of demanding mono-energetic particle transport problems

  5. Lattice Boltzmann simulation of electrostatic double layer interaction force for nanoparticles

    Science.gov (United States)

    Shi, Grace X.; Jin, Yan; Lazouskaya, Volha; Wang, Chao; Wang, Lian-Ping

    2011-11-01

    Modeling the transport and retention of nanoparticles (NPs) through soil porous media requires an accurate description of the electrostatic interaction force between a nanoparticle and soil grain. In this study, we apply the lattice Boltzmann method to directly solve the nonlinear Poisson Boltzmann (PB) equation for several geometric configurations including plate-plate, NP-plate, and NP-NP interactions, for any surface potentials and interaction distances and for different boundary conditions. Interaction energy and force are then derived from the simulations. For the case of plate-plate interaction, the simulation results are compared to the exact solution of the nonlinear PB equation. It is shown that the linear PB solution is valid when the nondimensional surface potential is less than one, and that the linear PB solution over-predicts the interaction force for intermediate gap distances but under-predicts the force for small gap distances. For NP-plate and NP-NP interactions, an axisymmetric lattice Boltzmann formulation is developed to solve the governing equations. The results will be compared to the classic approximate expressions of interaction force to evaluate their validity and to study the effect of nanoparticle size. Work supported by NSF and USDA.

  6. An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry

    International Nuclear Information System (INIS)

    Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the PN approximation, the SN method (discrete ordinates method) and their variants. In the discrete ordinates (SN) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to SN two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a monoenergetic electron beam in a rectangular domain. The main idea relies on applying the PN approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x-variable. Numerical results are given to illustrate the accuracy of deterministic methods presented. (author)

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

    KAUST Repository

    Allen, Rebecca

    2013-01-01

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

  8. Modeling cardiovascular hemodynamics using the lattice Boltzmann method on massively parallel supercomputers

    Science.gov (United States)

    Randles, Amanda Elizabeth

    Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable

  9. Event Segmentation Ability Uniquely Predicts Event Memory

    OpenAIRE

    Sargent, Jesse Q.; Zacks, Jeffrey M.; Hambrick, David Z.; Zacks, Rose T.; Kurby, Christopher A.; Bailey, Heather R.; Eisenberg, Michelle L.; Beck, Taylor M.

    2013-01-01

    Memory for everyday events plays a central role in tasks of daily living, autobiographical memory, and planning. Event memory depends in part on segmenting ongoing activity into meaningful units. This study examined the relationship between event segmentation and memory in a lifespan sample to answer the following question: Is the ability to segment activity into meaningful events a unique predictor of subsequent memory, or is the relationship between event perception and memory accounted for...

  10. Event Index - an LHCb Event Search System

    OpenAIRE

    Ustyuzhanin, Andrey; Artemov, Alexey; Kazeev, Nikita; Redkin, Artem

    2015-01-01

    During LHC Run 1, the LHCb experiment recorded around $10^{11}$ collision events. This paper describes Event Index - an event search system. Its primary function is to quickly select subsets of events from a combination of conditions, such as the estimated decay channel or number of hits in a subdetector. Event Index is essentially Apache Lucene optimized for read-only indexes distributed over independent shards on independent nodes.

  11. Event Index - an LHCb Event Search System

    CERN Document Server

    Ustyuzhanin, Andrey

    2015-01-01

    During LHC Run 1, the LHCb experiment recorded around 1011 collision events. This paper describes Event Index | an event search system. Its primary function is to quickly select subsets of events from a combination of conditions, such as the estimated decay channel or number of hits in a subdetector. Event Index is essentially Apache Lucene [1] optimized for read-only indexes distributed over independent shards on independent nodes.

  12. Extracting Event Dynamics from Event-by-Event Analysis

    OpenAIRE

    Fu, Jinghua; Liu, Lianshou

    2003-01-01

    The problem of eliminating the statistical fluctuations and extracting the event dynamics from event-by-event analysis is discussed. New moments $G_p$ (for continuous distribution), and $G_{q,p}$ (for anomalous distribution) are proposed, which are experimentally measurable and can eliminate the Poissonian type statistical fluctuations to recover the dynamical moments $C_p$ and $C_{q,p}$. In this way, the dynamical distribution of the event-averaged transverse momentum $\\bar{\\pt}$ can be extr...

  13. Lattice-Boltzmann simulation methods for chemically reactive systems in the micro area; Lattice Boltzmann Simulationsmethoden fuer chemisch reaktive Systeme im Microbereich - Schlussbericht

    Energy Technology Data Exchange (ETDEWEB)

    Karlin, I.; Frouzakis, Ch.; Boulouchos, K.

    2007-07-01

    This final report for the Swiss Federal Office of Energy (SFOE) reports on work done in 2007 at the Swiss Federal Institute of Technology ETH in Zurich on simulation methods for chemically reactive systems at the micrometer scale. The Lattice-Boltzmann method using lattice models is examined and the results obtained are discussed. A three-dimensional thermal model was developed and used to analyse flows with considerable temperature and density variations. The model was also used for the analysis of flows in diluted gases. A method for the reduction of complex reaction mechanisms was developed and tested for future combustion applications. 30 publications are noted and new possibilities for the analysis of flows in micro-channels and porous media - as used in reformers, catalyzers and fuel cells - are discussed.

  14. Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes; Solucion de la ecuacion de transporte de Boltzmann-Fokker-Planck usando esquemas nodales exponenciales

    Energy Technology Data Exchange (ETDEWEB)

    Ortega J, R.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: roj@correo.azc.uam.mx

    2003-07-01

    There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S{sub 4} with expansions of the dispersion cross sections until P{sub 3} order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

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

    Science.gov (United States)

    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

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

    International Nuclear Information System (INIS)

    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

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

    Energy Technology Data Exchange (ETDEWEB)

    Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr; Noutchegueme, Norbert, E-mail: nnoutch@yahoo.fr [Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)

    2015-01-15

    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

  18. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms

    International Nuclear Information System (INIS)

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms. (paper)

  19. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms

    Science.gov (United States)

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

  20. Dual Lattice Boltzmann method for electrokinetic coupling : behavior at high and low salinities in rough channels.

    Science.gov (United States)

    Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence

    2014-05-01

    We study the coupling between hydraulic and electric flows in a porous medium at small scale using the Lattice Boltzmann method. This method is a computational fluid dynamics technique that is used for advection and diffusion modeling. We implement a coupled Lattice Boltzmann algorithm that solves both the mass transport and the electric field arising from charges displacements. The streaming potential and electroosmosis phenomena occur in a variety of situations and derive from this coupling. We focus on the streaming potential which is described using the ratio between the created potential difference and the applied pressure gradient. The streaming potential is assumed to be a linear function of the fluid conductivity, but experimental results highlight anomalous behaviors at low and high salinity. We try to account for them by setting extreme conditions that are likely to generate non-linearities. Several pore radii are tested so as to determine what is the effect of a radius that is comparable to the Debye length, the screening length of the electric potential, due to the ions in the electrolyte. The volumetric integral of the electrical current is calculated for comparison with the 2D simulations. High values of zeta potential are tested to verify if the discrepancy regarding the theoretical result is concentration-dependent. We try to include a surface conductivity term in the coefficient formulation. Some tests including a rugosity on the channel walls are performed. All of these attempts show a normal behaviour of the streaming potential at high salinity. We observe a decrease of the ratio at low conductivity, showing that this ratio is modified when the pore radius becomes negligible compared with the Debye length, which is physically meaningful in little pores at low concentrations. References : S. Pride. Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50 : 15678-15696, 1994. D. A. Wolf

  1. Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

    Energy Technology Data Exchange (ETDEWEB)

    Uddin, Rizwan

    2012-01-01

    This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.

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

    International Nuclear Information System (INIS)

    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

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

    International Nuclear Information System (INIS)

    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)

  4. Empirical Analysis of the Divergence of Gibbs Sampling Based Learning Algorithms for Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Fischer, A.; Igel, Christian

    2010-01-01

    Learning algorithms relying on Gibbs sampling based stochastic approximations of the log-likelihood gradient have become a common way to train Restricted Boltzmann Machines (RBMs). We study three of these methods, Contrastive Divergence (CD) and its refined variants Persistent CD (PCD) and Fast PCD...... (FPCD). As the approximations are biased, the maximum of the log-likelihood is not necessarily obtained. Recently, it has been shown that CD, PCD, and FPCD can even lead to a steady decrease of the log-likelihood during learning. Taking artificial data sets from the literature we study these divergence...

  5. Symmetry-energy dependence of the dynamical dipole mode in the Boltzmann-Uehling-Uhlenbeck model

    CERN Document Server

    Ye, S Q; Ma, Y G; Shen, W Q

    2013-01-01

    Using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we have studied the connection between the symmetry energy and features of the dynamical dipole mode in fusion reactions with charge-asymmetric entrance channel. The yield and angular distribution of the prompt photon emission are extracted by a bremsstrahlung approach. The experimental data of $^{36}$Ar+$^{96}$Zr at 16 MeV/nucleon and $^{32}$S + $^{100}$Mo at 9.3 MeV/nucleon are compared with IBUU model calculations, and the soft symmetry energy is found to describe the data reasonably well.

  6. Solution Poisson-Boltzmann equation: Application in the Human Neuron Membrane

    CERN Document Server

    Soares, M A G; Cortez, C M

    2008-01-01

    With already demonstrated in previous work the equations that describe the space dependence of the electric potential are determined by the solution of the equation of Poisson-Boltzmann. In this work we consider these solutions for the membrane of the human neuron, using a model simplified for this structure considering the distribution of electrolytes in each side of the membrane, as well as the effect of glycocalyx and the lipidic bilayer. It was assumed that on both sides of the membrane the charges are homogeneously distributed and that the potential depends only on coordinate z.

  7. A novel protocol for linearization of the Poisson-Boltzmann equation

    CERN Document Server

    Tsekov, R

    2014-01-01

    A new protocol for linearization of the Poisson-Boltzmann equation is proposed and the resultant electrostatic equation coincides formally with the Debye-Huckel equation, the solution of which is well known for many electrostatic problems. The protocol is examined on the example of electrostatically stabilized nano-bubbles and it is shown that stable nano-bubbles could be present in aqueous solutions of anionic surfactants near the critical temperature, if the surface potential is constant. At constant surface charge non nano-bubbles could exist.

  8. Simulation of residual oil displacement in a sinusoidal channel with the lattice Boltzmann method

    CERN Document Server

    Otomo, Hiroshi; Hazlett, Randy; Li, Yong; Staroselsky, Ilya; Zhang, Raoyang; Chen, Hudong

    2016-01-01

    We simulate oil slug displacement in a sinusoidal channel in order to validate computational models and algorithms for multi-component flow. This case fits in the gap between fully realistic cases characterized by complicated geometry and academic cases with simplistic geometry. Our computational model is based on the lattice Boltzmann method and allows for variation of physical parameters such as wettability and viscosity. The effect of variation of model parameters is analyzed, in particular via comparison with analytical solutions. We discuss the requirements for accurate solution of the oil slug displacement problem.

  9. Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.

    Science.gov (United States)

    Hejranfar, Kazem; Hajihassanpour, Mahya

    2015-01-01

    In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential

  10. Numerical solution of the Boltzmann equation for the shock wave in a gas mixture

    CERN Document Server

    Raines, A A

    2014-01-01

    We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use the Conservative Projection Method developed by F.G. Tscheremissine which we extended to gas mixtures in cylindrical coordinates. The transition from the upstream to downstream uniform state is presented by macroscopic values and distribution functions. The obtained results were compared with numerical and experimental results of other authors.

  11. A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE- DIMENSIONAL DROP IMPACT ON A LIQUID FILM

    Institute of Scientific and Technical Information of China (English)

    SHI Zi-yuan; YAN Yong-hua; YANG Fan; QIAN Yue-hong; HU Guo-hui

    2008-01-01

    A single-phase free surface tracking model based on the Lattice Boltzmann Method (LBM), which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.

  12. New Fundamental Light Particle and Breakdown of Stefan-Boltzmann's Law

    Directory of Open Access Journals (Sweden)

    Samoilov V.

    2011-04-01

    Full Text Available Recently, we predicted the existence of fundamental particles in Nature, neutral Light Particles with spin 1 and rest mass m = 1.8 x 10^{-4} m_e, in addition to electrons, neutrons and protons. We call these particles Light Bosons because they create electromagnetic field which represents Planck's gas of massless photons together with a gas of Light Particles in the condensate. Such reasoning leads to a breakdown of Stefan-Boltzmann's law at low temperature. On the other hand, the existence of new fundamental neutral Light Particles leads to correction of such physical concepts as Bose-Einstein condensation of photons, polaritons and exciton polaritons.

  13. Flow simulation of fiber reinforced self compacting concrete using Lattice Boltzmann method

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skocek, Jan; Stang, Henrik;

    2011-01-01

    fibers is necessary. Computational fluid dynamics (CFD) comes to play at this stage. Formulation of a possible CFD model that is able to solve multi-phase and multi component non-Newtonian flow with complex boundary conditions and fiber suspension and preferably in reasonable time brings a very...... challenging task. A relatively new group of models - Lattice Boltzmann Modeling (LBM) - is presented in this paper. The conventional LBM is modified to include fiber and particle suspensions and non-Newtonian rheology and is used to model the fiber reinforced self compacting concrete flow....

  14. Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jun; TAO Rui-Bao

    2002-01-01

    Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and set up adata base of free energy calculated by means of Tao-Sheng Lin's extended molecular field theory that can explain theexperiments of the equilibrium properties of nematic liquid crystal very well. Then we use the free energy method oflattice Boltzmann developed by Oxford group to study the phase decomposition, pattern formation in the flow of theliquid crystal near transition temperature.

  15. Cyclic Heating-Annealing and Boltzmann Distribution of Free Energies in a Spin-Glass System

    Institute of Scientific and Technical Information of China (English)

    ZHOU Hai-Jun

    2007-01-01

    Ergodicity of a spin-glass is broken at low temperatures; the system is trapped in one of many ergodic configurational domains. Transitions between different ergodic domains are achievable through a heating-annealing procedure. If this experiment is repeated infinite times, all ergodic configurational domains will be visited with frequences that decreasing exponentially with their free energies. The mean free energy density of a spin-glass system on a random graph is calculated based on this free energy Boltzmann distribution in the present work, by means of the cavity approach.

  16. High order numerical methods for the space non-homogeneous Boltzmann equation

    International Nuclear Information System (INIS)

    In this paper we present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. The transport is solved by a third order accurate (in space) positive and flux conservative (PFC) method. The collision step is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity, coupled with several high order integrators in time. Strang splitting is used to achieve second order accuracy in space and time. Several numerical tests illustrate the properties of the methods

  17. Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime

    International Nuclear Information System (INIS)

    We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-(1/2) particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 2 spin-density (‘Wigner’) matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the t→∞ thermal (Fermi–Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting. (paper)

  18. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    OpenAIRE

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially relevant topic is the Fischer-Tropsch Synthesis (FTS) in the Gas-to-Liquid (GtL) conversion process of methane. The research described in this thesis was carried out in the context of a twin projec...

  19. On the completeness of the multigroup eigenfunctions set of a reactor system Boltzmann operator

    International Nuclear Information System (INIS)

    An example is given, which illustrates how the set of the eigenfunctions shifts from incompleteness to completeness when a coupling relationship is established between the spectrum of the neutrons produced by fission and the energy of the neutrons which generate the fissions. The proposed method allows one to complete the set of eigenfunctions of the Boltzmann operator in the multigroup case. That, in principle, enlarges the possibility to apply the SM, Standard Method, and the GSM, Generalized Standard Method, to any problem in reactor physics, regardless of the number of energy groups. (author)

  20. Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear

    CERN Document Server

    Xu, A; Xu, Aiguo

    2003-01-01

    We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required to obtain a triangular profile is inversely proportional to the viscosity and proportional to the square of the size of the system. We find that the same behaviour also occurs for binary mixtures, for any component ratio in the mixture and independently from the time when shear flow is switched on during phase separation.