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Sample records for boltzmann statistics

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

    Science.gov (United States)

    Tirnakli, Ugur; Borges, Ernesto P

    2016-03-23

    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.

  2. 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.

  3. 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.

  4. Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

    CERN Document Server

    Sui, Ning; He, Ping

    2014-01-01

    In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivat...

  5. 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.

  6. Error statistics of hidden Markov model and hidden Boltzmann model results

    Directory of Open Access Journals (Sweden)

    Newberg Lee A

    2009-07-01

    Full Text Available Abstract Background Hidden Markov models and hidden Boltzmann models are employed in computational biology and a variety of other scientific fields for a variety of analyses of sequential data. Whether the associated algorithms are used to compute an actual probability or, more generally, an odds ratio or some other score, a frequent requirement is that the error statistics of a given score be known. What is the chance that random data would achieve that score or better? What is the chance that a real signal would achieve a given score threshold? Results Here we present a novel general approach to estimating these false positive and true positive rates that is significantly more efficient than are existing general approaches. We validate the technique via an implementation within the HMMER 3.0 package, which scans DNA or protein sequence databases for patterns of interest, using a profile-HMM. Conclusion The new approach is faster than general naïve sampling approaches, and more general than other current approaches. It provides an efficient mechanism by which to estimate error statistics for hidden Markov model and hidden Boltzmann model results.

  7. Investigation of Particles Statistics in large Eddy Simulated Turbulent Channel Flow using Generalized lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Mandana Samari Kermani

    2016-01-01

    Full Text Available The interaction of spherical solid particles with turbulent eddies in a 3-D turbulent channel flow with friction Reynolds number was studied. A generalized lattice Boltzmann equation (GLBE was used for computation of instantaneous turbulent flow field for which large eddy simulation (LES was employed. The sub-grid-scale (SGS turbulence effects were simulated through a shear-improved Smagorinsky model (SISM, which can predict turbulent near wall region without any wall function. Statistical properties of particles behavior such as root mean square (RMS velocities were studied as a function of dimensionless particle relaxation time ( by using a Lagrangian approach. Combination of SISM in GLBE with particle tracking analysis in turbulent channel flow is novelty of the present work. Both GLBE and SISM solve the flow field equations locally. This is an advantage of this method and makes it easy implementing. Comparison of the present results with previous available data indicated that SISM in GLBE is a reliable method for simulation of turbulent flows which is a key point to predict particles behavior correctly.

  8. Interview with Yves Pomeau, Boltzmann Medallist 2016 : The universality of statistical physics interpretation is ever more obvious.

    Science.gov (United States)

    Pomeau, Yves; Louët, Sabine

    2016-06-01

    During the StatPhys Conference on 20th July 2016 in Lyon, France, Yves Pomeau and Daan Frenkel will be awarded the most important prize in the field of Statistical Mechanics: the 2016 Boltzmann Medal, named after the Austrian physicist and philosopher Ludwig Boltzmann. The award recognises Pomeau's key contributions to the Statistical Physics of non-equilibrium phenomena in general. And, in particular, for developing our modern understanding of fluid mechanics, instabilities, pattern formation and chaos. He is recognised as an outstanding theorist bridging disciplines from applied mathematics to statistical physics with a profound impact on the neighbouring fields of turbulence and mechanics. In the article Sabine Louët interviews Pomeau, who is an Editor for the European Physical Journal Special Topics. He shares his views and tells how he experienced the rise of Statistical Mechanics in the past few decades. He also touches upon the need to provide funding to people who have the rare ability to discover new things and ideas, and not just those who are good at filling in grant application forms.

  9. 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.

  10. 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.

  11. Biases and statistical errors in Monte Carlo burnup calculations: an unbiased stochastic scheme to solve Boltzmann/Bateman coupled equations

    International Nuclear Information System (INIS)

    External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burn up may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data. Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like k(eff), reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as 'cycles', 'batches', or 'replicas'), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation

  12. 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...

  13. 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.)

  14. 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...

  15. 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...

  16. 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.

  17. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2006-01-01

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

  18. 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.

  19. 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.

  20. 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...

  1. 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...

  2. 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 ...

  3. On Boltzmann's genius and thermodynamics

    CERN Document Server

    Gyftopoulos, Elias P

    2007-01-01

    A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt of gratitude for his ingenious and pathfinding contributions. However, the essay chooses to illustrate this important memorial by statements and inferences that perhaps are questionable today even to Boltzmann himself. I will comment only on three issues.

  4. 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.

  5. Statistics

    CERN Document Server

    Hayslett, H T

    1991-01-01

    Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the

  6. 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.

  7. Statistics

    Science.gov (United States)

    Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.

  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. 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

  10. 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.

  11. 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...

  12. 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…

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  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. Multiphase cascaded lattice Boltzmann method

    OpenAIRE

    Lycett-Brown, D.; Luo, K. H.

    2014-01-01

    To improve the stability of the lattice Boltzmann method (LBM) at high Reynolds number the cascaded LBM has recently been introduced. As in the multiple relaxation time (MRT) method the cascaded LBM introduces additional relaxation times into the collision operator, but does so in a co-moving reference frame. This has been shown to significantly increase stability at low viscosity in the single phase case. Here the cascaded LBM is further developed to include multiphase flow. For this the for...

  19. Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines

    CERN Document Server

    Huang, Li

    2016-01-01

    Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feedforward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine for efficient Monte Carlo updates and to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate improved acceptance ratio and autocorrelation time near the phase transition point.

  20. The Statistical Interpretation of Entropy: An Activity

    Science.gov (United States)

    Timmberlake, Todd

    2010-01-01

    The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the…

  1. SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS

    Institute of Scientific and Technical Information of China (English)

    Yan Guangwu; Hu Shouxin

    2000-01-01

    A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed.Using the Chapman-Enskog expansion and multi-scale technique,we obtain the higher-order moments of equilibrium distribution function.A simple traffic light problem is simulated by using the present lattice Boltzmann model,and the result agrees well with analytical solution.

  2. Lattice Boltzmann scheme for relativistic fluids

    OpenAIRE

    Mendoza, M.; B. Boghosian; Herrmann, H. J.; Succi, S.

    2009-01-01

    A Lattice Boltzmann formulation for relativistic fluids is presented and numerically verified through quantitative comparison with recent hydrodynamic simulations of relativistic shock-wave propagation in viscous quark-gluon plasmas. This formulation opens up the possibility of exporting the main advantages of Lattice Boltzmann methods to the relativistic context, which seems particularly useful for the simulation of relativistic fluids in complicated geometries.

  3. The Einstein-Boltzmann system and positivity

    CERN Document Server

    Lee, Ho

    2012-01-01

    The Einstein-Boltzmann system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and by Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the Einstein-Boltzmann system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the Einstein-Boltzmann system so as to include scattering kernels which are physically well-motivated.

  4. Thermal cascaded lattice Boltzmann method

    CERN Document Server

    Fei, Linlin

    2016-01-01

    In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \\emph{et al.}, Phys. Rev. E \\textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green f...

  5. 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

  6. 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.)

  7. 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...

  8. Ergodicity, ensembles, irreversibility in Boltzmann and beyond

    CERN Document Server

    Gallavotti, G

    1994-01-01

    The implications of the original misunderstanding of the etymology of the word "ergodic" are discussed, and the contents of a not too well known paper by Boltzmann are critically examined. The connection with the modern theory of Ruelle is attempted

  9. Ergodicity, ensembles, irreversibility in Boltzmann and beyond

    Science.gov (United States)

    Gallavotti, Giovanni

    1995-03-01

    The contents of a not too well-known paper by Boltzmann are critically examined. The etymology of the word ergodic and its implications are discussed. A connection with the modern theory of Ruelle is attempted.

  10. 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

  11. 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

  12. 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.

  13. 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...

  14. 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

  15. 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.

  16. Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems.

    Science.gov (United States)

    Wilson, Alan

    2008-08-01

    It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of 'scale-free' networks.

  17. 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.

  18. Coupling of replica exchange simulations to a non-Boltzmann structure reservoir.

    Science.gov (United States)

    Roitberg, Adrian E; Okur, Asim; Simmerling, Carlos

    2007-03-15

    Computing converged ensemble properties remains challenging for large biomolecules. Replica exchange molecular dynamics (REMD) can significantly increase the efficiency of conformational sampling by using high temperatures to escape kinetic traps. Several groups, including ours, introduced the idea of coupling replica exchange to a pre-converged, Boltzmann-populated reservoir, usually at a temperature higher than that of the highest temperature replica. This procedure reduces computational cost because the long simulation times needed for extensive sampling are only carried out for a single temperature. However, a weakness of the approach is that the Boltzmann-weighted reservoir can still be difficult to generate. We now present the idea of employing a non-Boltzmann reservoir, whose structures can be generated through more efficient conformational sampling methods. We demonstrate that the approach is rigorous and derive a correct statistical mechanical exchange criterion between the reservoir and the replicas that drives Boltzmann-weighted probabilities for the replicas. We test this approach on the trpzip2 peptide and demonstrate that the resulting thermal stability profile is essentially indistinguishable from that obtained using very long (>100 ns) standard REMD simulations. The convergence of this reservoir-aided REMD is significantly faster than for regular REMD. Furthermore, we demonstrate that modification of the exchange criterion is essential; REMD simulations using a standard exchange function with the non-Boltzmann reservoir produced incorrect results.

  19. 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.

  20. Fast lattice Boltzmann solver for relativistic hydrodynamics.

    Science.gov (United States)

    Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S

    2010-07-01

    A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.

  1. 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

  2. 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.

  3. Fast lattice Boltzmann solver for relativistic hydrodynamics.

    Science.gov (United States)

    Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S

    2010-07-01

    A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows. PMID:20867451

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Multispeed models in off-lattice Boltzmann simulations

    NARCIS (Netherlands)

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

    2008-01-01

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

  9. 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.

  10. 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...

  11. Stefan-Boltzmann Law for Massive Photons

    Science.gov (United States)

    Moreira, E. S.; Ribeiro, T. G.

    2016-08-01

    This paper generalizes the Stefan-Boltzmann law to include massive photons. A crucial ingredient to obtain the correct formula for the radiance is to realize that a massive photon does not travel at the speed of (massless) light. It follows that, contrary to what could be expected, the radiance is not proportional to the energy density times the speed of light.

  12. Pruning Boltzmann networks and hidden Markov models

    DEFF Research Database (Denmark)

    Pedersen, Morten With; Stork, D.

    1996-01-01

    We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linea...... and thus the proper weight is pruned at each pruning step. In all our experiments in small problems, pruning reduces the generalization error; in most cases the pruned networks facilitate interpretation as well......We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...

  13. 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.

  14. THREE WAY DECOMPOSITION FOR THE BOLTZMANN EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ilgis Ibragimov; Sergej Rjasanow

    2009-01-01

    The initial value problem for the spatially homogeneous Boltzmann equation is considered. A deterministic numerical scheme for this problem is developed by the use of the three way decomposition of the unknown function as well as of the collision integral. On this way, almost linear complexity of the algorithm is achieved. Some numerical examples are presented.

  15. 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.

  16. 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.

  17. Approximate message passing with restricted Boltzmann machine priors

    Science.gov (United States)

    Tramel, Eric W.; Drémeau, Angélique; Krzakala, Florent

    2016-07-01

    Approximate message passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problems. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernoulli prior which utilizes a restricted Boltzmann machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple i.i.d. 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.

  18. Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines

    CERN Document Server

    Cadieu, Charles F

    2010-01-01

    We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.

  19. 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.

  20. Boltzmann, Darwin and Directionality theory

    Science.gov (United States)

    Demetrius, Lloyd A.

    2013-09-01

    Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and

  1. Boltzmann, Darwin and Directionality theory

    Energy Technology Data Exchange (ETDEWEB)

    Demetrius, Lloyd A., E-mail: ldemetr@oeb.harvard.edu

    2013-09-01

    Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and

  2. 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

  3. 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...

  4. 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.

  5. 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 ...

  6. 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.

  7. 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...

  8. 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.

  9. Nonextensive statistical mechanics of ionic solutions

    Energy Technology Data Exchange (ETDEWEB)

    Varela, L.M. [Grupo de Nanomateriales y Materia Blanda, Departamento de Fisica de la Materia Condensada, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela (Spain)], E-mail: fmluis@usc.es; Carrete, J. [Grupo de Nanomateriales y Materia Blanda, Departamento de Fisica de la Materia Condensada, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela (Spain); Munoz-Sola, R. [Departamento de Matematica Aplicada, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela (Spain); Rodriguez, J.R.; Gallego, J. [Grupo de Nanomateriales y Materia Blanda, Departamento de Fisica de la Materia Condensada, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela (Spain)

    2007-10-29

    Classical mean-field Poisson-Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson-Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye-Hueckel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q.

  10. 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.

  11. 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

  12. 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.

  13. Lattice-Boltzmann-based Simulations of Diffusiophoresis

    Science.gov (United States)

    Castigliego, Joshua; Kreft Pearce, Jennifer

    We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles by their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. This simulation, in particular, was intended to model an oceanic system where the particles of interest were zooplankton, phytoplankton and microplastics. The separation of plankton from the microplastics was achieved.

  14. 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.

  15. Basics of statistical physics

    CERN Document Server

    Müller-Kirsten, Harald J W

    2013-01-01

    Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles, and attempts to explain these in simple terms supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin-Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose-Eins...

  16. Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

    CERN Document Server

    Saida, Hiromi

    2013-01-01

    We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equat...

  17. Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force

    Institute of Scientific and Technical Information of China (English)

    Seiji UKAI; Tong YANG; Huijiang ZHAO

    2006-01-01

    For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to stationary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. Statistical thermodynamics of nonequilibrium processes

    CERN Document Server

    Keizer, Joel

    1987-01-01

    The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo­ dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com­ bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and...

  5. Pathway Model and Nonextensive Statistical Mechanics

    Science.gov (United States)

    Mathai, A. M.; Haubold, H. J.; Tsallis, C.

    2015-12-01

    The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential series. One such pathway, from the mathematical statistics point of view, results in distributions which naturally emerge within nonextensive statistical mechanics and Beck-Cohen superstatistics, as pursued in generalizations of Boltzmann-Gibbs statistics.

  6. Comparing Tsallis statistics effects at high and very high energy $pp$ collisions

    CERN Document Server

    Parvan, A S

    2016-01-01

    We considered the energy dependence of Tsallis statistics parameters and found that deviation from Boltzmann statistics is monotonically growing with energy. This may be attributed to the dominance of low $x$ at higher energies leading to the power-like NLO QCD spectra for which Tsallis statistics may serve as effective theory. At the same time, for larger $x$ at lower energies the Gaussian falloff of transverse-momentum-dependent distributions is crucial and correspondent effective description is provided by the Boltzmann distribution.

  7. 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.

  8. 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

  9. 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.

  10. Heavy Flavor Suppression: Boltzmann vs Langevin

    CERN Document Server

    Das, Santosh K; Plumari, Salvatore; Greco, Vincenzo

    2013-01-01

    The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor $R_{AA}$ has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable.

  11. 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.

  12. 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...

  13. 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.

  14. Lattice Boltzmann modelling of intrinsic permeability

    CERN Document Server

    Li, Jun; Wu, Lei; Zhang, Yonghao

    2016-01-01

    Lattice Boltzmann method (LBM) has been applied to predict flow properties of porous media including intrinsic permeability, where it is implicitly assumed that the LBM is equivalent to the incompressible (or near incompressible) Navier-Stokes equation. However, in LBM simulations, high-order moments, which are completely neglected in the Navier-Stokes equation, are still available through particle distribution functions. To ensure that the LBM simulation is correctly working at the Navier-Stokes hydrodynamic level, the high-order moments have to be negligible. This requires that the Knudsen number (Kn) is small so that rarefaction effect can be ignored. In this technical note, we elaborate this issue in LBM modelling of porous media flows, which is particularly important for gas flows in ultra-tight media.

  15. Flux Limiter Lattice Boltzmann for Compressible Flows

    Institute of Scientific and Technical Information of China (English)

    陈峰; 许爱国; 张广财; 李英骏

    2011-01-01

    In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

  16. 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.

  17. 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:

  18. Accurate deterministic solutions for the classic Boltzmann shock profile

    Science.gov (United States)

    Yue, Yubei

    The Boltzmann equation or Boltzmann transport equation is a classical kinetic equation devised by Ludwig Boltzmann in 1872. It is regarded as a fundamental law in rarefied gas dynamics. Rather than using macroscopic quantities such as density, temperature, and pressure to describe the underlying physics, the Boltzmann equation uses a distribution function in phase space to describe the physical system, and all the macroscopic quantities are weighted averages of the distribution function. The information contained in the Boltzmann equation is surprisingly rich, and the Euler and Navier-Stokes equations of fluid dynamics can be derived from it using series expansions. Moreover, the Boltzmann equation can reach regimes far from the capabilities of fluid dynamical equations, such as the realm of rarefied gases---the topic of this thesis. Although the Boltzmann equation is very powerful, it is extremely difficult to solve in most situations. Thus the only hope is to solve it numerically. But soon one finds that even a numerical simulation of the equation is extremely difficult, due to both the complex and high-dimensional integral in the collision operator, and the hyperbolic phase-space advection terms. For this reason, until few years ago most numerical simulations had to rely on Monte Carlo techniques. In this thesis I will present a new and robust numerical scheme to compute direct deterministic solutions of the Boltzmann equation, and I will use it to explore some classical gas-dynamical problems. In particular, I will study in detail one of the most famous and intrinsically nonlinear problems in rarefied gas dynamics, namely the accurate determination of the Boltzmann shock profile for a gas of hard spheres.

  19. Lattice Boltzmann Simulation of Viscous Flow past Elliptical Cylinder

    Directory of Open Access Journals (Sweden)

    D.Arumuga Perumal

    2012-09-01

    Full Text Available This work is concerned with the vortex structures of two-dimensional elliptical cylinder by lattice Boltzmann method. It is known that, the nature of the flow past cylindrical obstacles is very complex. Therefore, in the present work a kinetic based approach, namely, lattice Boltzmann method is used to compute both for steady and unsteady flows. A two dimensional nine-velocity square lattice (D2Q9 model is used in the present simulation. Effects of blockage ratio, Reynolds number and channel length are studied in detail. Here we conclude that lattice Boltzmann method can be effectively used to capture vortex shedding and other features.

  20. 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...

  1. Permit Allocation in Emissions Trading using the Boltzmann Distribution

    CERN Document Server

    Park, Ji-Won; Isard, Walter

    2011-01-01

    In emissions trading, the initial permit allocation is an intractable issue because it needs to be essentially fair to the participating countries. There are many ways to distribute a given total amount of emissions permits among countries, but the existing distribution methods such as auctioning and grandfathering have been debated. Here we describe a new model for permit allocation in emissions trading using the Boltzmann distribution. The Boltzmann distribution is introduced to permit allocation by combining it with concepts in emissions trading. A price determination mechanism for emission permits is then developed in relation to the {\\beta} value in the Boltzmann distribution. Finally, it is demonstrated how emissions permits can be practically allocated among participating countries in empirical results. The new allocation model using the Boltzmann distribution describes a most probable, natural, and unbiased distribution of emissions permits among multiple countries. Based on its simplicity and versati...

  2. 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.

  3. 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.

  4. 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...

  5. Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy

    CERN Document Server

    Lemarchand, Cyril; Darquié, Benoît; Bordé, Christian J; Chardonnet, Christian; Daussy, Christophe

    2010-01-01

    In this paper, we present significant progress performed on an experiment dedicated to the determination of the Boltzmann constant, k, by accurately measuring the Doppler absorption profile of a line in a gas of ammonia at thermal equilibrium. This optical method based on the first principles of statistical mechanics is an alternative to the acoustical method which has led to the unique determination of k published by the CODATA with a relative accuracy of 1.7 ppm. We report on the first measurement of the Boltzmann constant by laser spectroscopy with a statistical uncertainty below 10 ppm, more specifically 6.4 ppm. This progress results from improvements in the detection method and in the statistical treatment of the data. In addition, we have recorded the hyperfine structure of the probed saQ(6,3) rovibrational line of ammonia by saturation spectroscopy and thus determine very precisely the induced 4.36 (2) ppm broadening of the absorption linewidth. We also show that, in our well chosen experimental condi...

  6. Axiomatic nonextensive statistics at NICA energies

    CERN Document Server

    Tawfik, Abdel Nasser

    2016-01-01

    We discuss the possibility of implementing axiomatic nonextensive statistics, where it is conjectured that the phase-space volume determines the (non)extensive entropy, on the particle production at NICA energies. Both Boltzmann-Gibbs and Tsallis statistics are very special cases of this generic (non)extensivity. We conclude that the lattice thermodynamics is {\\it ab initio} extensive and additive and thus the nonextensive approaches including Tsallis statistics categorically are not matching with them, while the particle production, for instance the particle ratios at various center-of-mass energies, is likely a nonextensive process but certainly not of Tsallis type. The resulting freezeout parameters, the temperature and the chemical potentials, are approximately compatible with the ones deduced from Boltzmann-Gibbs statistics.

  7. Direct and Large-Eddy Simulation of Turbulent Flows on Composite Multi-Resolution Grids by the Lattice Boltzmann Method

    OpenAIRE

    Touil, Hatem; Ricot, Denis; Lévêque, Emmanuel

    2013-01-01

    In order to properly address the simulation of complex (weakly compressible) turbulent flows, the lattice Boltzmann method, originally designed for uniform structured grids, needs to be extended to composite multi-domain grids displaying various levels of spatial resolution. Therefore, physical conditions must be specified to determine the mapping of statistical information (about the populations of moving particles) at the interface between two domains of different resolutions. It is here ar...

  8. Statistical mechanics a short treatise

    CERN Document Server

    Gallavotti, Giovanni

    1999-01-01

    This book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works The author emphasizes the relation between microscopic reversibility and macroscopic irreversibility Students will find a clear and detailed explanation of fundamental concepts such as equipartition, entropy, and ergodicity They will learn about Brownian motion, the modern treatment of the thermodynamic limit phase transitions, the microscopic and macroscopic theory of the coexistence of phases, statistical mechanics of stationary states, and fluctuations and dissipation in chaotic motions

  9. 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

  10. 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...

  11. Modeling adsorption with lattice Boltzmann equation.

    Science.gov (United States)

    Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling

    2016-01-01

    The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325

  12. 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

  13. Modeling adsorption with lattice Boltzmann equation

    Science.gov (United States)

    Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling

    2016-01-01

    The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325

  14. Reconciliation of Statistical Mechanics and Astro-Physical Statistics. The errors of conventional canonical thermostatistics

    CERN Document Server

    Gross, D H E

    2005-01-01

    Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. (Only in this case this is equivalent to the fundamental microcanonical ensemble.) However, some 170 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential physics is the separation of the gas phase from the liquid. Of course, boiling water is inhomogeneous and as such cannot be treated by conventional thermo-statistics. Then it is not astonishing, that a phase transition of first order is signaled canonically by a Yang-Lee singularity. Thus it is only treated correctly by microcanonical Boltzmann-Planck statistics. It turns out that the Boltzmann-Planck statistics is much richer and gives fundamental insight into statistical mechanics and especially into entropy. This can be done to a far extend rigorously and analytically. As no extensivity, no thermodynamic limit, no concavity, no homogeneity is needed, it also applies to astro-physical syst...

  15. An Integrated, Statistical Molecular Approach to the Physical Chemistry Curriculum

    Science.gov (United States)

    Cartier, Stephen F.

    2009-01-01

    As an alternative to the "thermodynamics first" or "quantum first" approaches to the physical chemistry curriculum, the statistical definition of entropy and the Boltzmann distribution are introduced in the first days of the course and the entire two-semester curriculum is then developed from these concepts. Once the tools of statistical mechanics…

  16. Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation.

    Science.gov (United States)

    Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S

    2013-10-18

    We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).

  17. Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation.

    Science.gov (United States)

    Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S

    2013-10-18

    We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution). PMID:24182245

  18. Spherical galaxy models as equilibrium configurations in nonextensive statistics

    CERN Document Server

    Cardone, V F; Del Popolo, A

    2011-01-01

    Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the gravitational force contrasts with the underlying assumptions of Boltzmann statistics where the interactions among particles are assumed to be short ranged. A particular generalization of the classical Boltzmann formalism is available within the nonextensive context of Tsallis q -statistics, subject to non -additivity of the entropies of sub - systems. Assuming stationarity and isotropy in the velocity space, it is possible solving the generalized collsionless Boltzmann equation to derive the galaxy distribution function and density profile. We present a particular set of nonextensive models and investigate their dynamical and observable properties. As a test of the viability of this generalized context, we fit the rotation curve of M33 showing that the proposed approach leads to da...

  19. 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.

  20. 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...

  1. Navier-Stokes Dynamics by a Discrete Boltzmann Model

    Science.gov (United States)

    Rubinstein, Robet

    2010-01-01

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

  2. 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

  3. Accounting for adsorption and desorption in Lattice Boltzmann simulations

    CERN Document Server

    Levesque, Maximilien; Pagonabarraga, Ignacio; Frenkel, Daan; Rotenberg, Benjamin

    2013-01-01

    We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. Associated to the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g. in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic, but also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a Lattice-Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is ...

  4. 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...

  5. An integrable 3D lattice model with positive Boltzmann weights

    CERN Document Server

    Mangazeev, Vladimir V; Sergeev, Sergey M

    2013-01-01

    In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. The weights depend on a free parameter 0Boltzmann weights.

  6. Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory.

    Science.gov (United States)

    Mahakrishnan, Sathiya; Chakraborty, Subrata; Vijay, Amrendra

    2016-09-15

    Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example

  7. Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory.

    Science.gov (United States)

    Mahakrishnan, Sathiya; Chakraborty, Subrata; Vijay, Amrendra

    2016-09-15

    Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example

  8. 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 ...... by 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...

  9. Spinor Boltzmann Equation with Two Momenta at the Fermi Level

    Institute of Scientific and Technical Information of China (English)

    王正川

    2012-01-01

    Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The lon- gitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.

  10. 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.

  11. 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.

  12. 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.

  13. Learning Feature Hierarchies with Centered Deep Boltzmann Machines

    CERN Document Server

    Montavon, Grégoire

    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 our suggestion, the centered deep Boltzmann machine, learns a hierarchy of increasingly abstract representations and a better generative model of data.

  14. CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

    Institute of Scientific and Technical Information of China (English)

    FENG SHI-DE; REN RONG-CAI; CUI XIAO-PENG; JI ZHONG-ZHEN

    2001-01-01

    With the discrete method of the hexagonal cell and three different velocities of particle population in each cell,a two-dimensional lattice Boltzmann model is developed in this paper.[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q19 model is verified.

  15. Injury Statistics

    Science.gov (United States)

    ... Data Consumer Opinion Surveys Home / Research & Statistics Injury Statistics This is the statistic reports page for scientific ... Home Appliances, Maintenance and Construction Injury Statistics Injury Statistics September 30, 2012 Submersions Related to Non-Pool ...

  16. Elementary principles in statistical mechanics

    CERN Document Server

    Gibbs, J Willard

    2014-01-01

    Written by J. Willard Gibbs, the most distinguished American mathematical physicist of the nineteenth century, this book was the first to bring together and arrange in logical order the works of Clausius, Maxwell, Boltzmann, and Gibbs himself. The lucid, advanced-level text remains a valuable collection of fundamental equations and principles. Topics include the general problem and the fundamental equation of statistical mechanics, the canonical distribution of the average energy values in a canonical ensemble of systems, and formulas for evaluating important functions of the energies of a sys

  17. Nonextensive statistical mechanics and high energy physics

    Directory of Open Access Journals (Sweden)

    Tsallis Constantino

    2014-04-01

    Full Text Available The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q, which, in the q → 1 limit, recovers the standard Boltzmann-Gibbs entropy and associated nonextensive statistical mechanics. We then present somerecent applications to systems such as high-energy collisions, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Lévy distributions and q-exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature

  18. 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...

  19. A Parallel Lattice Boltzmann Model of a Carotid Artery

    Science.gov (United States)

    Boyd, J.; Ryan, S. J.; Buick, J. M.

    2008-11-01

    A parallel implementation of the lattice Boltzmann model is considered for a three dimensional model of the carotid artery. The computational method and its parallel implementation are described. The performance of the parallel implementation on a Beowulf cluster is presented, as are preliminary hemodynamic results.

  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. 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.)

  2. Boundary conditions for surface reactions in lattice Boltzmann simulations

    NARCIS (Netherlands)

    Gillissen, J.J.J.; Looije, N.

    2014-01-01

    A surface reaction boundary condition in multicomponent lattice Boltzmann simulations is developed. The method is applied to a test case with nonlinear reaction rates and nonlinear density profiles. The results are compared to the corresponding analytical solution, which shows that the error of 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. An exactly solvable non-linear Boltzmann equation

    NARCIS (Netherlands)

    Ernst, M.H.; Hendriks, E.M.

    1979-01-01

    The initial value problem for a model Boltzmann equation of a two dimensional gas with a continuous or discrete energy distribution function and a transition probability δ(ε - ε') is solved exactly; ε and ε' are the total energies before and after collision.

  5. Nuclear Multifragmentation in the Non-extensive Statistics - Canonical Formulation

    Energy Technology Data Exchange (ETDEWEB)

    Gudima, K.K. [Grand Accelerateur National d' Ions Lourds - GANIL, CEA/DSM - CNRS/IN2P3, BP 5027, F-14021 Caen Cedex (France); Institute of Applied Physics, Moldova Academy of Sciences, MD-2028 Kishineu (Moldova, Republic of); Parvan, A.S.; Toneev, V.D. [Institute of Applied Physics, Moldova Academy of Sciences, MD-2028 Kishineu (Moldova, Republic of); Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds - GANIL, CEA/DSM - CNRS/IN2P3, BP 5027, F-14076 Caen Cedex (France)

    2000-04-21

    We apply the canonical quantum statistical model of nuclear multifragmentation generalized in the framework of recently proposed Tsallis non-extensive thermo-statistics for the description of nuclear multifragmentation process. The test calculation in the system with A = 197 nucleons shows strong modification of the 'critical' behaviour associated with the nuclear liquid-gas phase transition for small deviations from the conventional Boltzmann-Gibbs statistical mechanics. (authors)

  6. Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs: Confined laser-cooled atoms in a nonthermal state

    Science.gov (United States)

    Dechant, Andreas; Shafier, Shalom Tzvi; Kessler, David A.; Barkai, Eli

    2016-08-01

    The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.

  7. Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs: Confined laser-cooled atoms in a nonthermal state.

    Science.gov (United States)

    Dechant, Andreas; Shafier, Shalom Tzvi; Kessler, David A; Barkai, Eli

    2016-08-01

    The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density. PMID:27627290

  8. Quantum statistical ensemble for emissive correlated systems

    Science.gov (United States)

    Shakirov, Alexey M.; Shchadilova, Yulia E.; Rubtsov, Alexey N.

    2016-06-01

    Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N -particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems.

  9. Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation.

    Science.gov (United States)

    Radtke, Gregg A; Hadjiconstantinou, Nicolas G

    2009-05-01

    We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated. PMID:19518597

  10. Coupling Lattice Boltzmann with Atomistic Dynamics for the multiscale simulation of nano-biological flows

    CERN Document Server

    Fyta, Maria; Kaxiras, Efthimios; Succi, Sauro

    2007-01-01

    We describe a recent multiscale approach based on the concurrent coupling of constrained molecular dynamics for long biomolecules with a mesoscopic lattice Boltzmann treatment of solvent hydrodynamics. The multiscale approach is based on a simple scheme of exchange of space-time information between the atomistic and mesoscopic scales and is capable of describing self-consistent hydrodynamic effects on molecular motion at a computational cost which scales linearly with both solute size and solvent volume. For an application of our multiscale method, we consider the much studied problem of biopolymer translocation through nanopores: we find that the method reproduces with remarkable accuracy the statistical scaling behavior of the translocation process and provides valuable insight into the cooperative aspects of biopolymer and hydrodynamic motion.

  11. Analysis of droplet jumping phenomenon with lattice Boltzmann simulation of droplet coalescence

    Science.gov (United States)

    Peng, Benli; Wang, Sifang; Lan, Zhong; Xu, Wei; Wen, Rongfu; Ma, Xuehu

    2013-04-01

    Droplet jumping from condensing surfaces induced by droplet coalescence during dropwise condensation of mixed steam on a superhydrophobic surface can significantly enhance condensation heat transfer of mixed steam with non-condensable gas. This phenomenon was visually observed and theoretically analyzed in the present paper. The dynamic evolution of droplet and the velocity distribution inside the droplet during coalescence were simulated using multiphase lattice Boltzmann method. The energy distribution released by droplet coalescence was calculated statistically, and the jumping height induced by droplet coalescence on a superhydrophobic surface was predicted based on the energy conservation method. The theoretical predictions obtained by the modified model proposed in this paper agree well with the experimental observations.

  12. Turbulent channel flow simulations using a coarse-grained extension of the Lattice Boltzmann method

    CERN Document Server

    Amati, G; Benzi, R; Amati, Giorgio; Succi, Sauro; Benzi, Roberto

    1996-01-01

    A coarse-grained version of the Lattice Boltzmann (LB) method is developed with the intent of enhancing its geometrical flexibility so as to be able to tackle a wider class of flows of engineering interest. To this purpose, the original uniform LB technique is combined with standard finite-volume techniques based upon a blend of piecewise constant and piecewise linear interpolation schemes. A series of validation tests for the three dimensional channel flow with one-dimensional (cross-channel) statistical behaviour are presented. The main conclusion is that, although the method does indeed mark a significant stride forward with respect to the original uniform LB scheme, better interpolation schemes should be developed before the coarse-grain LB can become fully competitive with modern CFD schemes.

  13. About the statistical description of gas-liquid flows

    Energy Technology Data Exchange (ETDEWEB)

    Sanz, D.; Guido-Lavalle, G.; Carrica, P. [Centro Atomico Bariloche and Instituto Balseiro (Argentina)] [and others

    1995-09-01

    Elements of the probabilistic geometry are used to derive the bubble coalescence term of the statistical description of gas liquid flows. It is shown that the Boltzmann`s hypothesis, that leads to the kinetic theory of dilute gases, is not appropriate for this kind of flows. The resulting integro-differential transport equation is numerically integrated to study the flow development in slender bubble columns. The solution remarkably predicts the transition from bubbly to slug flow pattern. Moreover, a bubbly bimodal size distribution is predicted, which has already been observed experimentally.

  14. Image segmentation based on Boltzmann entropy%基于玻耳兹曼熵分析的图像分割方法研究

    Institute of Scientific and Technical Information of China (English)

    曹建农

    2011-01-01

    This paper presented a new definition of image Boltzmann entropy mainly based on the image gray-level according to thermodynamics Boltzmann relational expression, which revealed the facts that the image local fabrics were embedded in their gray-level sequence by image Boltzmann entropy. Then image segmentation was come true by statistically computing in local neighbor pixels to identify characteristics of image Boltzmann entropy. The experiments and comparing analysis indicate that this method is remarkable superiority.%根据热力学玻耳兹曼熵关系式,定义基于图像灰度谱的玻耳兹曼熵谱,将图像空间局部结构隐含于灰度谱的客观事实与玻耳兹曼熵谱联系在一起.最后在像素近邻空间进行统计计算,通过识别玻耳兹曼熵谱特征,实现图像分割.实验与比较分析表明,该方法具有显著优势.

  15. 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.

  16. Lattice Boltzmann method with the cell-population equilibrium

    Institute of Scientific and Technical Information of China (English)

    Zhou Xiao-Yang; Cheng Bing; Shi Bao-Chang

    2008-01-01

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

  17. 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.

  18. 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...

  19. Conjugate heat transfer with the entropic lattice Boltzmann method.

    Science.gov (United States)

    Pareschi, G; Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-07-01

    A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

  20. 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...

  1. 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.

  2. 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 ...

  3. Multi-reflection boundary conditions for lattice Boltzmann models

    OpenAIRE

    d´Humiéres, D.; Ginzburg, I

    2002-01-01

    We present a unified approach of several boundary conditions for lattice Boltzmann models. Its general framework is a generalization of previously introduced schemes such as the bounce-back rule, linear or quadratic interpolations, etc. The objectives are two fold: first to give theoretical tools to study the existing boundary conditions and their corresponding accuracy; secondly to design formally third- order accurate boundary conditions for general flows. Using these boundary conditions, C...

  4. 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...

  5. 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...

  6. 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...

  7. 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 ...

  8. 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...

  9. 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...

  10. 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.

  11. On the Spectral Problems for the Discrete Boltzmann Models

    Institute of Scientific and Technical Information of China (English)

    Aq Kwang-Hua Chu; J. FANG Jing

    2000-01-01

    The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propaogation in monatomic gases which are fundamental in the nonequilibrium tatistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation of sound modes quite well, after comparison with the continuum-mechanical results.

  12. 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...

  13. 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...

  14. 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.

  15. 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.)

  16. High-order hydrodynamics via lattice Boltzmann methods.

    Science.gov (United States)

    Colosqui, Carlos E

    2010-02-01

    In this work, closure of the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function f onto a space H(N) spanned by N-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of f , the presented procedure produces a hierarchy of (single) N-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by ( N-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=taunuk(2) (i.e., Knudsen number Kn=lambdak=square root Wi); k is the wave number, [corrected] tau is the relaxation time of the system, and lambda approximately tauc(s) is the mean-free path, where c(s) is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.

  17. Wall Crossing from Boltzmann Black Hole Halos

    CERN Document Server

    Manschot, Jan; Sen, Ashoke

    2010-01-01

    A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multi-centered black hole solutions in N=2 supergravity, we provide two fully general and explicit formulae for the change in the (refined) index across the wall. The first, "Higgs branch" formula relies on Reineke's results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, "Coulomb branch" formula results from evaluating an integral over the classical phase space of multi-centered solutions by localization. We provide extensive evidence that these new formulae agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the Bose-Fermi statistics of individual black holes participating in the bound state can be tra...

  18. Cancer Statistics

    Science.gov (United States)

    ... What Is Cancer? Cancer Statistics Cancer Disparities Cancer Statistics Cancer has a major impact on society in ... success of efforts to control and manage cancer. Statistics at a Glance: The Burden of Cancer in ...

  19. An introduction to statistical mechanics and thermodynamics

    CERN Document Server

    Swendsen, Robert H

    2012-01-01

    This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is the development ofentropy based on Boltzmann's 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. D

  20. Generalized simulated annealing algorithms using Tsallis statistics : Application to the discrete-time optimal growth problem

    OpenAIRE

    稻垣, 陽介; イナガキ, ヨウスケ; Yousuke, Inagaki

    2007-01-01

    The efficiency of Monte Carlo simulated annealing algorithm based on the generalized statistics of Tsallis (GSA) is compared with conventional simulated annealing (CSA) based on Boltzmann-Gibbs statistics. Application to the discrete-time optimal growth problem demonstrates that the replacement of CSA by GSA has the potential to speed up optimizations with no loss of accuracy in finding optimal policy function.

  1. 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...

  2. Global Solutions of the Boltzmann Equation Over {{R}^D} Near Global Maxwellians with Small Mass

    Science.gov (United States)

    Bardos, Claude; Gamba, Irene M.; Golse, François; Levermore, C. David

    2016-09-01

    We study the dynamics defined by the Boltzmann equation set in the Euclidean space {{R}^D} in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

  3. 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.

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

    Science.gov (United States)

    Sun, Chenghai; Hsu, Andrew T

    2003-07-01

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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. On the Krook-Wu model of the Boltzmann equation

    Science.gov (United States)

    Cornille, H.

    1980-08-01

    The distribution function of the Krook-Wu model of the nonlinear Boltzmann equation (elastic differential cross sections inversely proportional to the relative speed of the colliding particles) is obtained as a generalized Laguerre polynomial expansion where the only time dependence is provided by the coefficients. In a recent paper M. Barnsley and the present author have shown that these coefficients are recursively determined from the resolution of a nonlinear differential system. Here we explicitly show how to construct the solutions of the Krook-Wu model and study the properties of the corresponding Krook-Wu distribution functions.

  10. 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.

  11. 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.

  12. 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...

  13. A lattice Boltzmann method for dilute polymer solutions.

    Science.gov (United States)

    Singh, Shiwani; Subramanian, Ganesh; Ansumali, Santosh

    2011-06-13

    We present a lattice Boltzmann approach for the simulation of non-Newtonian fluids. The method is illustrated for the specific case of dilute polymer solutions. With the appropriate local equilibrium distribution, phase-space dynamics on a lattice, driven by a Bhatnagar-Gross-Krook (BGK) relaxation term, leads to a solution of the Fokker-Planck equation governing the probability density of polymer configurations. Results for the bulk rheological characteristics for steady and start-up shear flow are presented, and compare favourably with those obtained using Brownian dynamics simulations. The new method is less expensive than stochastic simulation techniques, particularly in the range of small to moderate Weissenberg numbers (Wi).

  14. 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.

  15. Numerical Poisson-Boltzmann Model for Continuum Membrane Systems.

    Science.gov (United States)

    Botello-Smith, Wesley M; Liu, Xingping; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

    2013-01-01

    Membrane protein systems are important computational research topics due to their roles in rational drug design. In this study, we developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. Two numerical solvers were adapted for periodic systems to alleviate possible edge effects. Validation on systems ranging from organic molecules to membrane proteins up to 200 residues, demonstrated good numerical properties. This lays foundations for sophisticated models with variable dielectric treatments and second-order accurate modeling of solvation interactions.

  16. Lattice Boltzmann Simulation for the Spiral Wave Dynamics

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    We investigated the dynamics of the simple spiral waves of the Selkov reaction-diffusion system with the Lattice Boltzmann method. The results of computer simulation lead to the conclusion that the trajectory of the spiral tip is a small circle, the wavelength and the period decay exponentially when the value of parameter b increases; and the relation between the wavelength and the period is A oc T1 , which is qualitatively the same as that obtained by Ou-Yang Qi from Belousov-Zhabotinsky reaction system.

  17. Introduction to Nonextensive Statistical Mechanics Approaching a Complex World

    CERN Document Server

    Tsallis, Constantino

    2009-01-01

    This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, and extensions of the standard central limit theorems, among others – is presented in this book, as well as a selection of paradigmatic applications in various sciences and diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mec...

  18. Bayesian statistics

    OpenAIRE

    Draper, D.

    2001-01-01

    © 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography

  19. Usage Statistics

    Science.gov (United States)

    ... www.nlm.nih.gov/medlineplus/usestatistics.html MedlinePlus Statistics To use the sharing features on this page, ... By Quarter View image full size Quarterly User Statistics Quarter Page Views Unique Visitors Oct-Dec-98 ...

  20. Library statistics.

    OpenAIRE

    Melita Ambrožič

    1991-01-01

    The contribution deals with the purpose, beginnings and development of library statistics and the strivings for international standardization in this field. International recommendations are presented, as well as the ISO standard for library statistics. An overview is given of the theoretical contributions and statistical practice in Slovenian librarianship. Cautionary notice on the limitations of the applicability of library statistics in determining library performance is given and the inte...

  1. Mathematical statistics

    CERN Document Server

    Pestman, Wiebe R

    2009-01-01

    This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. Three-dimensional lattice Boltzmann model for electrodynamics.

    Science.gov (United States)

    Mendoza, M; Muñoz, J D

    2010-11-01

    In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.

  8. 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 ...

  9. Avoiding Boltzmann Brain domination in holographic dark energy models

    Science.gov (United States)

    Horvat, R.

    2015-11-01

    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 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.

  10. 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.

  11. 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)

  12. 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...

  13. 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

  14. Statistical Inference

    CERN Document Server

    Casella, George

    2002-01-01

    "Statistical Inference is a delightfully modern text on statistical theory and deserves serious consideration from every teacher of a graduate- or advanced undergraduate-level first course in statistical theory. . . Chapters 1-5 provide plenty of interesting examples illustrating either the basic concepts of probability or the basic techniques of finding distribution. . . The book has unique features [throughout Chapters 6-12] for example, I have never seen in any comparable text such extensive discussion of ancillary statistics [Ch. 6], including Basu's theorem, dealing with the independence of complete sufficient statistics and ancillary statistics. Basu's theorem is such a useful tool that it should be available to every graduate student of statistics. . . The derivation of the analysis of variance (ANOVA)F test in Chapter 11 via the union-intersection principle is very nice. . . Chapter 12 contains, in addition to the standard regression model, errors-in-variables models. This topic will be of considerabl...

  15. 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.)

  16. Dynamic statistical information theory

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel

  17. Statistical physics and ecology

    Science.gov (United States)

    Volkov, Igor

    This work addresses the applications of the methods of statistical physics to problems in population ecology. A theoretical framework based on stochastic Markov processes for the unified neutral theory of biodiversity is presented and an analytical solution for the distribution of the relative species abundance distribution both in the large meta-community and in the small local community is obtained. It is shown that the framework of the current neutral theory in ecology can be easily generalized to incorporate symmetric density dependence. An analytically tractable model is studied that provides an accurate description of beta-diversity and exhibits novel scaling behavior that leads to links between ecological measures such as relative species abundance and the species area relationship. We develop a simple framework that incorporates the Janzen-Connell, dispersal and immigration effects and leads to a description of the distribution of relative species abundance, the equilibrium species richness, beta-diversity and the species area relationship, in good accord with data. Also it is shown that an ecosystem can be mapped into an unconventional statistical ensemble and is quite generally tuned in the vicinity of a phase transition where bio-diversity and the use of resources are optimized. We also perform a detailed study of the unconventional statistical ensemble, in which, unlike in physics, the total number of particles and the energy are not fixed but bounded. We show that the temperature and the chemical potential play a dual role: they determine the average energy and the population of the levels in the system and at the same time they act as an imbalance between the energy and population ceilings and the corresponding average values. Different types of statistics (Boltzmann, Bose-Einstein, Fermi-Dirac and one corresponding to the description of a simple ecosystem) are considered. In all cases, we show that the systems may undergo a first or a second order

  18. Statistical optics

    CERN Document Server

    Goodman, Joseph W

    2015-01-01

    This book discusses statistical methods that are useful for treating problems in modern optics, and the application of these methods to solving a variety of such problems This book covers a variety of statistical problems in optics, including both theory and applications.  The text covers the necessary background in statistics, statistical properties of light waves of various types, the theory of partial coherence and its applications, imaging with partially coherent light, atmospheric degradations of images, and noise limitations in the detection of light. New topics have been introduced i

  19. Statistical distributions

    CERN Document Server

    Forbes, Catherine; Hastings, Nicholas; Peacock, Brian J.

    2010-01-01

    A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with re

  20. Statistical methods

    CERN Document Server

    Szulc, Stefan

    1965-01-01

    Statistical Methods provides a discussion of the principles of the organization and technique of research, with emphasis on its application to the problems in social statistics. This book discusses branch statistics, which aims to develop practical ways of collecting and processing numerical data and to adapt general statistical methods to the objectives in a given field.Organized into five parts encompassing 22 chapters, this book begins with an overview of how to organize the collection of such information on individual units, primarily as accomplished by government agencies. This text then

  1. Statistical mechanics and the description of the early universe I

    DEFF Research Database (Denmark)

    Pessah, Martin Elias; F. Torres, Diego; Vucetich, H.

    2001-01-01

    We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related with the ......We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related...... with the existence of long range forces, memory effects, or evolution in fractal or multi-fractal space. In the early universe, it is usually assumed that the distribution functions are the standard ones. Then, considering the evolution in a larger theoretical framework will allow to test this assumption...

  2. 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...

  3. Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study

    CERN Document Server

    Gross, Markus

    2014-01-01

    Spreading of nano-droplets is an interesting and technologically relevant phenomenon where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating non-ideal lattice Boltzmann method [Gross et al., J. Stat. Mech., P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [PRL 95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two- and three-dimensional geometry. The cross over from the deterministic Tanner's law, where the drop's base radius $b$ grows (in 3D) with time as $b \\sim t^{1/10}$ and the noise dominated regime where $b \\sim t^{1/6}$ is also observed by tuning the strength of thermal noise.

  4. 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).

  5. 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.

  6. 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

  7. 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.)

  8. 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.

  9. 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.

  10. Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

    Directory of Open Access Journals (Sweden)

    Deming Nie

    2015-01-01

    Full Text Available The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.

  11. Lattice Boltzmann method for shape optimization of fluid distributor

    CERN Document Server

    Wang, Limin; Luo, Lingai

    2013-01-01

    This paper presents the shape optimization of a flat-type arborescent fluid distributor for the purpose of process intensification. A shape optimization algorithm based on the lattice Boltzmann method (LBM) is proposed with the objective of decreasing the flow resistance of such distributor at the constraint of constant fluid volume. Prototypes of the initial distributor as well as the optimized one are designed. Fluid distribution and hydraulic characteristics of these distributors are investigated numerically. Results show that the pressure drop of the optimized distributor is between 15.9% and 25.1% lower than that of the initial reference while keeping a uniform flow distribution, demonstrating the process intensification in fluid distributor, and suggesting the interests of the proposed optimization algorithm in engineering optimal design.

  12. 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.

  13. Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation

    Directory of Open Access Journals (Sweden)

    Panjit MUSIK

    2004-01-01

    Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.

  14. Lattice Boltzmann modeling of water-like fluids

    Directory of Open Access Journals (Sweden)

    Sauro eSucci

    2014-04-01

    Full Text Available We review recent advances on the mesoscopic modeling of water-like fluids,based on the lattice Boltzmann (LB methodology.The main idea is to enrich the basic LB (hydro-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules.The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs between $3$ and $4$, as well as a qualitatively correctstatistics of the hydrogen bond angle as a function of the temperature.Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies,such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments.

  15. Chemical-potential-based Lattice Boltzmann Method for Nonideal Fluids

    CERN Document Server

    Wen, Binghai; He, Bing; Zhang, Chaoying; Fang, Haiping

    2016-01-01

    Chemical potential is an effective way to drive phase transition or express wettability. In this letter, we present a chemical-potential-based lattice Boltzmann model to simulate multiphase flows. The nonideal force is directly evaluated by a chemical potential. The model theoretically satisfies thermodynamics and Galilean invariance. The computational efficiency is improved owing to avoiding the calculation of pressure tensor. We have derived several chemical potentials of the popular equations of state from the free-energy density function. An effective chemical-potential boundary condition is implemented to investigate the wettability of a solid surface. Remarkably, the numerical results show that the contact angle can be linearly tuned by the surface chemical potential.

  16. 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.

  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. PMID:27059561

  18. 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.

  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. 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

  1. 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...

  2. Lattice Boltzmann implementation for Fluids Flow Simulation in Porous Media

    Directory of Open Access Journals (Sweden)

    Xinming Zhang

    2011-06-01

    Full Text Available In this paper, the lattice-Boltzmann method is developed to investigate the behavior of isothermal two-phase fluid flow in porous media. The method is based on the Shan–Chen multiphase model of nonideal fluids that allow coexistence of two phases of a single substance. We reproduce some different idealized situations (phase separation, surface tension, contact angle, pipe flow, and fluid droplet motion, et al in which the results are already known from theory or laboratory measurements and show the validity of the implementation for the physical two-phase flow in porous media. Application of the method to fluid intrusion in porous media is discussed and shows the effect of wettability on the fluid flow. The capability of reproducing critical flooding phenomena under strong wettability conditions is also proved.

  3. Lattice Boltzmann simulation of turbulent natural convection in tall enclosures

    Directory of Open Access Journals (Sweden)

    Sajjadi Hasan

    2015-01-01

    Full Text Available In this paper Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES in tall enclosures which is filled by air with Pr=0.71 has been studied. Calculations were performed for high Rayleigh numbers (Ra=107-109 and aspect ratios change between 0.5 to 2 (0.5

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

    Energy Technology Data Exchange (ETDEWEB)

    Dou, Nicholas G.; Minnich, Austin J. [Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125 (United States)

    2016-01-04

    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.

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

    Directory of Open Access Journals (Sweden)

    J. M. Greenberg

    1991-05-01

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

  6. 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.

  7. A Lattice Boltzmann Model for Oscillating Reaction-Diffusion

    Science.gov (United States)

    Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio

    2016-07-01

    A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.

  8. 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.

  9. A Boltzmann machine for the organization of intelligent machines

    Science.gov (United States)

    Moed, Michael C.; Saridis, George N.

    1989-01-01

    In the present technological society, there is a major need to build machines that would execute intelligent tasks operating in uncertain environments with minimum interaction with a human operator. Although some designers have built smart robots, utilizing heuristic ideas, there is no systematic approach to design such machines in an engineering manner. Recently, cross-disciplinary research from the fields of computers, systems AI and information theory has served to set the foundations of the emerging area of the design of intelligent machines. Since 1977 Saridis has been developing an approach, defined as Hierarchical Intelligent Control, designed to organize, coordinate and execute anthropomorphic tasks by a machine with minimum interaction with a human operator. This approach utilizes analytical (probabilistic) models to describe and control the various functions of the intelligent machine structured by the intuitively defined principle of Increasing Precision with Decreasing Intelligence (IPDI) (Saridis 1979). This principle, even though resembles the managerial structure of organizational systems (Levis 1988), has been derived on an analytic basis by Saridis (1988). The purpose is to derive analytically a Boltzmann machine suitable for optimal connection of nodes in a neural net (Fahlman, Hinton, Sejnowski, 1985). Then this machine will serve to search for the optimal design of the organization level of an intelligent machine. In order to accomplish this, some mathematical theory of the intelligent machines will be first outlined. Then some definitions of the variables associated with the principle, like machine intelligence, machine knowledge, and precision will be made (Saridis, Valavanis 1988). Then a procedure to establish the Boltzmann machine on an analytic basis will be presented and illustrated by an example in designing the organization level of an Intelligent Machine. A new search technique, the Modified Genetic Algorithm, is presented and proved

  10. 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

  11. Scan Statistics

    CERN Document Server

    Glaz, Joseph

    2009-01-01

    Suitable for graduate students and researchers in applied probability and statistics, as well as for scientists in biology, computer science, pharmaceutical science and medicine, this title brings together a collection of chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics.

  12. 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.

  13. High Performance Computation of a Jet in Crossflow by Lattice Boltzmann Based Parallel Direct Numerical Simulation

    Directory of Open Access Journals (Sweden)

    Jiang Lei

    2015-01-01

    Full Text Available Direct numerical simulation (DNS of a round jet in crossflow based on lattice Boltzmann method (LBM is carried out on multi-GPU cluster. Data parallel SIMT (single instruction multiple thread characteristic of GPU matches the parallelism of LBM well, which leads to the high efficiency of GPU on the LBM solver. With present GPU settings (6 Nvidia Tesla K20M, the present DNS simulation can be completed in several hours. A grid system of 1.5 × 108 is adopted and largest jet Reynolds number reaches 3000. The jet-to-free-stream velocity ratio is set as 3.3. The jet is orthogonal to the mainstream flow direction. The validated code shows good agreement with experiments. Vortical structures of CRVP, shear-layer vortices and horseshoe vortices, are presented and analyzed based on velocity fields and vorticity distributions. Turbulent statistical quantities of Reynolds stress are also displayed. Coherent structures are revealed in a very fine resolution based on the second invariant of the velocity gradients.

  14. Modeling the CO2 Sequestration Convection Problem Using the Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Hassen M. Ouakad

    2013-01-01

    Full Text Available This paper presents an investigation of the density-driven problem that rises during the CO2 sequestration into saline aquifer. The lattice Boltzmann method (LBM is implemented in a way to solve this mixing problem (the brine problem along with the solute transport. The CO2-brine interface was located at the top of the considered domain. Different Rayleigh numbers were used in order to investigate this problem. When Rayleigh number is low, we got steady-state concentration contours describing a Rayleigh-Bénard type of convection. Moreover, when the Rayleigh number was selected to be big enough, we observe that the system is less stable and a convective fingering is initiated. This instability is caused by a higher density difference between the brine and the sequestrated CO2. Note here that the turbulence is not taken into account in the study. After the onset this convective instability, the brine with a high CO2 concentration migrates down into the porous medium. This study is based on a statistical LBM theory without assuming periodicity in any directions and without considering any type of disturbances in order to turnon the instability behavior.

  15. A new function based on boltzmann statistisc to model the distribution of photosynthetically active radiation data

    Science.gov (United States)

    Tovar-Pescador, J.; Pozo-Vázquez, D.; Batlles, J.; López, G.; Rubio, M. A.

    2003-04-01

    To obtain simple correlations for the estimation of the performance of biological systems, which transform the solar energy by photosynthesis, and to generate synthetic data, it is necessary to know the frequency distributions of photosynthetically active radiation (PAR). In this work we carried out an analysis of the properties of hourly values of PAR data collected in southern Spain. Its dependence on the optical mass for all type of skies, including cloudy skies, is analyzed. Results show that, for a given value of the optical mass, the PAR density distributions are not symmetrical and have certain degree of bimodality. The increment in the optical mass value has two effects on the PAR distributions, the first one is a shift toward lower values of the maximum and the second one is a decrease in the range of PAR values. A model of the frequency distribution of PAR values, based on a new kind of functions related to the Boltzmann´s statistic, is proposed. The parameters of these functions depend just on the optical mass. Results show a very good agreement between the data and the model proposed

  16. A precise Boltzmann distribution law for the fluorescence intensity ratio of two thermally coupled levels

    Science.gov (United States)

    Qin, Feng; Zhao, Hua; Cai, Wei; Zhang, Zhiguo; Cao, Wenwu

    2016-06-01

    Noncontact monitoring temperature is very important in modern medicine, science, and technologies. The fluorescence intensity ratio (FIR) technique based on the Boltzmann distribution law exhibits excellent application potential, but the observed FIR deviates from the Boltzmann distribution law in the low temperature range. We propose a fluorescence intensity ratio relation FIR* = ηFIR by introducing a quantity η representing thermal population degree, which can be obtained from measured fluorescence decay curves of the upper emitting level. Using Eu3+ as an example, the method is confirmed that the deviated FIR is able to be corrected and return to follow the Boltzmann law.

  17. THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

    Institute of Scientific and Technical Information of China (English)

    Yuanjie LEI

    2014-01-01

    This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

  18. SDI: Statistical dynamic interactions

    Energy Technology Data Exchange (ETDEWEB)

    Blann, M.; Mustafa, M.G. (Lawrence Livermore National Lab., CA (USA)); Peilert, G.; Stoecker, H.; Greiner, W. (Frankfurt Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)

    1991-04-01

    We focus on the combined statistical and dynamical aspects of heavy ion induced reactions. The overall picture is illustrated by considering the reaction {sup 36}Ar + {sup 238}U at a projectile energy of 35 MeV/nucleon. We illustrate the time dependent bound excitation energy due to the fusion/relaxation dynamics as calculated with the Boltzmann master equation. An estimate of the mass, charge and excitation of an equilibrated nucleus surviving the fast (dynamic) fusion-relaxation process is used as input into an evaporation calculation which includes 20 heavy fragment exit channels. The distribution of excitations between residue and clusters is explicitly calculated, as is the further deexcitation of clusters to bound nuclei. These results are compared with the exclusive cluster multiplicity measurements of Kim et al., and are found to give excellent agreement. We consider also an equilibrated residue system at 25% lower initial excitation, which gives an unsatisfactory exclusive multiplicity distribution. This illustrates that exclusive fragment multiplicity may provide a thermometer for system excitation. This analysis of data involves successive binary decay with no compressional effects nor phase transitions. Several examples of primary versus final (stable) cluster decay probabilities for an A = 100 nucleus at excitations of 100 to 800 MeV are presented. From these results a large change in multifragmentation patterns may be understood as a simple phase space consequence, invoking neither phase transitions, nor equation of state information. These results are used to illustrate physical quantities which are ambiguous to deduce from experimental fragment measurements. 14 refs., 4 figs.

  19. SDI: Statistical dynamic interactions

    International Nuclear Information System (INIS)

    We focus on the combined statistical and dynamical aspects of heavy ion induced reactions. The overall picture is illustrated by considering the reaction 36Ar + 238U at a projectile energy of 35 MeV/nucleon. We illustrate the time dependent bound excitation energy due to the fusion/relaxation dynamics as calculated with the Boltzmann master equation. An estimate of the mass, charge and excitation of an equilibrated nucleus surviving the fast (dynamic) fusion-relaxation process is used as input into an evaporation calculation which includes 20 heavy fragment exit channels. The distribution of excitations between residue and clusters is explicitly calculated, as is the further deexcitation of clusters to bound nuclei. These results are compared with the exclusive cluster multiplicity measurements of Kim et al., and are found to give excellent agreement. We consider also an equilibrated residue system at 25% lower initial excitation, which gives an unsatisfactory exclusive multiplicity distribution. This illustrates that exclusive fragment multiplicity may provide a thermometer for system excitation. This analysis of data involves successive binary decay with no compressional effects nor phase transitions. Several examples of primary versus final (stable) cluster decay probabilities for an A = 100 nucleus at excitations of 100 to 800 MeV are presented. From these results a large change in multifragmentation patterns may be understood as a simple phase space consequence, invoking neither phase transitions, nor equation of state information. These results are used to illustrate physical quantities which are ambiguous to deduce from experimental fragment measurements. 14 refs., 4 figs

  20. Semiconductor statistics

    CERN Document Server

    Blakemore, J S

    1962-01-01

    Semiconductor Statistics presents statistics aimed at complementing existing books on the relationships between carrier densities and transport effects. The book is divided into two parts. Part I provides introductory material on the electron theory of solids, and then discusses carrier statistics for semiconductors in thermal equilibrium. Of course a solid cannot be in true thermodynamic equilibrium if any electrical current is passed; but when currents are reasonably small the distribution function is but little perturbed, and the carrier distribution for such a """"quasi-equilibrium"""" co

  1. Introductory statistics

    CERN Document Server

    Ross, Sheldon M

    2005-01-01

    In this revised text, master expositor Sheldon Ross has produced a unique work in introductory statistics. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, and an explanation of intuition and ideas behind the statistical methods. To quote from the preface, ""It is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data."" Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions and examples.* Ross's clear writin

  2. Introductory statistics

    CERN Document Server

    Ross, Sheldon M

    2010-01-01

    In this 3rd edition revised text, master expositor Sheldon Ross has produced a unique work in introductory statistics. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, and an explanation of intuition and ideas behind the statistical methods. Concepts are motivated, illustrated and explained in a way that attempts to increase one's intuition. To quote from the preface, ""It is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data."" Ross achieves this

  3. Statistics Clinic

    Science.gov (United States)

    Feiveson, Alan H.; Foy, Millennia; Ploutz-Snyder, Robert; Fiedler, James

    2014-01-01

    Do you have elevated p-values? Is the data analysis process getting you down? Do you experience anxiety when you need to respond to criticism of statistical methods in your manuscript? You may be suffering from Insufficient Statistical Support Syndrome (ISSS). For symptomatic relief of ISSS, come for a free consultation with JSC biostatisticians at our help desk during the poster sessions at the HRP Investigators Workshop. Get answers to common questions about sample size, missing data, multiple testing, when to trust the results of your analyses and more. Side effects may include sudden loss of statistics anxiety, improved interpretation of your data, and increased confidence in your results.

  4. Statistical physics

    CERN Document Server

    Wannier, Gregory H

    2010-01-01

    Until recently, the field of statistical physics was traditionally taught as three separate subjects: thermodynamics, statistical mechanics, and kinetic theory. This text, a forerunner in its field and now a classic, was the first to recognize the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics. It has been widely adopted in graduate and advanced undergraduate courses, and is recommended throughout the field as an indispensable aid to the independent study and research of statistical physics.Designed for

  5. 3D analysis, modeling and simulation of transport processes in compressed fibrous microstructures, using the Lattice Boltzmann method

    International Nuclear Information System (INIS)

    In this paper we combine a stochastic 3D microstructure model of a fiber based gas diffusion layer of polymer electrolyte fuel cells with a Lattice Boltzmann model for fluid transport. We focus on a simple approach of compressing the planar oriented virtual geometry of paper-type gas diffusion layer from Toray. Material parameters – permeability and tortuosity – are calculated from simulation of one phase, one component gas flow in stochastic geometries. We analyze the statistical spread of simulation results on ensembles of the virtual geometry, both uncompressed and compressed. The influence of the compression is discussed with regard to the Kozeny–Carman equation. The effective transport properties calculated from transport simulations in compressed gas diffusion layers agree well with a trend based on the Kozeny–Carman equation

  6. SEER Statistics

    Science.gov (United States)

    The Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute works to provide information on cancer statistics in an effort to reduce the burden of cancer among the U.S. population.

  7. Reversible Statistics

    DEFF Research Database (Denmark)

    Tryggestad, Kjell

    2004-01-01

    The study aims is to describe how the inclusion and exclusion of materials and calculative devices construct the boundaries and distinctions between statistical facts and artifacts in economics. My methodological approach is inspired by John Graunt's (1667) Political arithmetic and more recent work...... within constructivism and the field of Science and Technology Studies (STS). The result of this approach is here termed reversible statistics, reconstructing the findings of a statistical study within economics in three different ways. It is argued that all three accounts are quite normal, albeit...... in different ways. The presence and absence of diverse materials, both natural and political, is what distinguishes them from each other. Arguments are presented for a more symmetric relation between the scientific statistical text and the reader. I will argue that a more symmetric relation can be achieved...

  8. Accident Statistics

    Data.gov (United States)

    Department of Homeland Security — Accident statistics available on the Coast Guard’s website by state, year, and one variable to obtain tables and/or graphs. Data from reports has been loaded for...

  9. CMS Statistics

    Data.gov (United States)

    U.S. Department of Health & Human Services — The CMS Center for Strategic Planning produces an annual CMS Statistics reference booklet that provides a quick reference for summary information about health...

  10. Multiparametric statistics

    CERN Document Server

    Serdobolskii, Vadim Ivanovich

    2007-01-01

    This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. ...

  11. Statistical Microeconomics

    OpenAIRE

    Baaquie, Belal E.

    2012-01-01

    A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an independent random variable: all prices and quantities are considered to be stochastic processes, with the observed market prices being a random sample of the stochastic prices. The dynamics of market prices is determined by an action functional and, for concretene...

  12. Equivalence Between Forward and Backward Boltzmann Equations in Multi-Component Medium

    Institute of Scientific and Technical Information of China (English)

    张竹林

    2002-01-01

    The author generalized the propagator function theory introduced first by Sigmund, and gave a explicitly proof of a equivalence between forward and backward Boltzmann equations in a multi-component medium by using the generalized propagator function theory.

  13. Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity

    OpenAIRE

    Shi-you Lin

    2014-01-01

    The Cauchy problem of the nonlinear spatially homogeneous Boltzmann equation without angular cutoff is studied. By using analytic techniques, one proves the Gevrey regularity of the ${C}^{\\infty }$ solutions in non-Maxwellian and strong singularity cases.

  14. Lattice Boltzmann simulation of transverse wave travelling in Maxwell viscoelastic fluid

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Bing; Fang Hai-Ping

    2004-01-01

    A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wave in Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rate agree with theoretical results very well.

  15. 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

  16. 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.

  17. 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.

  18. Lattice Boltzmann model for the perfect gas flows with near-vacuum region

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiYUAN

    2000-01-01

    It is known that the standard lattice Boltzmann method has near-vacuum limit,i. e., when the density is near zero, this method is invalid. In this letter, we propose a simple lattice Boltzmann model for one-dimensional flows. It possesses the ability of simulating nearvacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.

  19. A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANGChao-Ying; TANHui-Li; LIUMu-Ren; KONGLing-Jiang

    2004-01-01

    A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.

  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. Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

    Institute of Scientific and Technical Information of China (English)

    RAN Zheng

    2007-01-01

    Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background.It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE),especially for shock calculation.Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.

  2. 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...

  3. 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.

  4. Statistical mechanics

    CERN Document Server

    Jana, Madhusudan

    2015-01-01

    Statistical mechanics is self sufficient, written in a lucid manner, keeping in mind the exam system of the universities. Need of study this subject and its relation to Thermodynamics is discussed in detail. Starting from Liouville theorem gradually, the Statistical Mechanics is developed thoroughly. All three types of Statistical distribution functions are derived separately with their periphery of applications and limitations. Non-interacting ideal Bose gas and Fermi gas are discussed thoroughly. Properties of Liquid He-II and the corresponding models have been depicted. White dwarfs and condensed matter physics, transport phenomenon - thermal and electrical conductivity, Hall effect, Magneto resistance, viscosity, diffusion, etc. are discussed. Basic understanding of Ising model is given to explain the phase transition. The book ends with a detailed coverage to the method of ensembles (namely Microcanonical, canonical and grand canonical) and their applications. Various numerical and conceptual problems ar...

  5. Statistical mechanics

    CERN Document Server

    Schwabl, Franz

    2006-01-01

    The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, kinetic theories, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechan...

  6. Statistical mechanics

    CERN Document Server

    Davidson, Norman

    2003-01-01

    Clear and readable, this fine text assists students in achieving a grasp of the techniques and limitations of statistical mechanics. The treatment follows a logical progression from elementary to advanced theories, with careful attention to detail and mathematical development, and is sufficiently rigorous for introductory or intermediate graduate courses.Beginning with a study of the statistical mechanics of ideal gases and other systems of non-interacting particles, the text develops the theory in detail and applies it to the study of chemical equilibrium and the calculation of the thermody

  7. Statistical Physics

    CERN Document Server

    Mandl, Franz

    1988-01-01

    The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition E. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient

  8. Statistical methods

    CERN Document Server

    Freund, Rudolf J; Wilson, William J

    2010-01-01

    Statistical Methods, 3e provides students with a working introduction to statistical methods offering a wide range of applications that emphasize the quantitative skills useful across many academic disciplines. This text takes a classic approach emphasizing concepts and techniques for working out problems and intepreting results. The book includes research projects, real-world case studies, numerous examples and data exercises organized by level of difficulty. This text requires that a student be familiar with algebra. New to this edition: NEW expansion of exercises a

  9. AP statistics

    CERN Document Server

    Levine-Wissing, Robin

    2012-01-01

    All Access for the AP® Statistics Exam Book + Web + Mobile Everything you need to prepare for the Advanced Placement® exam, in a study system built around you! There are many different ways to prepare for an Advanced Placement® exam. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge. This book, and the online tools that come with it, will help you personalize your AP® Statistics prep

  10. Statistical inference

    CERN Document Server

    Rohatgi, Vijay K

    2003-01-01

    Unified treatment of probability and statistics examines and analyzes the relationship between the two fields, exploring inferential issues. Numerous problems, examples, and diagrams--some with solutions--plus clear-cut, highlighted summaries of results. Advanced undergraduate to graduate level. Contents: 1. Introduction. 2. Probability Model. 3. Probability Distributions. 4. Introduction to Statistical Inference. 5. More on Mathematical Expectation. 6. Some Discrete Models. 7. Some Continuous Models. 8. Functions of Random Variables and Random Vectors. 9. Large-Sample Theory. 10. General Meth

  11. 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.

  12. 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.

  13. A Lattice-Boltzmann Method for Partially Saturated Computational Cells

    Science.gov (United States)

    Noble, D. R.; Torczynski, J. R.

    The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.

  14. 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.

  15. 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

  16. 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

  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. 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...

  19. 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

  20. 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.

  1. 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...

  2. 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...

  3. 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.

  4. New Boundary Treatment Methods for Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    Cheng Yong-guang; Suo Li-sheng

    2003-01-01

    In practical fluid dynamic simulations, the boundary condition should be treated carefully because it always has crucial influence on the numerical accuracy, stability and efficiency. Two types of boundary treatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the approximation of boundaries that are not located at the regular lattice nodes. The first type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain second-order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expressed as the analogous forms of their corresponding equilibrium distributions. Therefore, the number of unknowns can be reduced and an always-closed set of equations can be obtained for the solutions to pressure, velocity and special boundary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second-order accuracy. Basic ideas, implementation procedures and verifications with typical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable, general and efficient for practical simulations.

  5. Macroscopic model and truncation error of discrete Boltzmann method

    Science.gov (United States)

    Hwang, Yao-Hsin

    2016-10-01

    A derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete Boltzmann method is proffered in this paper. Essential presumptions of two time scales and a small parameter in the Chapman-Enskog expansion are disposed of in the present formulation. Equilibrium particle distribution function instead of its original non-equilibrium form is chosen as key variable in the derivation route. Taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart. A self-contained and comprehensive practice for the linear one-dimensional convection-diffusion equation is illustrated in details. Numerical validations on the incurred truncation error in one- and two-dimensional cases with various distribution functions are conducted to verify present formulation. As shown in the computational results, excellent agreement between numerical result and theoretical prediction are found in the test problems. Straightforward extensions to more complicated systems including convection-diffusion-reaction, multi-relaxation times in collision operator as well as multi-dimensional Navier-Stokes equations are also exposed in the Appendix to point out its expediency in solving complicated flow problems.

  6. Application of Lattice Boltzmann Method to Flows in Microgeometries

    Directory of Open Access Journals (Sweden)

    Anoop K. Dass

    2010-07-01

    Full Text Available In the present investigation, Lattice Boltzmann Method (LBM is used to simulate rarefied gaseous microflows in three microgeometries. These are micro-couette, micro lid-driven cavity and micro-poiseuille flows. The Knudsen number is used to measure the degree of rarefaction in the microflows. First, micro-couette flow is computed with the effects of varying Knudsen number in the slip and threshold of the transition regime and the results compare well with existing results. After having thus established the credibility of the code and the method including boundary conditions, LBM is then used to investigate the micro lid-driven cavity flow with various aspect ratios. Simulation of microflow not only requires an appropriate method, it also requires suitable boundary conditions to provide a well-posed problem and unique solution. In this work, LBM and three slip boundary conditions, namely, diffuse scattering boundary condition, specular reflection and a combination of bounce-back and specular reflection is used to predict the micro lid-driven cavity flow fields. Then the LBM simulation is extended to micro-poiseuille flow. The results are substantiated through comparison with existing results and it is felt that the present methodology is reasonable to be employed in analyzing the flow in micro-systems.

  7. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Directory of Open Access Journals (Sweden)

    Yonggang Zheng

    2016-08-01

    Full Text Available In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  8. 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

  9. 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.

  10. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Science.gov (United States)

    Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu

    2016-08-01

    In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  11. Fractional statistic

    OpenAIRE

    Bergère, M. C.

    1999-01-01

    We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes sense for finite $N=pm+r$ with $p$ integer and $0

  12. Statistical ensembles for money and debt

    Science.gov (United States)

    Viaggiu, Stefano; Lionetto, Andrea; Bargigli, Leonardo; Longo, Michele

    2012-10-01

    We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann-Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as a conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.

  13. Statistical Physics for Humanities: A Tutorial

    CERN Document Server

    Stauffer, Dietrich

    2011-01-01

    The image of physics is connected with simple "mechanical" deterministic events: that an apple always falls down, that force equals mass times acceleleration. Indeed, applications of such concept to social or historical problems go back two centuries (population growth and stabilisation, by Malthus and by Verhulst) and use "differential equations", as recently revierwed by Vitanov and Ausloos [2011]. However, since even today's computers cannot follow the motion of all air molecules within one cubic centimeter, the probabilistic approach has become fashionable since Ludwig Boltzmann invented Statistical Physics in the 19th century. Computer simulations in Statistical Physics deal with single particles, a method called agent-based modelling in fields which adopted it later. Particularly simple are binary models where each particle has only two choices, called spin up and spin down by physicists, bit zero and bit one by computer scientists, and voters for the Republicans or for the Democrats in American politic...

  14. Statistical Mechanics of Money, Income, and Wealth

    Science.gov (United States)

    Yakovenko, Victor

    2006-03-01

    In Ref. [1], we proposed an analogy between the exponential Boltzmann-Gibbs distribution of energy in physics and the equilibrium probability distribution of money in a closed economic system. Analogously to energy, money is locally conserved in interactions between economic agents, so the thermal Boltzmann-Gibbs distribution function is expected for money. Since then, many researchers followed and expanded this idea [2]. Much work was done on the analysis of empirical data, mostly on income, for which a lot of tax and census data is available. We demonstrated [3] that income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (``thermal'') distribution. The upper class (1-3% of population) has a Pareto power-law (``superthermal'') distribution, whose parameters change in time with the rise and fall of stock market. We proposed a concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively demonstrated that it applies to the majority of population. Income distribution in other countries shows similar patterns. For more references, see http://www2.physics.umd.edu/˜yakovenk/econophysics.html. References: [1] A. A. Dragulescu and V. M. Yakovenko, ``Statistical mechanics of money'', Eur. Phys. J. B 17, 723 (2000). [2] ``Econophysics of Wealth Distributions'', edited by A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti, Springer, 2005. [3] A. C. Silva and V. M. Yakovenko, ``Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001'', Europhys. Lett. 69, 304 (2005).

  15. Learning algorithms for perceptrons from statistical physics

    Science.gov (United States)

    Gordon, Mirta B.; Peretto, Pierre; Berchier, Dominique

    1993-02-01

    Learning algorithms for perceptrons are deduced from statistical mechanics. Thermodynamical quantities are used as cost functions which may be extremalized by gradient dynamics to find the synaptic efficacies that store the learning set of patterns. The learning rules so obtained are classified in two categories, following the statistics used to derive the cost functions, namely, Boltzmann statistics, and Fermi statistics. In the limits of zero or infinite temperatures some of the rules behave like already known algorithms, but new strategies for learning are obtained at finite temperatures, which minimize the number of errors on the training set. Nous déduisons des algorithmes d'apprentissage pour des perceptrons à partir de considérations de mécanique statistique. Des quantités thermodynamiques sont considérées comme des fonctions de coût, dont on obtient, par une dynamique de gradient, les efficacités synaptiques qui apprennent l'ensemble d'apprentissage. Les règles ainsi obtenues sont classées en deux catégories suivant les statistiques, de Boltzmann ou de Fermi, utilisées pour dériver les fonctions de coût. Dans les limites de températures nulle ou infinie, la plupart des règles trouvées tendent vers les algorithmes connus, mais à température finie on trouve des stratégies nouvelles, qui minimisent le nombre d'erreurs dans l'ensemble d'apprentissage.

  16. 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 ...

  17. Statistical Optics

    Science.gov (United States)

    Goodman, Joseph W.

    2000-07-01

    The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

  18. Experimental statistics

    CERN Document Server

    Natrella, Mary Gibbons

    2005-01-01

    Formulated to assist scientists and engineers engaged in army ordnance research and development programs, this well-known and highly regarded handbook is a ready reference for advanced undergraduate and graduate students as well as for professionals seeking engineering information and quantitative data for designing, developing, constructing, and testing equipment. Topics include characterizing and comparing the measured performance of a material, product, or process; general considerations in planning experiments; statistical techniques for analyzing extreme-value data; use of transformations

  19. Fractal Statistics

    OpenAIRE

    B. G. Sidharth

    2000-01-01

    We consider the recent description of elementary particles in terms of Quantum Mechanical Kerr-Newman Black Holes, a description which provides a rationale for and at the same time reconciles the Bohm-hydrodynamical formulation on the one hand and the Nelsonian stochastiic formulation on the other. The Boson-Fermion divide is discussed, and it is pointed out that in special situations, anomalous statistics, rather than Bose-Einstein or Fermi-Dirac states, can be encountered.

  20. Engineering Statistics

    OpenAIRE

    Vardeman, Stephen B.

    2003-01-01

    In this entry we seek to put into perspective some of the ways in which statistical methods contribute to modern engineering practice. Engineers design and oversee the production, operation, and maintenance of the products and systems that under-gird modern technological society. Their work is built on the foundation of physical (and increasingly biological) science. However, it is of necessity often highly empirical, because there simply isn’t scientific theory complete and simple enough to ...

  1. Arc Statistics

    CERN Document Server

    Meneghetti, M; Dahle, H; Limousin, M

    2013-01-01

    The existence of an arc statistics problem was at the center of a strong debate in the last fifteen years. With the aim to clarify if the optical depth for giant gravitational arcs by galaxy clusters in the so called concordance model is compatible with observations, several studies were carried out which helped to significantly improve our knowledge of strong lensing clusters, unveiling their extremely complex internal structure. In particular, the abundance and the frequency of strong lensing events like gravitational arcs turned out to be a potentially very powerful tool to trace the structure formation. However, given the limited size of observational and theoretical data-sets, the power of arc statistics as a cosmological tool has been only minimally exploited so far. On the other hand, the last years were characterized by significant advancements in the field, and several cluster surveys that are ongoing or planned for the near future seem to have the potential to make arc statistics a competitive cosmo...

  2. 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.

  3. 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.

  4. Polar-coordinate lattice Boltzmann modeling of compressible flows

    Science.gov (United States)

    Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Succi, Sauro

    2014-01-01

    We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.

  5. 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

  6. Implementing the lattice Boltzmann model on commodity graphics hardware

    Science.gov (United States)

    Kaufman, Arie; Fan, Zhe; Petkov, Kaloian

    2009-06-01

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

  7. 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

  8. 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)

  9. 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)

  10. Lattice Boltzmann for Simulation of Gases Mixture in Fruit Storage Chambers

    Science.gov (United States)

    Fabero, J. C.; Barreiro, P.; Casasús, L.

    2003-04-01

    Fluid Dynamics can be modelled through the Navier-Stokes equations. This description corresponds to a macroscopic definition of the fluid motion phenomena. During the past 20 year new simulation procedures are emerging from Statistical Physics and Computer Science domains. One of them is the Lattice Gas Cellular Automata (LGCA) method. This approach, which is considered to be a microscopic description of the world, in spite of its intuitiveness and numerical efficiency, fails to simulate the real Navier-Stokes equations. Another classical simulation procedure for the fluid motion phenomena is the so called Lattice Boltzmann method [1]. This corresponds to a meso-scale description of the world [2]. Simulation of laminar and turbulent motions of fluids, specially when considering several gas species is still an ongoing research [3]. Nowadays, the use of Low Oxygen and Ultra Low Oxygen Controlled Atmospheres has been recognized as a reliable method to extend the storage life of fruits an vegetables. However, small spatial gradients in gas concentration during storage may generate internal disorders in the commodities. In this work, four different gases will be considered: oxygen, carbon dioxide, water vapor and ethylene. Physiological effects such as transpiration, which affects the level of water vapor, respiration, which modifies both oxygen and carbon dioxide concentrations, and ethylene emission, must be taken into account in the hole model. The numerical model, based on that proposed by Shan and Chen, is implemented, being able to consider the behavior of multiple mixable gas species. Forced air motion, needed to obtain a correct ventilation of the chamber, has also been modelled.

  11. The development of ensemble theory. A new glimpse at the history of statistical mechanics

    Science.gov (United States)

    Inaba, Hajime

    2015-12-01

    This paper investigates the history of statistical mechanics from the viewpoint of the development of the ensemble theory from 1871 to 1902. In 1871, Ludwig Boltzmann introduced a prototype model of an ensemble that represents a polyatomic gas. In 1879, James Clerk Maxwell defined an ensemble as copies of systems of the same energy. Inspired by H.W. Watson, he called his approach "statistical". Boltzmann and Maxwell regarded the ensemble theory as a much more general approach than the kinetic theory. In the 1880s, influenced by Hermann von Helmholtz, Boltzmann made use of ensembles to establish thermodynamic relations. In Elementary Principles in Statistical Mechanics of 1902, Josiah Willard Gibbs tried to get his ensemble theory to mirror thermodynamics, including thermodynamic operations in its scope. Thermodynamics played the role of a "blind guide". His theory of ensembles can be characterized as more mathematically oriented than Einstein's theory proposed in the same year. Mechanical, empirical, and statistical approaches to foundations of statistical mechanics are presented. Although it was formulated in classical terms, the ensemble theory provided an infrastructure still valuable in quantum statistics because of its generality.

  12. [Statistical materials].

    Science.gov (United States)

    1986-01-01

    Official population data for the USSR are presented for 1985 and 1986. Part 1 (pp. 65-72) contains data on capitals of union republics and cities with over one million inhabitants, including population estimates for 1986 and vital statistics for 1985. Part 2 (p. 72) presents population estimates by sex and union republic, 1986. Part 3 (pp. 73-6) presents data on population growth, including birth, death, and natural increase rates, 1984-1985; seasonal distribution of births and deaths; birth order; age-specific birth rates in urban and rural areas and by union republic; marriages; age at marriage; and divorces. PMID:12178831

  13. 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

  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. 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.

  16. 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

  17. 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...

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

    Science.gov (United States)

    Berglund, Mathias; Raiko, Tapani; Cho, Kyunghyun

    2015-04-01

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

  19. 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...

  20. Simulation of Magnetorheological Fluids Based on Lattice Boltzmann Method with Double Meshes

    Directory of Open Access Journals (Sweden)

    Xinhua Liu

    2012-01-01

    Full Text Available In order to study the rheological characteristics of magnetorheological fluids, a novel approach based on the two-component Lattice Boltzmann method with double meshes was proposed, and the micro-scale structures of magnetorheological fluids in different strength magnetic fields were simulated. The framework composed of three steps for the simulation of magnetorheological fluids was addressed, and the double meshes method was elaborated. Moreover, the various internal and external forces acting on the magnetic particles were analyzed and calculated. The two-component Lattice Boltzmann model was set up, and the flowchart for the simulation of magnetorheological fluids based on the two-component Lattice Boltzmann method with double meshes was designed. Finally, a physics experiment was carried out, and the simulation examples were provided. The comparison results indicated that the proposed approach was feasible, efficient, and outperforming others.

  1. The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential

    Science.gov (United States)

    Liu, Shuangqian; Yang, Xiongfeng

    2016-08-01

    Boundary effects are central to the dynamics of the dilute particles governed by the Boltzmann equation. In this paper, we study both the diffuse reflection and the specular reflection boundary value problems for the Boltzmann equation with a soft potential, in which the collision kernel is ruled by the inverse power law. For the diffuse reflection boundary condition, based on an L 2 argument and its interplay with intricate {L^∞} analysis for the linearized Boltzmann equation, we first establish the global existence and then obtain the exponential decay in {L^∞} space for the nonlinear Boltzmann equation in general classes of bounded domain. It turns out that the zero lower bound of the collision frequency and the singularity of the collision kernel lead to some new difficulties for achieving the a priori {L^∞} estimates and time decay rates of the solution. In the course of the proof, we capture some new properties of the probability integrals along the stochastic cycles and improve the {L^2-L^∞} theory to give a more direct approach to overcome those difficulties. As to the specular reflection condition, our key contribution is to develop a new time-velocity weighted {L^∞} theory so that we could deal with the greater difficulties stemming from the complicated velocity relations among the specular cycles and the zero lower bound of the collision frequency. From this new point, we are also able to prove that the solutions of the linearized Boltzmann equation tend to equilibrium exponentially in {L^∞} space with the aid of the L 2 theory and a bootstrap argument. These methods, in the latter case, can be applied to the Boltzmann equation with soft potential for all other types of boundary condition.

  2. 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.

  3. 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.

  4. 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.

  5. 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...

  6. 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.

  7. 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.

  8. Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

    Science.gov (United States)

    Kang, Xiu-Ying; Liu, Da-He; Zhou, Jing; Jin, Yong-Juan

    2005-11-01

    The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail. The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.

  9. A Lattice Boltzmann Model for Fluid-Solid Coupling Heat Transfer in Fractal Porous Media

    Institute of Scientific and Technical Information of China (English)

    CAI Jun; HUAI Xiu-Lan

    2009-01-01

    We report a lattice Boltzmann model that can be used to simulate fluid-solid coupling heat transfer in fractal porous media.A numerical simulation is conducted to investigate the temperature evolution under different ratios of thermal conductivity of solid matrix of porous media to that of fluid.The accordance of our simulation results with the solutions from the conventional CFD method indicates the feasibility and the reliability for the developed lattice Boltzmann model to reveal the phenomena and rules of fluid-solid coupling heat transfer in complex porous structures.

  10. An H Theorem for Boltzmann's Equation for the Yard-Sale Model of Asset Exchange

    Science.gov (United States)

    Boghosian, Bruce M.; Johnson, Merek; Marcq, Jeremy A.

    2015-12-01

    In recent work (Boghosian, Phys Rev E 89:042804-042825, 2014; Boghosian, Int J Mod Phys 25:1441008-1441015, 2014), Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy—complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an H function of both the Boltzmann and Fokker-Planck equations for the model.

  11. 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.

  12. 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)

  13. 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.

  14. 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.

  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. 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.

  17. 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...

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

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

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

  19. Introduction to probability with statistical applications

    CERN Document Server

    Schay, Géza

    2016-01-01

    Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises

  20. Statistical mechanics of driven diffusive systems

    CERN Document Server

    Schmittmann, B

    1995-01-01

    Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension. Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail. Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these syst...

  1. 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

  2. 受限玻尔兹曼机的新混合稀疏惩罚机制%New hybrid sparse penalty mechanism of restricted Boltzmann machine

    Institute of Scientific and Technical Information of China (English)

    刘凯; 张立民; 张超

    2015-01-01

    为解决受限玻尔兹曼机(RB M )在学习过程中出现的特征同质化问题,在RB M 已有的稀疏模型基础上提出新的混合稀疏惩罚机制(HSPM )。鉴于隐单元之间存在的统计相关性,该机制通过在RBM 训练过程中引入交叉熵稀疏惩罚因子,实现对RBM 的初步处理;按照基于 RBM 连接权值列相似性的自适应分组策略,构建稀疏组RBM ,并按照稀疏组受限玻尔兹曼机(SGRBM )的形式继续进行隐单元稀疏化。实验结果表明:HSPM 能够有效解决RBM特征同质化问题,在隐单元的稀疏程度上优于以往的稀疏惩罚因子,可以整体提高RBM的特征提取能力,并可以成功应用于深度玻尔兹曼机(DBM )的训练。%A new hybrid sparse penalty mechanism ( HSPM ) was proposed to resolve the features homogenization problem of restricted Boltzmann machine (RBM ) .HSPM was based on the existing sparse restricted Boltzmann machine (SRBM ) . Since the statistical correlation among hidden units , a cross‐entropy factor to optimize the training of RBMs was first implemented by HSPM .Then ,hidden units were grouped according to adaptive grouping strategy based on the column similarity of connection weights . Finally ,hidden units sparse processing was carried out in the form of sparse group restricted Boltzmann machine (SGRBM ) .The experimental results confirmed that HSPM could effectively resolve the feature homogenization problem of RBM and was better than ever sparse penalty factor on degree of signals sparsity .HSPM can improve the feature extraction capability of RBM and be applied to the training of deep Boltzmann machine (DBM ) successfully .

  3. Investigations of microscale fluid-thermal phenomena based on the deterministic Boltzmann-ESBGK model

    Science.gov (United States)

    Guo, Xiaohui

    physical space is discretized in Cartesian coordinate, while the velocity space is discretized in polar coordinate. The Gaussian-Hermite quadrature is applied to the velocity magnitude. Boundary conditions including temperature, pressure, symmetry as well as far-field are implemented. The interfacial gas-phonon coupling is solved based on conservations of mass, momentum and energy. Good agreements have been obtained from comparisons of current simulations with other numerical models, analytical solutions and experimental data for benchmark cases. The work on temperature-driven microflows includes two major parts: contact thermal resistance over constrictions and thermal transpiration flows in a closed system. The verification of heat transfer at gas-solid surfaces is conducted by comparison with theoretical solutions, where the infinite thin constrictions are considered. For finite constrictions, the heat flux through the interface can be much less than analytical predictions. The coupling effects in thermal transpiration flows can not be ignored when gas flows are in transitional and free-molecular regimes. The effective temperature gradient should be calculated using the wall temperatures at the entrance and exit of the channel, which are different from the temperatures at the inlet and outlet chamber. In addition, when the phonon mean-free-path becomes comparable to the membrane thickness, the assumption for linear wall temperature distribution becomes invalid. The deterministic Boltzmann solver has been also applied to micro-scale aerodynamic damping problems. Based on fifty simulations over a broad range of Knudsen number and geometry, a compact model in the form of a rational function is generated. The fitting is examined by various statistical criteria. The developed compact model is accurate for cantilever/squeeze-film damping problems with small amplitude vibrations by comparison with experimental measurements with various geometries and flow conditions. The

  4. 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.

  5. 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.

  6. 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

  7. Combining Generative and Discriminative Representation Learning for Lung CT Analysis With Convolutional Restricted Boltzmann Machines

    NARCIS (Netherlands)

    G. van Tulder (Gijs); M. de Bruijne (Marleen)

    2016-01-01

    textabstractThe 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 ma

  8. 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

  9. 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…

  10. Lattice-Boltzmann-based two-phase thermal model for simulating phase change

    NARCIS (Netherlands)

    Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.

    2013-01-01

    A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A

  11. A New Regularization Mechanism for the Boltzmann Equation Without Cut-Off

    Science.gov (United States)

    Silvestre, Luis

    2016-11-01

    We apply recent results on regularity for general integro-differential equations to derive a priori estimates in Hölder spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in {L^∞} which applies in the space inhomogeneous case as well, provided that the macroscopic quantities remain bounded.

  12. 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

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

    Science.gov (United States)

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

    2016-10-01

    The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274092 and 1140040119) and the Natural Science Foundation of Jiangsu Province, China (Grant No. SBK2014043338).

  14. 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...

  15. 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.

  16. 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

  17. 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.

  18. High-Resolution Vibration-Rotation Spectroscopy of CO[subscript 2]: Understanding the Boltzmann Distribution

    Science.gov (United States)

    Castle, Karen J.

    2007-01-01

    In this undergraduate physical chemistry laboratory experiment, students acquire a high-resolution infrared absorption spectrum of carbon dioxide and use their data to show that the rotational-vibrational state populations follow a Boltzmann distribution. Data are acquired with a mid-infrared laser source and infrared detector. Appropriate…

  19. Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow

    NARCIS (Netherlands)

    Kromkamp, J.; Ende, van den D.; Kandhai, D.; Sman, van der R.G.M.; Boom, R.M.

    2006-01-01

    In this study, the Lattice Boltzmann (LB) method is applied for computer simulation of suspension flow in Couette systems. Typical aspects of Couette flow such as wall effects and non-zero Reynolds numbers can be studied well with the LB method because of its time-dependent character. Couette flow o

  20. Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E

    2015-07-01

    Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.

  1. 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.

  2. 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.

  3. 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...

  4. 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…

  5. Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

    DEFF Research Database (Denmark)

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

    2007-01-01

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

  6. Calibrating the Shan-Chen lattice Boltzmann model for immiscible displacement in porous media

    DEFF Research Database (Denmark)

    Christensen, Britt Stenhøj Baun; Schaap, M.G.; Wildenschild, D.;

    2006-01-01

    The lattice Boltzmann (LB) modeling technique is increasingly being applied in a variety of fields where computational fluid dynamics are investigated. In our field of interest, environmentally related flow processes in porous media, the use of the LB method is still not common. For the LB...

  7. Simulation of three-phase displacement mechanisms using a 2D lattice-Boltzmann model

    NARCIS (Netherlands)

    Kats, F.M. van; Egberts, P.J.P.

    1999-01-01

    Using a numerical technique, known as the lattice-Boltzmann method, we study immiscible three-phase flow at the pore scale. An important phenomenon at this scale is the spreading of oil onto the gas-water interface. In this paper, we recognize from first principles how injected gas remobilizes initi

  8. Lattice Boltzmann based multicomponent reactive transport model coupled with geochemical solver for scale simulations

    NARCIS (Netherlands)

    Patel, R.A.; Perko, J.; Jaques, D.; De Schutter, G.; Ye, G.; Van Breugel, K.

    2013-01-01

    A Lattice Boltzmann (LB) based reactive transport model intended to capture reactions and solid phase changes occurring at the pore scale is presented. The proposed approach uses LB method to compute multi component mass transport. The LB multi-component transport model is then coupled with the well

  9. Moisture transport in swelling media modelled with a Lattice Boltzmann scheme having a deforming lattice

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2014-01-01

    In this paper we present a novel numerical scheme for simulating the one-dimensional deformation of hydrogel material due to drying or rehydration. The scheme is based on the versatile Lattice Boltzmann method, which has been extended such that the computational grid (lattice) deforms due to shrinka

  10. 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...

  11. 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.

  12. 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.

  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. Fully coupled Lattice Boltzmann simulation of fiber reinforced self compacting concrete flow

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skocek, Jan; Stang, Henrik;

    accurately the most important phenomena is introduced. A conventional Lattice Boltzmann method has been chosen as a fluid dynamics solver of the non-Newtonian fluid. A Mass Tracking Algorithm has been implemented to correctly represent a free surface and a modified Immersed Boundary Method (IBM) with direct...

  15. About the statistical description of gas-liquid flows

    International Nuclear Information System (INIS)

    Elements of the probabilistic geometry are used to derive the bubble coalescence term of the statistical description of gas liquid flows. It is shown that the Boltzmann's hypothesis, that leads to the kinetic theory of dilute gases, is not appropriate for this kind of flows. The resulting integro-differential transport equation is numerically integrated to study the flow development in slender bubble columns. The solution remarkably predicts the transition from bubbly to slug flow pattern. Moreover, a bubbly bimodal size distribution is predicted, which has already been observed experimentally

  16. The q-Statistics and QCD Thermodynamics at LHC

    CERN Document Server

    Bhattacharyya, Trambak; Sahoo, Pragati; Garg, Prakhar; Pareek, Pooja; Sahoo, Raghunath; Cleymans, Jean

    2016-01-01

    We perform a Taylor series expansion of Tsallis distribution by assuming the Tsallis parameter $q$ close to 1. The $q$ value shows the deviation of a system from a thermalised Boltzmann distribution. By taking up to first order in $(q-1)$, we derive an analytical result for Tsallis distribution including radial flow. Further, in the present work, we also study the speed of sound ($c_s$) as a function of temperature using the non-extensive Tsallis statistics for different $q$ values and for different mass cut-offs.

  17. Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows.

    Science.gov (United States)

    Premnath, Kannan N; Pattison, Martin J; Banerjee, Sanjoy

    2009-02-01

    In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu, Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids

  18. 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.

  19. Wind-Driven, Double-Gyre, Ocean Circulation in a Reduced-Gravity, 2.5-Layer, Lattice Boltzmann Model

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    A coupled lattice Boltzmann (LB) model with second-order accuracy is applied to the reduced-gravity,shallow water, 2.5-layer model for wind-driven double-gyre ocean circulation. By introducing the secondorder integral approximation for the collision operator, the model becomes fully explicit. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretization accuracy of the LB equation. The feature of the multiple equilibria solutions is found in the numerical experiments under different Reynolds numbers based on this LB scheme. With the Reynolds number increasing from 3000 to 4000, the solution of this model is destabilized from the anti-symmetric double-gyre solution to the subtropic gyre solution and then to the subpolar gyre solution. The transitions between these equilibria states are also found in some parameter ranges. The time-dependent variability of the circulation based on this LB simulation is also discussed for varying viscosity regimes. The flow of this model exhibits oscillations with different timescales varying from subannual to interannual. The corresponding statistical oscillation modes are obtained by spectral analysis. By analyzing the spatiotemporal structures of these modes, it is found that the subannual oscillation with a 9-month period originates from the barotropic Rossby basin mode, and the interannual oscillations with periods ranging from 1.5 years to 4.6 years originate from the recirculation gyre modes, which include the barotropic and the baroclinic recirculation gyre modes.

  20. On nonextensive thermo-statistics: systematization, clarification of scope and interpretation, and illustrations

    OpenAIRE

    Luzzi, Roberto; Vasconcellos, Áurea R.; Ramos, J. Galvão

    2004-01-01

    When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard approach to the well established, physically and logically sound, Boltzmann-Gibbs statistics. To circumvent such difficulties, in order to make predictions on properties of the system and looking for an understanding of the physics involved (for example in analyzi...

  1. Cosmetic Plastic Surgery Statistics

    Science.gov (United States)

    2014 Cosmetic Plastic Surgery Statistics Cosmetic Procedure Trends 2014 Plastic Surgery Statistics Report Please credit the AMERICAN SOCIETY OF PLASTIC SURGEONS when citing statistical data or using ...

  2. On Infinite Quon Statistics and "Ambiguous" Statistics

    OpenAIRE

    Meljanac, S.; Milekovic, M.; Ristic, R.

    1999-01-01

    We critically examine a recent suggestion that "ambiguous" statistics is equivalent to infinite quon statistics and that it describes a dilute, nonrelativistics ideal gas of extremal black holes. We show that these two types of statistics are different and that the description of extremal black holes in terms of "ambiguous" statistics cannot be applied.

  3. Statistical mechanics in the context of special relativity

    Science.gov (United States)

    Kaniadakis, G.

    2002-11-01

    In Ref. [Physica A 296, 405 (2001)], starting from the one parameter deformation of the exponential function exp{κ}(x)=((1+κ2x2)+κx)1/κ, a statistical mechanics has been constructed which reduces to the ordinary Boltzmann-Gibbs statistical mechanics as the deformation parameter κ approaches to zero. The distribution f=exp{κ}(-β E+βμ) obtained within this statistical mechanics shows a power law tail and depends on the nonspecified parameter β, containing all the information about the temperature of the system. On the other hand, the entropic form Sκ=∫d3p(cκ f1+κ+c-κ f1-κ), which after maximization produces the distribution f and reduces to the standard Boltzmann-Shannon entropy S0 as κ-->0, contains the coefficient cκ whose expression involves, beside the Boltzmann constant, another nonspecified parameter α. In the present effort we show that Sκ is the unique existing entropy obtained by a continuous deformation of S0 and preserving unaltered its fundamental properties of concavity, additivity, and extensivity. These properties of Sκ permit to determine unequivocally the values of the above mentioned parameters β and α. Subsequently, we explain the origin of the deformation mechanism introduced by κ and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter κ which results to depend on the light speed c and reduces to zero as c-->∞ recovering in this way the ordinary statistical mechanics and thermodynamics. The statistical mechanics here presented, does not contain free parameters, preserves unaltered the mathematical and epistemological structure of the ordinary statistical mechanics and is suitable to describe a very large class of experimentally observed

  4. Towards Direct Numerical Simulation of mass and energy fluxes at the soil-atmospheric interface with advanced Lattice Boltzmann methods

    Science.gov (United States)

    Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin

    2014-05-01

    The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the

  5. 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)

  6. Numerical simulation of ski-jump jet motion using lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    Based on the lattice Boltzmann method,a lattice Boltzmann(LB) model of the ski-jump jet two-phase flow is developed first and the corresponding boundary conditions are studied.A simple case study of a droplet horizontal movement calculation is carried out to test and verify the model,where level set method is used to track and reconstruct the moving droplet free surface. Then,we numerically simulate a two dimensional flow field of the ski-jump jet with the LB model,derive the moving surface and velocity vector field of the jet flow.The simulation results are very consistent with the physical mechanisms.The effectiveness and reliability of the model are demonstrated by the numerical examples.

  7. 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...

  8. 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)

  9. Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

    Institute of Scientific and Technical Information of China (English)

    Mahdi Daemi; Mohammad Taeibi-Rahni; Hamidreza Massah

    2015-01-01

    Search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor. A long list of complex phenomena underlies physics of this problem. In the past decades, the lattice Boltzmann (LB) method has emerged as a promising tool to address such complexities. In this regard, we have applied a 121-velocity multiphase lattice Boltzmann model (LBM) to an asymmetric cluster of bubbles in an acoustic field. A problem as a benchmark is studied to check the consistency and applicability of the model. The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics, and the screening effect on an acoustic multi-bubble medium. It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.

  10. 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.

  11. 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.

  12. 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.

  13. 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...

  14. 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.

  15. Thermal Lattice Boltzmann Simulations for Vapor-Liquid Two-Phase Flows in Two Dimensions

    Science.gov (United States)

    Wei, Yikun; Qian, Yuehong

    2011-11-01

    A lattice Boltzmann model with double distribution functions is developed to simulate thermal vapor-liquid two-phase flows. In this model, the so-called mesoscopic inter-particle pseudo-potential for the single component multi-phase lattice Boltzmann model is used to simulate the fluid dynamics and the internal energy field is simulated by using a energy distribution function. Theoretical results for large-scale dynamics including the internal energy equation can be derived and numerical results for the coexistence curve of vapor-liquid systems are in good agreement with the theoretical predictions. It is shown from numerical simulations that the model has the ability to mimic phase transitions, bubbly flows and slugging flows. This research is support in part by the grant of Education Ministry of China IRT0844 and the grant of Shanghai CST 11XD1402300.

  16. 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...

  17. 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.

  18. 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.

  19. 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.

  20. Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

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

    2010-09-15

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

  1. 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 $L^2(\\R^n)$.

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

    CERN Document Server

    Asinari, Pietro

    2010-01-01

    The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both ...

  3. Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning

    CERN Document Server

    Premnath, Kannan N; Banerjee, Sanjoy

    2008-01-01

    Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature, requires a long time to attain steady state convergence, particularly at low Mach numbers due to the disparity in characteristic speeds of propagation of different quantities. In this paper, we present a preconditioned generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate steady state convergence to flows driven by external forces. The use of multiple relaxation times in the GLBE allows enhancement of the numerical stability. Particular focus is given in preconditioning external forces, which can be spatially and temporally dependent. In particular, correct forms of moment-projections of source/forcing terms are derived such that they recover preconditioned Navier-Stokes equations with non-uniform external forces. As an illustration, we solve an extende...

  4. A nonlocal modified Poisson-Boltzmann equation and finite element solver for computing electrostatics of biomolecules

    Science.gov (United States)

    Xie, Dexuan; Jiang, Yi

    2016-10-01

    The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson-Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson-Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.

  5. 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.

  6. 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...

  7. 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.

  8. 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.

  9. Double MRT Thermal Lattice Boltzmann Method for Simulating Natural Convection of Low Prandtl Number Fluids

    CERN Document Server

    Li, Zheng; Zhang, Yuwen

    2016-01-01

    The purposes of this paper are testing an efficiency algorithm based on LBM and using it to analyze two-dimensional natural convection with low Prandtl number. Steady state or oscillatory results are obtained using double multiple-relaxation-time thermal lattice Boltzmann method. The velocity and temperature fields are solved using D2Q9 and D2Q5 models, respectively. With different Rayleigh number, the tested natural convection can either achieve to steady state or oscillatory. With fixed Rayleigh number, lower Prandtl number leads to a weaker convection effect, longer oscillation period and higher oscillation amplitude for the cases reaching oscillatory solutions. At fixed Prandtl number, higher Rayleigh number leads to a more notable convection effect and longer oscillation period. Double multiple-relaxation-time thermal lattice Boltzmann method is applied to simulate the low Prandtl number fluid natural convection. Rayleigh number and Prandtl number effects are also investigated when the natural convection...

  10. Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluid flows

    CERN Document Server

    Yang, Zai-Bao

    2013-01-01

    In this article, we present a detailed asymptotic analysis of the lattice Boltzmann method with two different collision mechanisms of BGK-type on the D2Q9-lattice for generalized Newtonian fluids. Unlike that based on the Chapman-Enskog expansion leading to the compressible Navier-Stokes equations, our analysis gives the incompressible ones directly and exposes certain important features of the lattice Boltzmann solutions. Moreover, our analysis provides a theoretical basis for using the iteration to compute the rate-of-strain tensor, which makes sense specially for generalized Newtonian fluids. As a by-product, a seemingly new structural condition on the generalized Newtonian fluids is singled out. This condition reads as "the magnitude of the stress tensor increases with increasing the shear rate". We verify this condition for all the existing constitutive relations which are known to us. In addition, it it straightforward to extend our analysis to MRT models or to three-dimensional lattices.

  11. 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 ...

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*

    Directory of Open Access Journals (Sweden)

    Graille Benjamin

    2012-04-01

    Full Text Available In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on relaxation times and equilibrium states that characterizes a lattice Boltzmann scheme. We propose a method to select the parameters of the scheme according to the desired order of isotropy. Applying it to the D2Q9 scheme yields the classical constraints for the first and second orders and some non classical for the third and fourth orders.

  17. 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

  18. A simplistic pedagogical formulation of the Maxwell-Boltzmann Thermal Speed Distribution using a relativistic framework

    CERN Document Server

    Singh, Ashmeet

    2012-01-01

    A novel pedagogical technique is presented that can be used in the undergraduate (UG) class to formulate a relativistically extended Kinetic Theory of Gases and Maxwell-Boltzmann thermal speed distribution, while keeping the basic thermal symmetry arguments intact. The adopted framework can be used by students to understand the physics in a thermally governed system at high temperature and speeds, without having to indulge in high level tensor based mathematics. Our approach will first recapitulate what is taught and known in the UG class and then present a methodology that will help students to understand and derive the physics of relativistic thermal systems. The methodology uses simple tools well known in the UG class and involves a component of computational techniques that can be used to involve students in this exercise. We also present towards the end the interesting implications of the relativistically extended distribution and compare it with Maxwell-Boltzmann results at various temperatures.

  19. 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...

  20. 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.

  1. 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.

  2. 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...

  3. 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...

  4. Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings

    CERN Document Server

    Su, S -C

    2014-01-01

    The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\\sigma$. The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect. While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the non-linear effect of CMB lensing is formulated through the solutions of the geodesic equation. In this paper, we present a new formalism to the calculation of the lensing effect by \\emph{directly solving the Boltzmann equation}, as we did in the calculation of the CMB anisotropies at recombination. In particular, we developed a diagrammatic approach to efficiently keep track of all the interaction terms and calculate all possible non-trivial correlations to arbitrary high orders. Using this formalism, we explicitly articulate the approximations required to recover the usual remapping a...

  5. 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.

  6. 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...

  7. Power-law distributions in economics: a nonextensive statistical approach

    CERN Document Server

    Queiros, S M D; Tsallis, C; Queiros, Silvio M. Duarte; Anteneodo, Celia; Tsallis, Constantino

    2005-01-01

    The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \\equiv -k\\int dx f(x)\\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory has exibited, along more than one century, great success in the treatment of systems where short spatio/temporal correlations dominate. There are, however, anomalous natural and artificial systems that violate the basic requirements for its applicability. Different physical entropies, other than the standard one, appear to be necessary in order to satisfactorily deal with such anomalies. One of such entropies is $S_q \\equiv k (1-\\int dx [f(x)]^q)/(1-q)$ (with $S_1=S_{BG}$), where the entropic index $q$ is a real parameter. It has been proposed as the basis for a generalization, referred to as {\\it nonextensive statistical mechanics}, of the $BG$ theory. $S_q$ shares with $S_{BG}$ four remarkable properties, namely {\\it concavity} ($\\forall q>0$), {\\it Lesche-stability} ($\\for...

  8. Microscopic statistical description of incompressible Navier-Stokes granular fluids

    CERN Document Server

    Tessarotto, Massimo; Asci, Claudio

    2016-01-01

    Based on the recently-established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic $1-$body PDF evolving in time by means of M...

  9. Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time

    CERN Document Server

    Takou, Etienne

    2016-01-01

    In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is for the hard potentials case and the background space-time in which the study is done is the Robertson-Walker space-time. Unique global (in time) mild solution is obtained in a suitable weighted space.

  10. Lattice-Boltzmann-based two-phase thermal model for simulating phase change

    OpenAIRE

    Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.

    2013-01-01

    A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum l...

  11. 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.

  12. 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...

  13. LATTICE BOLTZMANN SIMULATIONS OF TRIAGULAR CAVITY FLOW AND FREE-SURFACE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    DUAN Ya-li; LIU Ru-xun

    2007-01-01

    The Lattice Boltzmann Method (LBM) was investigated to solve triangular cavity flow and free-surface problems in hydraulic dynamics. Some cases of triangular cavity flow and backward step flow were simulated to show the efficiency and stability of this method. Two-dimensional partial dam breaking problem and the propagation and diffraction of dam-break wave around rectangular and circular cylinder were numerically studied successfully. Excellent agreement was obtained between numerical predictions and available results.

  14. 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.

  15. 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...

  16. 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...

  17. A bound for the convergence rate of parallel tempering for sampling restricted Boltzmann machines

    DEFF Research Database (Denmark)

    Fischer, Asja; Igel, Christian

    2015-01-01

    Abstract Sampling from restricted Boltzmann machines (RBMs) is done by Markov chain Monte Carlo (MCMC) methods. The faster the convergence of the Markov chain, the more efficiently can high quality samples be obtained. This is also important for robust training of RBMs, which usually relies...... for contrastive divergence learning, our bound on the mixing time implies an upper bound on the error of the gradient approximation when the method is used for RBM training....

  18. 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.

  19. 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...

  20. 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...

  1. LATTICE BOLTZMANN METHOD SIMULATION ON THE FLOW OF TWO IMMISCIBLE FLUIDS IN COMPLEX GEOMETRY

    Institute of Scientific and Technical Information of China (English)

    Fang Hai-ping; Wan Rong-zheng; Fan Le-wen

    2000-01-01

    The multicomponent nonideal gas lattice Boltzmann model byShan and Chen (S-C) can be used to simulate the immiscible fluidflow. In this paper, weshow that the relaxation constant 1 is a necessarycondition for the immiscible fluid flow in the S-C model. In asystem with very complex boundary geometry, for 0.8 1, the S-C model describes the immiscible flow quite well, and=1 is the best.

  2. 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.

  3. 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...

  4. 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...

  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 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.

  7. 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...

  8. 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.

  9. 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.

  10. 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.

  11. Numerical Simulation of Driven Convective Heat Transfer Based Lattice Boltzmann Method in a Porous Cavity

    Directory of Open Access Journals (Sweden)

    You-Sheng Xu

    2015-01-01

    Full Text Available A lattice Boltzmann model of the uniform velocity, driven convective thermal conductivity in a porous cavity is studied. The Darcy, Richardson, and Reynolds numbers are shown to have a significant influence on the heat transfer behavior and the horizontal velocity of the flow field, while the porosity has little influence on either. The model is validated by the average Nusselt number at different Reynolds numbers, and the numerical results are in good agreement with available published data.

  12. 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 ...

  13. 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.

  14. 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.

  15. Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    Yuan LI; Ya-li DUAN; Yan GUO; Ru-xun LIU

    2009-01-01

    In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method (LBM) with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.

  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. Modeling flue pipes: Subsonic flow, lattice Boltzmann, and parallel distributed computers

    Science.gov (United States)

    Skordos, Panayotis A.

    1995-01-01

    The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial-viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80 percent parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts.

  18. 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.

  19. Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

    Institute of Scientific and Technical Information of China (English)

    LI; Zhihui; ZHANG; Hanxin; FU; Song

    2005-01-01

    The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.

  20. 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)