Boltzmann's Concept of Reality
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...
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
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.)
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...
On Boltzmann's genius and thermodynamics
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.
Crystallographic Lattice Boltzmann Method.
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
Crystallographic Lattice Boltzmann Method
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.
Joint Training of Deep Boltzmann Machines
Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua
2012-01-01
We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.
Ludwig Boltzmann A Pioneer of Modern Physics
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...
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.
Multiphase cascaded lattice Boltzmann method
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...
Directory of Open Access Journals (Sweden)
Igor V. Karyakin
2016-02-01
Full Text Available The 9th ARRCN Symposium 2015 was held during 21st–25th October 2015 at the Novotel Hotel, Chumphon, Thailand, one of the most favored travel destinations in Asia. The 10th ARRCN Symposium 2017 will be held during October 2017 in the Davao, Philippines. International Symposium on the Montagu's Harrier (Circus pygargus «The Montagu's Harrier in Europe. Status. Threats. Protection», organized by the environmental organization «Landesbund für Vogelschutz in Bayern e.V.» (LBV was held on November 20-22, 2015 in Germany. The location of this event was the city of Wurzburg in Bavaria.
Student understanding of the Boltzmann factor
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...
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.
Lattice Boltzmann scheme for relativistic fluids
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.
The Einstein-Boltzmann system and positivity
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.
Thermal cascaded lattice Boltzmann method
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...
Multiphase lattice Boltzmann methods theory and application
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
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.)
Relativistic Entropy and Related Boltzmann Kinetics
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...
Ergodicity, ensembles, irreversibility in Boltzmann and beyond
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
Ergodicity, ensembles, irreversibility in Boltzmann and beyond
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.
An introduction to the theory of the Boltzmann equation
Harris, Stewart
2011-01-01
Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes
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.
A Viscosity Adaptive Lattice Boltzmann Method
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...
Lattice Boltzmann approach for complex nonequilibrium flows.
Montessori, A; Prestininzi, P; La Rocca, M; Succi, S
2015-10-01
We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion. PMID:26565365
Matrix-valued Quantum Lattice Boltzmann Method
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.
Student understanding of the Boltzmann factor
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.
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.
Phantom cosmology and Boltzmann brains problem
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 $t
Fast lattice Boltzmann solver for relativistic hydrodynamics.
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.
Kinetic Boltzmann, Vlasov and Related Equations
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
Grid refinement for entropic lattice Boltzmann models
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.
Fast lattice Boltzmann solver for relativistic hydrodynamics.
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
Celebrating Cercignani's conjecture for the Boltzmann equation
Villani, Cédric
2011-01-01
Cercignani\\'s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann\\'s nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.
Test of Information Theory on the Boltzmann Equation
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.
Test of Information Theory on the Boltzmann Equation
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.
A Fluctuating Lattice Boltzmann Method for the Diffusion Equation
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.
Multispeed models in off-lattice Boltzmann simulations
Bardow, A.; Karlin, I.V.; Gusev, A.A.
2008-01-01
The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods. T
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...
Stefan-Boltzmann Law for Massive Photons
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.
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...
Lattice Boltzmann Models for Complex Fluids
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.
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.
Lattice Boltzmann approaches to magnetohydrodynamics and electromagnetism
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.
Lattice-Boltzmann simulations of droplet evaporation
Ledesma-Aguilar, Rodrigo
2014-09-04
© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is
Privacy-Preserving Restricted Boltzmann Machine
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...
Geometry of the restricted Boltzmann machine
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 ...
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.
Nuclear Flow in Consistent Boltzmann Algorithm Models
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 ...
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.
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.
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.
Privacy-preserving restricted boltzmann machine.
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
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.
Lattice-Boltzmann-based Simulations of Diffusiophoresis
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.
Celebrating Cercignani's conjecture for the Boltzmann equation
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.
Convolution Inequalities for the Boltzmann Collision Operator
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.
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.
Thermal equation of state for lattice Boltzmann gases
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.
Droplet collision simulation by multi-speed lattice Boltzmann method
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.
Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics
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.
A probabilistic view on the general relativistic Boltzmann equation
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.
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
Lattice-Boltzmann Simulation of Tablet Disintegration
Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip
Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems. PMID:26986435
Thermal lattice Boltzmann method for complex microflows
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.
Heavy Flavor Suppression: Boltzmann vs Langevin
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.
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.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
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...
Autotagging music with conditional restricted Boltzmann machines
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.
Lattice Boltzmann modelling of intrinsic permeability
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.
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.
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Accurate deterministic solutions for the classic Boltzmann shock profile
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.
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.
Langevin theory of fluctuations in the discrete Boltzmann equation
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.
Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project
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...
Permit Allocation in Emissions Trading using the Boltzmann Distribution
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...
Analysis of spectral methods for the homogeneous Boltzmann equation
Filbet, Francis
2011-04-01
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.
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.
A Boltzmann model for rod alignment and schooling fish
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...
Advanced Mean Field Theory of Restricted Boltzmann Machine
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...
Lattice Boltzmann algorithm for continuum multicomponent flow.
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
Analysis of Jeans instability from Boltzmann equation
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...
Modeling adsorption with lattice Boltzmann equation.
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
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
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
Modeling adsorption with lattice Boltzmann equation
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
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.
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.)
Systematic Study of the Boundary Composition in Poisson Boltzmann Calculations
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...
Navier-Stokes Dynamics by a Discrete Boltzmann Model
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
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
Accounting for adsorption and desorption in Lattice Boltzmann simulations
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 ...
Lattice Boltzmann Large Eddy Simulation Model of MHD
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...
An integrable 3D lattice model with positive Boltzmann weights
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.
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
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...
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.
Asymptotic-preserving Boltzmann model equations for binary gas mixture
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.
On a Boltzmann-type price formation model
Burger, Martin
2013-06-26
In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann-type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore, we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments. © 2013 The Author(s) Published by the Royal Society. All rights reserved.
Multiphase lattice Boltzmann simulations for porous media applications -- a review
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.
Learning Feature Hierarchies with Centered Deep Boltzmann Machines
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.
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.
Knotted Vortices: Entropic Lattice Boltzmann Method for Simulation of Vortex dynamics
Boesch, Fabian; Chikatamarla, Shyam; Karlin, Ilya
2013-11-01
Knotted and interlinked vortex structures in real fluids are conjectured to play a major role in hydrodynamic flow dissipation. Much interest lies in determining their temporal stability and the mechanism through which knots dissolve. Kleckner and Irvine recently have shown the existence of such knotted vortices experimentally by accelerating hydrofoils in water. In the present work we employ the entropic lattice Boltzmann method (ELBM) to perform DNS simulations of the creation and dynamics of knotted vortex rings inspired by the experimental setup in. ELBM renders LBM scheme unconditionally stable by restoring the second law of thermodynamics (the Boltzmann H-theorem), and thus enables simulations of large domains and high Reynolds numbers with DNS quality. The results presented in this talk provide an in-depth study of the dynamics of knotted vortices and vortex reconnection events and confirm the existence of trefoil knots in silicio for the first time. This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s347.
Distribution Learning in Evolutionary Strategies and Restricted Boltzmann Machines
DEFF Research Database (Denmark)
Krause, Oswin
The thesis is concerned with learning distributions in the two settings of Evolutionary Strategies (ESs) and Restricted Boltzmann Machines (RBMs). In both cases, the distributions are learned from samples, albeit with different goals. Evolutionary Strategies are concerned with finding an optimum...
A Parallel Lattice Boltzmann Model of a Carotid Artery
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.
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzman
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...
Measuring Boltzmann's Constant with Carbon Dioxide
Ivanov, Dragia; Nikolov, Stefan
2013-01-01
In this paper we present two experiments to measure Boltzmann's constant--one of the fundamental constants of modern-day physics, which lies at the base of statistical mechanics and thermodynamics. The experiments use very basic theory, simple equipment and cheap and safe materials yet provide very precise results. They are very easy and…
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.)
Boundary conditions for surface reactions in lattice Boltzmann simulations
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
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.
An exactly solvable non-linear Boltzmann equation
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.
Tervo, J; Frank, M; Herty, M
2016-01-01
The paper considers a coupled system of linear Boltzmann transport equation (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in radiation therapy. The evolution of charged particles (e.g. electrons and positrons) are in practice often modelled using the CSDA version of BTE because of the so-called forward peakedness of scattering events contributing to the particle fluencies (or particle densities), which causes severe problems for numerical methods. First, we prove the existence and uniqueness of solutions, under sufficient criteria and in appropriate $L^2$-based spaces, of a single (particle) CSDA-equation by using two complementary techniques, the Lions-Lax-Milgram Theorem (variational approach), and the theory evolution operators (semigroup approach). The necessary a priori estimates are shown. In addition, we prove the corresponding results and estimates for the system of coupled transport equat...
Kang, KyeongJin
2016-03-01
As a further elaboration of the recently devised Q10 scanning analysis ("Exceptionally high thermal sensitivity of rattlesnake TRPA1 correlates with peak current amplitude" [1]), the interval between current data points at two temperatures was shortened and the resulting parameters representing thermal sensitivities such as peak Q10s and temperature points of major thermosensitivity events are presented for two TRPA1 orthologues from rattlesnakes and boas. In addition, the slope factors from Boltzmann fitting and the change of molar heat capacity of temperature-evoked currents were evaluated and compared as alternative ways of thermal sensitivity appraisal of TRPA1 orthologues.
Big-Bang Nucleosynthesis verifies classical Maxwell-Boltzmann distribution
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.
Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
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.
Shock-wave structure using nonlinear model Boltzmann equations.
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.
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.
Quadrature-based Lattice Boltzmann Model for Relativistic Flows
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.
Contact angles in the pseudopotential lattice Boltzmann modeling of wetting
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...
Conjugate heat transfer with the entropic lattice Boltzmann method.
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.
Quantitative and qualitative Kac's chaos on the Boltzmann's sphere
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...
The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation
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.
Learning Feature Hierarchies with Centered Deep Boltzmann Machines
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 ...
Multi-reflection boundary conditions for lattice Boltzmann models
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...
Volume-Based Fabric Tensors through Lattice-Boltzmann Simulations
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...
Multi-component lattice-Boltzmann model with interparticle interaction
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...
A Lattice Boltzmann model for diffusion of binary gas mixtures
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...
Lattice Boltzmann Method for mixtures at variable Schmidt number
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 ...
Stochastic particle approximations for generalized Boltzmann models and convergence estimates
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...
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
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...
Acoustic levitation and the Boltzmann-Ehrenfest principle
Putterman, S.; Rudnick, Joseph; Barmatz, M.
1989-01-01
The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.
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.
Topological interactions in a Boltzmann-type framework
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...
Average Contrastive Divergence for Training Restricted Boltzmann Machines
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...
Discrete Boltzmann model of shallow water equations with polynomial equilibria
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.
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.)
High-order hydrodynamics via lattice Boltzmann methods.
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.
Capillary filling and Haines jump dynamics using free energy Lattice Boltzmann simulations
Zacharoudiou, Ioannis; Boek, Edo S.
2016-06-01
We investigate numerically the dynamics of capillary filling and Haines jump events using free energy Lattice Boltzmann (LB) simulations. Both processes are potentially important multi-phase pore-scale flow processes for geological CO2 sequestration and oil recovery. We first focus on capillary filling and demonstrate that the numerical method can capture the correct dynamics in the limit of long times for both high and low viscosity ratios, i.e. the method gives the correct scaling for the length of the penetrating fluid column as a function of time. Examining further the early times of capillary filling, three consecutive length vs. time regimes have been observed, in agreement with available experimental work in the literature. In addition, we carry out simulations of Haines jump events in idealised and realistic rock pore geometries. We observe that the Haines jump events are cooperative, non-local and associated with both drainage and imbibition dynamics. Our observations show that the pore filling dynamics is controlled by the Ohnesorge number, associated with the balance between viscous forces and inertial / surface tension forces. Using this concept, we are able to identify the type of pore filling dynamics that will occur.
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...
Global Solutions of the Boltzmann Equation Over {{R}^D} Near Global Maxwellians with Small Mass
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.
Lattice Boltzmann method for the fractional advection-diffusion equation.
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.
Three-dimensional lattice Boltzmann model for compressible flows.
Sun, Chenghai; Hsu, Andrew T
2003-07-01
A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.
Lattice Boltzmann method for the fractional advection-diffusion equation
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.
Appendix: Chapman-Enskog Expansion in the Lattice Boltzmann Method
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.
Lattice-Boltzmann Method for Geophysical Plastic Flows
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.
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.
Entropy inequality and hydrodynamic limits for the Boltzmann equation.
Saint-Raymond, Laure
2013-12-28
Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as huge systems of identical and indistinguishable elementary particles. The state of a gas can therefore be described in a statistical way. The evolution, which introduces couplings, loses part of the information, which is expressed by the decay of the so-called mathematical entropy (the opposite of physical entropy!). PMID:24249776
On the Krook-Wu model of the Boltzmann equation
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.
An alternative method for simulating particle suspensions using lattice Boltzmann
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.
Multi-component lattice-Boltzmann model with interparticle interaction
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.
Boltzmann Machines and Denoising Autoencoders for Image Denoising
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...
A lattice Boltzmann method for dilute polymer solutions.
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).
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.
Numerical Poisson-Boltzmann Model for Continuum Membrane Systems.
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.
Lattice Boltzmann Simulation for the Spiral Wave Dynamics
Institute of Scientific and Technical Information of China (English)
无
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.
Polyelectrolyte Microcapsules: Ion Distributions from a Poisson-Boltzmann Model
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.
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.
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.
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
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
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.
Three-dimensional lattice Boltzmann model for electrodynamics.
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.
Wall Orientation and Shear Stress in the Lattice Boltzmann Model
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 ...
Avoiding Boltzmann Brain domination in holographic dark energy models
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.
Avoiding Boltzmann Brain domination in holographic dark energy models
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.
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)
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...
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
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.
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.
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.)
Determination of the Boltzmann Constant Using the Differential - Cylindrical Procedure
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...
Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study
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.
Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
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).
Simulation of a Microfluidic Gradient Generator using Lattice Boltzmann Methods
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.
Approximate Message Passing with Restricted Boltzmann Machine Priors
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.
Approximate message passing with restricted Boltzmann machine priors
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.
Beyond Poisson-Boltzmann: Numerical Sampling of Charge Density Fluctuations.
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
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.)
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.
The peeling process of infinite Boltzmann planar maps
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.
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.
Lattice Boltzmann method for shape optimization of fluid distributor
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.
Comparison of different Propagation Steps for the Lattice Boltzmann Method
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.
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.
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.
Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines
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.
Chemical-potential-based Lattice Boltzmann Method for Nonideal Fluids
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.
Lattice Boltzmann method for mixtures at variable Schmidt number
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.
Lattice-Boltzmann hydrodynamics of anisotropic active matter.
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
Sedimentation analysis of small ice crystals by Lattice Boltzmann Method
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.
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations
Riotto, Antonio
1998-01-01
The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...
Full Eulerian lattice Boltzmann model for conjugate heat transfer.
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
Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics
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...
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.
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
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.
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.
Modeling of urban traffic networks with lattice Boltzmann model
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.
Free Surface Lattice Boltzmann with Enhanced Bubble Model
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.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
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.
Boltzmann electron PIC simulation of the E-sail effect
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.
A Boltzmann machine for the organization of intelligent machines
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
Generalizing the Boltzmann equation in complex phase space.
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
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.
Urban, Zdeněk
2013-01-01
The thesis deals with event management and is formally divided into three sections. The first section provides the theoretical basis for the practical part. It primarily defines the terms event, event management and event marketing. The theoretical part proceeds from the general introduction to more detailed examination of the issue, which includes the classification of event marketing within the marketing and communication mix of the company, the typology of events and explanation of various...
Jandová, Dita
2011-01-01
The thesis deal with event management. For better insight into this field event management is described on case of management of conference. The thesis has three main parts. In the theoretical part there are definitions of terms like event management, conference and other related terms. Further chapters are concerned with the position of event management in the communication mix, typologies of events and mostly with the crucial aspects of event management. In the second part of the thesis the...
Šubrtová, Veronika
2013-01-01
This bachelor thesis on the topic event management develops this concept, focuses mainly on the creation of the event and its application in practice. Management, event and event management are described in the theoretical section. The importace of event management in the marketing communications mix is shown subsequently and especially the creation of the event is more detailed described. This is then reflected in the practical part of the thesis, in which the awards gala is planed and orga...
Grebíková, Kristýna
2014-01-01
The thesis in theoretical part focuses on the concepts of event management and their interaction. The theoretical part focuses on the creation of event planning and marketing strategies, typology of events, and provides a situational analysis, objectives events, defines the target group, plan the resources, establish a budget and will focus on event controlling. The practical part carries theory into practice and deals with the organization of the event in the company TON in Chile. Based on a...
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.
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].
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.
Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity
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.
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.
Corrected Stefan—Boltzmann Law and Lifespan of Schwarzschild-de-sitter Black Hole
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
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.
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.
Pham, Quynh Trang
2008-01-01
This study aims to analyze event-marketing activities of the small firm and propose new events. At first the theoretical part describes marketing and communication mix and then especially planning and development of event marketing campaign. Research data were collected by the method of survey to propose the new events. Randomly selected customers were asked to fill the questionnaire. Its results were integrated into the proposal of the new events. The interview was realized with the owner of...
Pavléková, Markéta
2013-01-01
The main theme of the work is event management, which deals with the social events of various types. Event as a mean of communication is a common part of business strategy today and the organization became a separate industry. Procedures how to implement successful event are the essential part of the work. Organizationally demanding activity of event managers, which includes planning, organizing, staffing, leadership and control is supported by marketing activities, which are described in the...
Michňa, Michal
2011-01-01
The theoretical part of this thesis deals with event management in general. The stress of its theoretical part is put on relation between event management and the other communication channels usually used by marketing experts in a firm. There is also described a confrontation of event management with processes which are basically used in project management. The theoretical part is mainly concerned with event management and organisation of events. There is a deep description of its prepara...
Vomáčková, Kateřina
2013-01-01
This thesis deals with event management from theory to practice. First part of the thesis consists of literature review of this topic – from definition of basic terms, through event management’s classification in marketing of a company, to description of different stages of event management process. The second part of the thesis is based on practice – an agency that organized for the third year an event focusing on children and sport, is presented here. Last year of this event including...
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.
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.
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...
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.
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.
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
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...
Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)
Badino, M.
2011-11-01
An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.
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.
Palkosková, Barbora
2011-01-01
The diploma thesis deals with a term of event management and its connection to the event marketing. First part of the work focuses on terms that are superior to event management and those are marketing and marketing mix of 4P´s. Communication mix is than separated into smaller parts, defining the position of event marketing and management among them. Accent is put on the current possibilities of typology and separation of event and its practical use. Issue of events is connected to the...
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.
Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes
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.
A Lattice-Boltzmann Method for Partially Saturated Computational Cells
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.
Treatment of moving boundaries in lattice-Boltzmann simulations.
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.
One-dimensional transient radiative transfer by lattice Boltzmann method.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2013-10-21
The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed. PMID:24150298
Lattice Boltzmann modeling of three-phase incompressible flows.
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
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
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.
Boltzmann electron PIC simulation of the E-sail effect
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...
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
Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles
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.
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
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...
Lattice-Boltzmann Simulations of Microswimmer-Tracer Interactions
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...
Multiblock approach for the passive scalar thermal lattice Boltzmann method
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.
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.
Macroscopic model and truncation error of discrete Boltzmann method
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.
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.
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.
Lattice Boltzmann method for one-dimensional vector radiative transfer.
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
Lattice Boltzmann modeling of three-phase incompressible flows
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.
Lattice Boltzmann models for the grain growth in polycrystalline systems
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.
Štefl, Petr
2011-01-01
This bachelor thesis on the topic of event management deals with planning, organizing, managing, monitoring and implementation of special social events, termed event. It explains what they mean by this term we can imagine and as you can in terms of typology to distinguish events. Literature review consists of the acquired theoretical knowledge in management, project management and marketing. It describes the principles and procedure in place, we should keep the successful organization of ...
Strýhalová, Veronika
2013-01-01
The Diploma thesis is focused on the Event management company, which organizes a big family minded sport day and describes its activity plan. The thesis consists three main parts, the first – the teoretic part specifices proffesional terms about an event management. This part also describes different event forms which are focused on the right selection and final strategy, the following control of financial situation and event overall what is in general a part of marketing mixture. The second ...
Stružková, Tereza
2014-01-01
The main objective of this thesis is based on theoretical knowledge and analysis of the actual implementation event action in congress centre of 4*hotel. Asesment of importance, correctnesand effectivess of the vatious procedures of organizin events and create new complete schematic principle of organizin events Implementation actions will be considered from two sides – from side of the company organizer and from the side of event managment coordinator. All the outputs of these two aspect ...
Earthquake statistics inferred from plastic events in soft-glassy materials
Benzi, Roberto; Toschi, Federico; Trampert, Jeannot
2016-01-01
We propose a new approach for generating synthetic earthquake catalogues based on the physics of soft glasses. The continuum approach produces yield-stress materials based on Lattice-Boltzmann simulations. We show that, if the material is stimulated below yield stress, plastic events occur, which ha
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 ...
Directory of Open Access Journals (Sweden)
Anaïs Khuong
Full Text Available The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by [Formula: see text] rad ([Formula: see text] data points. At the population scale, support inclination favors dispersal along uphill and downhill directions. An ant's decision making process is modeled using a version of the Boltzmann Walker model, which describes an ant's random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ([Formula: see text] segments, this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the [Formula: see text] incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines.
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.
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.
Polar-coordinate lattice Boltzmann modeling of compressible flows
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.
Expected energy-based restricted Boltzmann machine for classification.
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
Implementing the lattice Boltzmann model on commodity graphics hardware
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
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
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)
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)
Coupling of replica exchange simulations to a non-Boltzmann structure reservoir.
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.
DEFF Research Database (Denmark)
Bækgaard, Lars
2001-01-01
The purpose of this chapter is to discuss conceptual event modeling within a context of information modeling. Traditionally, information modeling has been concerned with the modeling of a universe of discourse in terms of information structures. However, most interesting universes of discourse...... are dynamic and we present a modeling approach that can be used to model such dynamics. We characterize events as both information objects and change agents (Bækgaard 1997). When viewed as information objects events are phenomena that can be observed and described. For example, borrow events in a library can...
DEFF Research Database (Denmark)
Bækgaard, Lars
2001-01-01
The purpose of this chapter is to discuss conceptual event modeling within a context of information modeling. Traditionally, information modeling has been concerned with the modeling of a universe of discourse in terms of information structures. However, most interesting universes of discourse...... are dynamic and we present a modeling approach that can be used to model such dynamics.We characterize events as both information objects and change agents (Bækgaard 1997). When viewed as information objects events are phenomena that can be observed and described. For example, borrow events in a library can...
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
Development of a coarse-grained water forcefield via multistate iterative Boltzmann inversion
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.
Comment on ‘A low-uncertainty measurement of the Boltzmann constant’
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.
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics.
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.
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
Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions
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...
Measuring the usefulness of hidden units in Boltzmann machines with mutual information.
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.
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...
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.
The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential
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.
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.
Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations
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.
Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion
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.
From Newton's law to the linear Boltzmann equation without cut-off
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...
Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow
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.
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
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.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
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.
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.
An H Theorem for Boltzmann's Equation for the Yard-Sale Model of Asset Exchange
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.
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.
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)
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.
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.
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.
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
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.
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids
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.
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
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.
Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation
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...
A Fokker-Planck model of the Boltzmann equation with correct Prandtl number
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.
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...
Plechatý, Josef
2012-01-01
This theses focused on Event management is divided into two parts. First part includes theoretical knowledge while the second part is strictly practical. The first part is focused on marketing, its importance and basic terms. The chapter about marketing is followed by marketing mix, which is shortly characterized and divided into advertisement, sales promotion, public relations and other elements of the communication mix. The last part is a detailed study of Event marketing which includes th...
Lattice Boltzmann Hydrodynamic and Transport Modeling of Everglades Mangrove Estuaries
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
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.
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.
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
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
A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects
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
Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow
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…
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
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
A New Regularization Mechanism for the Boltzmann Equation Without Cut-Off
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.
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
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).
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...
Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure
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.
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
Podolsky Electromagnetism at Finite Temperature: Implications on Stefan-Boltzmann Law
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.
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…
Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow
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
Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.
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.
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.
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.
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...
Models, Their Application, and Scientific Anticipation: Ludwig Boltzmann's Work as Tacit Knowing
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…
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...
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...
Simulation of three-phase displacement mechanisms using a 2D lattice-Boltzmann model
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
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
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
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...
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.
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.
Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation
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.
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...
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.
Myslivcová, Hana Bc.
2007-01-01
V práci je popsán teoretický postup při pořádání eventů, který vychází ze zásad projektového řízení. Tyto postupy jsou také aplikovány v praktické realizaci eventu. Následuje výzkum aktuálních trendů v event managementu a výzkum cílových skupin s pomocí dat MML/TGI.
DEFF Research Database (Denmark)
Munck Petersen, Rikke
The aim of the paper is first to discuss how horizon and scale can be understood, secondly how they differ and what they might have in common? If topography can be seen as a way of working with these relations experiences, creations and latencies? Thirdly if diagrams and diagrammatology can bring...... space formation - to stimulate and elaborate the event of conception and topological thinking....
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)
Numerical simulation of ski-jump jet motion using lattice Boltzmann method
Institute of Scientific and Technical Information of China (English)
无
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.
Why Boltzmann Brains Don't Fluctuate Into Existence From the De Sitter Vacuum
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...
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)
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.
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.
On the Stability of the Finite Difference based Lattice Boltzmann Method
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.
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.
Pore-scale lattice Boltzmann simulation of laminar and turbulent flow through a sphere pack
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...
Thermal Lattice Boltzmann Simulations for Vapor-Liquid Two-Phase Flows in Two Dimensions
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.
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...
Generalized Boltzmann equations for on-shell particle production in a hot plasma
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.
Evaluation of the Performance of the Hybrid Lattice Boltzmann Based Numerical Flux
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.
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.
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)
Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
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 $L^2(\\R^n)$.
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 ...
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...
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.
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
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.
Pseudopotential MRT lattice Boltzmann model for cavitation bubble collapse with high density ratio
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...
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.
Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory
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.
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...
Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluid flows
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.
Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula
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...
Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study
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 ...
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.
U.S. stock market interaction network as learned by the Boltzmann machine
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.
Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory.
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
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
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.
Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach
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.
Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework
Neumann, Philipp
2012-01-01
We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to fur-ther reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.
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.
Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains?
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.
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.
Regularized lattice Boltzmann model for a class of convection-diffusion equations.
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
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.
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...
Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows
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.
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.
Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology
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...
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
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...
Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings
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...
Beyond Poisson–Boltzmann: fluctuations and fluid structure in a self-consistent theory
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.
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...
Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time
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.
Causality, realism and the two strands of Boltzmann's legacy (1896 - 1936)
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...
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.
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
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...
Finite-difference lattice Boltzmann simulation on acoustics-induced particle deposition
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.
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
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...
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.
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.
Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow
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...
PDB2PQR: an automated pipeline for the setup of Poisson–Boltzmann electrostatics calculations
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...
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....
On the asymptotic behavior of a boltzmann-type price formation model
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.
Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow
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...
Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear
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...
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.
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
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.
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
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...
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.
Online Semi-Supervised Learning with Deep Hybrid Boltzmann Machines and Denoising Autoencoders
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...
Sliding periodic boundary conditions for lattice Boltzmann and lattice kinetic equations
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 ...
A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation
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.
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
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...
Steady detonation waves via the Boltzmann equation for a reacting mixture
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.
Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances
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.
Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances
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.
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.
A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation
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 ...
Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework
Neumann, Philipp
2015-09-01
© 2014 Elsevier Inc. All rights reserved. We present a dynamically adaptive Lattice Boltzmann (LB) implementation for solving the shallow water equations (SWEs). Our implementation extends an existing LB component of the Peano framework. We revise the modular design with respect to the incorporation of new simulation aspects and LB models. The basic SWE-LB implementation is validated in different breaking dam scenarios. We further provide a numerical study on stability of the MRT collision operator used in our simulations.
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.
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.
Event Index - a LHCb Event Search System
Ustyuzhanin, Andrey; Kazeev, Nikita; Redkin, Artem
2015-01-01
LHC experiments generate up to $10^{12}$ events per year. This paper describes Event Index - an event search system. Event Index's primary function is quickly selecting subsets of events from a combination of conditions, such as the estimated decay channel or stripping lines output. Event Index is essentially Apache Lucene optimized for read-only indexes distributed over independent shards on independent nodes.
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).
On the Self-Consistent Event Biasing Schemes for Monte Carlo Simulations of Nanoscale MOSFETs
Islam, Sharnali; Ahmed, Shaikh
2009-01-01
Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the calculation of terminal current. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. After presenting a brief overview on the Monte Carlo technique for solving the Boltzmann transport equation, the basic steps of deriving the approach in presence of both the initial and the boundary conditions have been discussed. In the derivation, the linearity of the transport problem has been utilized first, where Coulomb forces between the carriers are initially neglected. The generalization of the approach for Hartree carriers has been established in the iterative procedure of coupling with the Poisson equation. It is shown that the weight of the particles, as obtained by biasing of the Boltzmann equation, survive...
Modeling flue pipes: Subsonic flow, lattice Boltzmann, and parallel distributed computers
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.
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.
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.
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)
Entropic Lattice Boltzmann Methods for Fluid Mechanics: Thermal, Multi-phase and Turbulence
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:
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Fokker-Planck Equation for Boltzmann-type and Active Particles transfer probability approach
Trigger, S A
2002-01-01
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is proved for the velocity-dependent friction and diffusion coefficients. For non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The collecting part of the ion drag force in a dusty plasma, arising...
Energy Technology Data Exchange (ETDEWEB)
Ferretti, C.; Bruzzone, L. [Techint Italimpianti, Milan (Italy)
2000-06-01
The Petacalco Marine terminal on the Pacific coast in the harbour of Lazaro Carclenas (Michoacan) in Mexico, provides coal to the thermoelectric power plant at Pdte Plutarco Elias Calles in the port area. The plant is being converted from oil to burn coal to generate 2100 MW of power. The article describes the layout of the terminal and equipment employed in the unloading, coal stacking, coal handling areas and the receiving area at the power plant. The contractor Techint Italimpianti has developed a software system, MHATIS, for marine terminal management which is nearly complete. The discrete event simulator with its graphic interface provides a real-type decision support system for simulating changes to the terminal operations and evaluating impacts. The article describes how MHATIS is used. 7 figs.
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca
2013-01-01
The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently
Randles, Amanda Elizabeth
Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable
2000-01-01
as Imperial College, the Royal Albert Hall, the Royal College of Art, the Natural History and Science Museums and the Royal Geographical Society. Under the heading `Shaping the future together' BA2000 will explore science, engineering and technology in their wider cultural context. Further information about this event on 6 - 12 September may be obtained from Sandra Koura, BA2000 Festival Manager, British Association for the Advancement of Science, 23 Savile Row, London W1X 2NB (tel: 0171 973 3075, e-mail: sandra.koura@britassoc.org.uk ). Details of the creating SPARKS events may be obtained from creating.sparks@britassoc.org.uk or from the website www.britassoc.org.uk . Other events 3 - 7 July, Porto Alegre, Brazil VII Interamerican conference on physics education: The preparation of physicists and physics teachers in contemporary society. Info: IACPE7@if.ufrgs.br or cabbat1.cnea.gov.ar/iacpe/iacpei.htm 27 August - 1 September, Barcelona, Spain GIREP conference: Physics teacher education beyond 2000. Info: www.blues.uab.es/phyteb/index.html
Energy Technology Data Exchange (ETDEWEB)
Ortega J, R.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: roj@correo.azc.uam.mx
2003-07-01
There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S{sub 4} with expansions of the dispersion cross sections until P{sub 3} order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)
Energy Technology Data Exchange (ETDEWEB)
Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr; Noutchegueme, Norbert, E-mail: nnoutch@yahoo.fr [Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)
2015-01-15
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
International Nuclear Information System (INIS)
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
Ayissi, Raoul Domingo; Noutchegueme, Norbert
2015-01-01
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
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
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
International Nuclear Information System (INIS)
To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms. (paper)
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2014-05-01
We study the coupling between hydraulic and electric flows in a porous medium at small scale using the Lattice Boltzmann method. This method is a computational fluid dynamics technique that is used for advection and diffusion modeling. We implement a coupled Lattice Boltzmann algorithm that solves both the mass transport and the electric field arising from charges displacements. The streaming potential and electroosmosis phenomena occur in a variety of situations and derive from this coupling. We focus on the streaming potential which is described using the ratio between the created potential difference and the applied pressure gradient. The streaming potential is assumed to be a linear function of the fluid conductivity, but experimental results highlight anomalous behaviors at low and high salinity. We try to account for them by setting extreme conditions that are likely to generate non-linearities. Several pore radii are tested so as to determine what is the effect of a radius that is comparable to the Debye length, the screening length of the electric potential, due to the ions in the electrolyte. The volumetric integral of the electrical current is calculated for comparison with the 2D simulations. High values of zeta potential are tested to verify if the discrepancy regarding the theoretical result is concentration-dependent. We try to include a surface conductivity term in the coefficient formulation. Some tests including a rugosity on the channel walls are performed. All of these attempts show a normal behaviour of the streaming potential at high salinity. We observe a decrease of the ratio at low conductivity, showing that this ratio is modified when the pore radius becomes negligible compared with the Debye length, which is physically meaningful in little pores at low concentrations. References : S. Pride. Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50 : 15678-15696, 1994. D. A. Wolf
Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems
Energy Technology Data Exchange (ETDEWEB)
Uddin, Rizwan
2012-01-01
This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.
Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition
Institute of Scientific and Technical Information of China (English)
ZHANG Jun; TAO Rui-Bao
2002-01-01
Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and set up adata base of free energy calculated by means of Tao-Sheng Lin's extended molecular field theory that can explain theexperiments of the equilibrium properties of nematic liquid crystal very well. Then we use the free energy method oflattice Boltzmann developed by Oxford group to study the phase decomposition, pattern formation in the flow of theliquid crystal near transition temperature.
Cyclic Heating-Annealing and Boltzmann Distribution of Free Energies in a Spin-Glass System
Institute of Scientific and Technical Information of China (English)
ZHOU Hai-Jun
2007-01-01
Ergodicity of a spin-glass is broken at low temperatures; the system is trapped in one of many ergodic configurational domains. Transitions between different ergodic domains are achievable through a heating-annealing procedure. If this experiment is repeated infinite times, all ergodic configurational domains will be visited with frequences that decreasing exponentially with their free energies. The mean free energy density of a spin-glass system on a random graph is calculated based on this free energy Boltzmann distribution in the present work, by means of the cavity approach.
Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method
Lycett-Brown, D.; Luo, K. H.; Liu, R.; Lv, P.
2014-01-01
Three-dimensional binary droplet collisions are studied using a multiphase cascaded lattice Boltzmann method (LBM). With this model it is possible to simulate collisions with a Weber number of up to 100 and a Reynolds number of up to 1000, at a liquid to gas density ratio of over 100. This is made possible by improvements to the collision operator of the LBM. The cascaded LBM in three dimensions is introduced, in which additional relaxation rates for higher order moments, defined in a co-movi...
GPU phase-field lattice Boltzmann simulations of growth and motion of a binary alloy dendrite
Takaki, T.; Rojas, R.; Ohno, M.; Shimokawabe, T.; Aoki, T.
2015-06-01
A GPU code has been developed for a phase-field lattice Boltzmann (PFLB) method, which can simulate the dendritic growth with motion of solids in a dilute binary alloy melt. The GPU accelerated PFLB method has been implemented using CUDA C. The equiaxed dendritic growth in a shear flow and settling condition have been simulated by the developed GPU code. It has been confirmed that the PFLB simulations were efficiently accelerated by introducing the GPU computation. The characteristic dendrite morphologies which depend on the melt flow and the motion of the dendrite could also be confirmed by the simulations.
On measure solutions of the Boltzmann equation, part I: Moment production and stability estimates
Lu, Xuguang; Mouhot, Clément
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of weak measure solutions, with and without angular cutoff on the collision kernel; the proof in particular makes use of an approximation argument based on the Mehler transform. Moment production estimates in the usual form and in the exponential form are obtained for these solutions. Finally for the Grad angular cutoff, we also establish uniqueness and strong stability estimate on these solutions.
Field-wide flow simulation in fractured porous media within lattice Boltzmann framework
Benamram, Z.; Tarakanov, A.; Nasrabadi, H.; Gildin, E.
2016-10-01
In this paper, a generalized lattice Boltzmann model for simulating fluid flow in porous media at the representative volume element scale is extended towards applications of hydraulically and naturally fractured reservoirs. The key element within the model is the development of boundary conditions for a vertical well and horizontal fracture with minimal node usage. In addition, the governing non-dimensional equations are derived and a new set of dimensionless numbers are presented for the simulation of a fractured reservoir system. Homogenous and heterogeneous vertical well and fracture systems are simulated and verified against commercial reservoir simulation suites. Results are in excellent agreement to analytical and finite difference solutions.
Bounds for the state-modulated resolvent of a linear Boltzmann generator
Clark, Jeremy
2011-01-01
We study a generalized resolvent for the generator of a Markovian semigroup. The Markovian generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential and colliding elastically with particles from an ideal background gas. We obtain bounds for the state-modulated resolvent which are relevant in the regime where the mass ratio between the test particle and a particle from the gas is large. These bounds relate to the typical amount of time that the particle spends in different regions of phase space before arriving to a region around the origin.
Solution Poisson-Boltzmann equation: Application in the Human Neuron Membrane
Soares, M A G; Cortez, C M
2008-01-01
With already demonstrated in previous work the equations that describe the space dependence of the electric potential are determined by the solution of the equation of Poisson-Boltzmann. In this work we consider these solutions for the membrane of the human neuron, using a model simplified for this structure considering the distribution of electrolytes in each side of the membrane, as well as the effect of glycocalyx and the lipidic bilayer. It was assumed that on both sides of the membrane the charges are homogeneously distributed and that the potential depends only on coordinate z.
A novel protocol for linearization of the Poisson-Boltzmann equation
Tsekov, R
2014-01-01
A new protocol for linearization of the Poisson-Boltzmann equation is proposed and the resultant electrostatic equation coincides formally with the Debye-Huckel equation, the solution of which is well known for many electrostatic problems. The protocol is examined on the example of electrostatically stabilized nano-bubbles and it is shown that stable nano-bubbles could be present in aqueous solutions of anionic surfactants near the critical temperature, if the surface potential is constant. At constant surface charge non nano-bubbles could exist.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan
2005-01-01
@@ The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in awide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation arepresented in detail. The flow separation zones revealed with increase of Reynolds number are located in theareas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particularblood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmannmethod is adaptive to simulating the flow in larger vessels under a high Reynolds number.
Ternary Free Energy Lattice Boltzmann Model with Tunable Surface Tensions and Contact Angles
Semprebon, Ciro; Kusumaatmaja, Halim
2015-01-01
We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model here presented here can be extended to include an arbitrary number of fluid components.
Lattice Boltzmann Simulation of Collision between 2D Circular Particles Suspension in Couette Flow
Directory of Open Access Journals (Sweden)
Li-Zhong Huang
2013-01-01
Full Text Available Collision between 2D circular particles suspension in Couette flow is simulated by using multiple-relaxation-time based lattice Boltzmann and direct forcing/fictitious domain method in this paper. The patterns of particle collisions are simulated and analyzed in detail by changing the velocity of top and bottom walls in the Couette flow. It can be seen from the simulation results that, while the velocity is large enough, the number of collisions between particles will change little as this velocity varies.
Simulation of residual oil displacement in a sinusoidal channel with the lattice Boltzmann method
Otomo, Hiroshi; Hazlett, Randy; Li, Yong; Staroselsky, Ilya; Zhang, Raoyang; Chen, Hudong
2016-01-01
We simulate oil slug displacement in a sinusoidal channel in order to validate computational models and algorithms for multi-component flow. This case fits in the gap between fully realistic cases characterized by complicated geometry and academic cases with simplistic geometry. Our computational model is based on the lattice Boltzmann method and allows for variation of physical parameters such as wettability and viscosity. The effect of variation of model parameters is analyzed, in particular via comparison with analytical solutions. We discuss the requirements for accurate solution of the oil slug displacement problem.
A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW
Institute of Scientific and Technical Information of China (English)
YANG Fan; LIU Shu-hong; WU Yu-lin; TANG Xue-lin
2005-01-01
In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.
On the completeness of the multigroup eigenfunctions set of a reactor system Boltzmann operator
International Nuclear Information System (INIS)
An example is given, which illustrates how the set of the eigenfunctions shifts from incompleteness to completeness when a coupling relationship is established between the spectrum of the neutrons produced by fission and the energy of the neutrons which generate the fissions. The proposed method allows one to complete the set of eigenfunctions of the Boltzmann operator in the multigroup case. That, in principle, enlarges the possibility to apply the SM, Standard Method, and the GSM, Generalized Standard Method, to any problem in reactor physics, regardless of the number of energy groups. (author)
Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear
Xu, A; Xu, Aiguo
2003-01-01
We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required to obtain a triangular profile is inversely proportional to the viscosity and proportional to the square of the size of the system. We find that the same behaviour also occurs for binary mixtures, for any component ratio in the mixture and independently from the time when shear flow is switched on during phase separation.
A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE- DIMENSIONAL DROP IMPACT ON A LIQUID FILM
Institute of Scientific and Technical Information of China (English)
SHI Zi-yuan; YAN Yong-hua; YANG Fan; QIAN Yue-hong; HU Guo-hui
2008-01-01
A single-phase free surface tracking model based on the Lattice Boltzmann Method (LBM), which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.
Lattice Boltzmann method to study the contraction of a viscous ligament
Srivastava, Sudhir; Jeurissen, Roger; Wijshoff, Herman; Toschi, Federico
2013-01-01
We employ a recently formulated axisymmetric version of the multiphase Shan-Chen (SC) lattice Boltzmann method (LBM) [Srivastava et al, in preparation (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ) approximation model [T. Driessen and R. Jeurissen, IJCFD {\\bf 25}, 333 (2011)]. We compare the retraction dynamics of the tail-end of the liquid ligament from the LBM simulation, the SJ model, Flow3D simulations and a simple model based on the force balance (FB). We find good agreement between the theoretical prediction (FB), the SJ model, and the LBM simulations.
Lattice Boltzmann Method used for the aircraft characteristics computation at high angle of attack
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Traditional Finite Volume Method(FVM)and Lattice Boltzmann Method(LBM)are both used to compute the high angle attack aerodynamic characteristics of the benchmark aircraft model named CT-1.Even though the software requires flow on the order of Ma<0.4,simulation at Ma=0.5 is run in PowerFLOW after theoretical analysis.The consistency with the wind tunnel testing is satisfied,especially for the LBM which can produce perfect results at high angle attack.PowerFLOW can accurately capture the detail of flows because it is inherently time-dependent and parallel and suits large-scale computation very well.
High order numerical methods for the space non-homogeneous Boltzmann equation
International Nuclear Information System (INIS)
In this paper we present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. The transport is solved by a third order accurate (in space) positive and flux conservative (PFC) method. The collision step is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity, coupled with several high order integrators in time. Strang splitting is used to achieve second order accuracy in space and time. Several numerical tests illustrate the properties of the methods
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential
New Fundamental Light Particle and Breakdown of Stefan-Boltzmann's Law
Directory of Open Access Journals (Sweden)
Samoilov V.
2011-04-01
Full Text Available Recently, we predicted the existence of fundamental particles in Nature, neutral Light Particles with spin 1 and rest mass m = 1.8 x 10^{-4} m_e, in addition to electrons, neutrons and protons. We call these particles Light Bosons because they create electromagnetic field which represents Planck's gas of massless photons together with a gas of Light Particles in the condensate. Such reasoning leads to a breakdown of Stefan-Boltzmann's law at low temperature. On the other hand, the existence of new fundamental neutral Light Particles leads to correction of such physical concepts as Bose-Einstein condensation of photons, polaritons and exciton polaritons.
Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
Morimoto, Yoshinori; Sakamoto, Shota
2016-10-01
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyze the collisional term of the equation, a Chemin-Lerner norm is combined with a non-isotropic norm with respect to a velocity variable, which yields an a priori estimate for an energy estimate. Together with local existence following from commutator estimates and the Hahn-Banach extension theorem, the desired solution is obtained.
Topology optimization of unsteady flow problems using the lattice Boltzmann method
DEFF Research Database (Denmark)
Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov
2016-01-01
This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems....... The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time......-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves....
Numerical solution of the Boltzmann equation for the shock wave in a gas mixture
Raines, A A
2014-01-01
We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use the Conservative Projection Method developed by F.G. Tscheremissine which we extended to gas mixtures in cylindrical coordinates. The transition from the upstream to downstream uniform state is presented by macroscopic values and distribution functions. The obtained results were compared with numerical and experimental results of other authors.
Riaud, Antoine; Zhao, Shufang; Wang, Kai; Cheng, Yi; Luo, Guangsheng
2014-05-01
Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds. PMID:25353915
Directory of Open Access Journals (Sweden)
Javier A. Dottori
2015-01-01
Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.
Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked compressible fluids,a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system.The unnecessity of the modification for systems under strong shock is analyzed.The model ...
Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas
Brewer, Jasmine; Mendoza, Miller; Young, Ryan E.; Romatschke, Paul
2016-01-01
We present fully nonlinear dissipative fluid dynamics simulations of a strongly interacting trapped two-dimensional Fermi gas using a lattice Boltzmann algorithm. We are able to simulate nonharmonic trapping potentials, temperature-dependent viscosities, as well as a discretized version of the ballistic (noninteracting) behavior. Our approach lends itself to direct comparison with experimental data, opening up the possibility of a precision determination of transport coefficients in the strongly interacting Fermi gas. Furthermore, we predict the presence of a strongly damped ("nonhydrodynamic") component in the quadrupole mode, which should be observable experimentally.
Molnár, Etele; Rischke, Dirk H
2016-01-01
In Moln\\'ar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.
Directory of Open Access Journals (Sweden)
Hose Rod
2009-10-01
Full Text Available Abstract Background Systolic blood flow has been simulated in the abdominal aorta and the superior mesenteric artery. The simulations were carried out using two different computational hemodynamic methods: the finite element method to solve the Navier Stokes equations and the lattice Boltzmann method. Results We have validated the lattice Boltzmann method for systolic flows by comparing the velocity and pressure profiles of simulated blood flow between methods. We have also analyzed flow-specific characteristics such as the formation of a vortex at curvatures and traces of flow. Conclusion The lattice Boltzmann Method is as accurate as a Navier Stokes solver for computing complex blood flows. As such it is a good alternative for computational hemodynamics, certainly in situation where coupling to other models is required.
Harting, J; Coveney, P V; Harting, Jens; Venturoli, Maddalena; Coveney, Peter V.
2003-01-01
Well designed lattice-Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large scale three-dimensional lattice-Boltzmann simulation of binary immiscible fluid flows through a porous medium derived from digitised x-ray microtomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering and we describe our implementation of steering within the lattice-Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large scale simulations benefit from the new concept of capability computing, designed to prioritise the execution of big jobs on major supercomputing resources. The a...
Event Index - an LHCb Event Search System
Ustyuzhanin, Andrey
2015-01-01
During LHC Run 1, the LHCb experiment recorded around 1011 collision events. This paper describes Event Index | an event search system. Its primary function is to quickly select subsets of events from a combination of conditions, such as the estimated decay channel or number of hits in a subdetector. Event Index is essentially Apache Lucene [1] optimized for read-only indexes distributed over independent shards on independent nodes.
Event Index - an LHCb Event Search System
Ustyuzhanin, Andrey; Artemov, Alexey; Kazeev, Nikita; Redkin, Artem
2015-01-01
During LHC Run 1, the LHCb experiment recorded around $10^{11}$ collision events. This paper describes Event Index - an event search system. Its primary function is to quickly select subsets of events from a combination of conditions, such as the estimated decay channel or number of hits in a subdetector. Event Index is essentially Apache Lucene optimized for read-only indexes distributed over independent shards on independent nodes.
Extracting Event Dynamics from Event-by-Event Analysis
Fu, Jinghua; Liu, Lianshou
2003-01-01
The problem of eliminating the statistical fluctuations and extracting the event dynamics from event-by-event analysis is discussed. New moments $G_p$ (for continuous distribution), and $G_{q,p}$ (for anomalous distribution) are proposed, which are experimentally measurable and can eliminate the Poissonian type statistical fluctuations to recover the dynamical moments $C_p$ and $C_{q,p}$. In this way, the dynamical distribution of the event-averaged transverse momentum $\\bar{\\pt}$ can be extr...
Gastrointestinal events with clopidogrel
DEFF Research Database (Denmark)
Grove, Erik Lerkevang; Würtz, Morten; Schwarz, Peter;
2013-01-01
Clopidogrel prevents cardiovascular events, but has been linked with adverse gastrointestinal (GI) complications, particularly bleeding events.......Clopidogrel prevents cardiovascular events, but has been linked with adverse gastrointestinal (GI) complications, particularly bleeding events....
Marenduzzo, D; Orlandini, E; Cates, M E; Yeomans, J M
2007-09-01
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently "extensile" rods, in the case of flow-aligning liquid crystals, and for sufficiently "contractile" ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of "convection rolls." These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics. PMID:17930285
Simulation of arrested salt wedges with a multi-layer Shallow Water Lattice Boltzmann model
Prestininzi, P.; Montessori, A.; La Rocca, M.; Sciortino, G.
2016-10-01
The ability to accurately and efficiently model the intrusion of salt wedges into river beds is crucial to assay its interaction with human activities and the natural environment. We present a 2D multi-layer Shallow Water Lattice Boltzmann (SWLB) model able to predict the salt wedge intrusion in river estuaries. The formulation usually employed for the simulation of gravity currents is here equipped with proper boundary conditions to handle both the downstream seaside outlet and the upstream river inlet. Firstly, the model is validated against highly accurate semi-analytical solutions of the steady state 1D two-layer Shallow Water model. Secondly, the model is applied to a more complex, fully 3D geometry, to assess its capability to handle realistic cases. The simple formulation proposed for the shear interlayer stress is proven to be consistent with the general 3D viscous solution. In addition to the accuracy, the model inherits the efficiency of the Lattice Boltzmann approach to fluid dynamics problems.
Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”
Energy Technology Data Exchange (ETDEWEB)
Hele, Timothy J. H.; Willatt, Michael J.; Muolo, Andrea; Althorpe, Stuart C., E-mail: sca10@cam.ac.uk [Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
2015-04-07
We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or “classical Wigner approximation”) results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their “Matsubara” values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ{sup 2} at ħ{sup 0} (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting “Matsubara” dynamics is inherently classical (since all terms O(ħ{sup 2}) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.
Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh
Patil, Dhiraj V.; Lakshmisha, K. N.
2009-08-01
A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.
A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation
Directory of Open Access Journals (Sweden)
José Colmenares
2014-01-01
Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.
International Nuclear Information System (INIS)
We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M ☉ progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method
Energy Technology Data Exchange (ETDEWEB)
Nagakura, Hiroki [Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502 (Japan); Sumiyoshi, Kohsuke [Numazu College of Technology, Ooka 3600, Numazu, Shizuoka 410-8501 (Japan); Yamada, Shoichi [Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan)
2014-10-01
We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M {sub ☉} progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method.
Simulation of three-component fluid flows using the multiphase lattice Boltzmann flux solver
Shi, Y.; Tang, G. H.; Wang, Y.
2016-06-01
In this work, we extend the multiphase lattice Boltzmann flux solver, which was proposed in [1] for simulating incompressible flows of binary fluids based on two-component Cahn-Hilliard model, to three-component fluid flows. In the present method, the multiphase lattice Boltzmann flux solver is applied to solve for the flow field and the three-component Cahn-Hilliard model is used to predict the evolution of the interfaces. The proposed method is first validated through the classical problem of simulation of partial spreading of a liquid lens between the other two components. Numerical results of interface shapes and contact angles agree well with theoretical solutions. After that, to further demonstrate the capability of the present method, several numerical examples of three-component fluid flows are presented, including a bubble rising across a fluid-fluid interface, single droplet falling through a fluid-fluid interface, the collision-coalescence of two droplets, and the non-contact collision of two droplets. It is shown that the present method can successfully handle complex interactions among three components.
Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.
2016-04-01
In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.
Perturbative and non-perturbative aspects non-Abelian Boltzmann-Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Boedeker, Dietrich. E-mail: bodeker@physik.uni-bielefeld.de
2002-12-30
We study the Boltzmann-Langevin equation which describes the dynamics of hot Yang-Mills fields with typical momenta of order of the magnetic screening scale g{sup 2}T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/g){sup -1}. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g{sup 2}T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann-Langevin equation.
Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy
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...
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.
Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls.
Šamaj, Ladislav; Trizac, Emmanuel
2016-01-01
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system). PMID:26871116
An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions
Energy Technology Data Exchange (ETDEWEB)
Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe [Laboratoire Informatique Signal et Image de la Côte d' Opale, 50 rue Ferdinand Buisson, 62100 Calais (France); Université du Littoral Côte d' Opale, 1 place de l' Yser, 59140, Dunkerque (France); Association INNOCOLD, MREI 1, 145 (France)
2014-10-06
Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan and Chen (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence to isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented. Multi-range interactions have been used for SC model, but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong and Cheng. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.
Enhancing Computational Precision for Lattice Boltzmann Schemes in Porous Media Flows
Directory of Open Access Journals (Sweden)
Farrel Gray
2016-02-01
Full Text Available We reassess a method for increasing the computational accuracy of lattice Boltzmann schemes by a simple transformation of the distribution function originally proposed by Skordos which was found to give a marginal increase in accuracy in the original paper. We restate the method and give further important implementation considerations which were missed in the original work and show that this method can in fact enhance the precision of velocity field calculations by orders of magnitude and does not lose accuracy when velocities are small, unlike the usual LB approach. The analysis is framed within the multiple-relaxation-time method for porous media flows, however the approach extends directly to other lattice Boltzmann schemes. First, we compute the flow between parallel plates and compare the error from the analytical profile for the traditional approach and the transformed scheme using single (4-byte and double (8-byte precision. Then we compute the flow inside a complex-structured porous medium and show that the traditional approach using single precision leads to large, systematic errors compared to double precision, whereas the transformed approach avoids this issue whilst maintaining all the computational efficiency benefits of using single precision.
A combined MPI-CUDA parallel solution of linear and nonlinear Poisson-Boltzmann equation.
Colmenares, José; Galizia, Antonella; Ortiz, Jesús; Clematis, Andrea; Rocchia, Walter
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 needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs. PMID:25013789
Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow
Huang, Rongzong
2016-01-01
In this work, a third-order Chapman-Enskog analysis of the multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for multiphase flow is performed for the first time. The leading terms on the interaction force, consisting of an anisotropic and an isotropic term, are successfully identified in the third-order macroscopic equation recovered by the lattice Boltzmann equation (LBE), and then new mathematical insights into the pseudopotential LB model are provided. For the third-order anisotropic term, numerical tests show that it can cause the stationary droplet to become out-of-round, which suggests the isotropic property of the LBE needs to be seriously considered in the pseudopotential LB model. By adopting the classical equilibrium moment or setting the so-called "magic" parameter to 1/12, the anisotropic term can be eliminated, which is found from the present third-order analysis and also validated numerically. As for the third-order isotropic term, when and only when it is considered, a...
Relaxation of hot and massive tracers using numerical solutions of the Boltzmann equation.
Khurana, Saheba; Thachuk, Mark
2016-03-14
A numerical method using B-splines is used to solve the linear Boltzmann equation describing the energy relaxation of massive tracer particles moving through a dilute bath gas. The smooth and rough hard sphere and Maxwell molecule models are used with a variety of mass ratios and initial energies to test the capability of the numerical method. Massive tracers are initialized with energies typically found in energy loss experiments in mass spectrometry using biomolecules. The method is also used to examine the applicability of known expressions for the kinetic energy decay from the Fokker-Planck equation for the Rayleigh gas, where we find that results are generally good provided that the initial energy is properly bounded. Otherwise, the energy decay is not constant and a more complex behaviour occurs. The validity of analytical expressions for drag coefficients for spherical particles under specular and diffuse scattering is also tested. We find such expressions are generally good for hard spheres but cannot account, as expected, for the softer repulsive walls of the Maxwell (and real) molecules. Overall, the numerical method performed well even when tracers more than 400 times as massive as the bath were initialized with energies very far from equilibrium. This is a range of applicability beyond many of the standard methods for solving the Boltzmann equation. PMID:26979675
Study on the melting process of phase change materials in metal foams using lattice Boltzmann method
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A thermal lattice Boltzmann model is developed for the melting process of phase change material (PCM) embedded in open-cell metal foams. Natural convection in the melt PCM is considered. Under the condition of local thermal non-equilibrium between the metal matrix and PCM, two evolution equations of temperature distribution function are pre-sented through selecting an equilibrium distribution function and a nonlinear source term properly. The enthalpy-based method is employed to copy with phase change problem. Melting process in a cavity of the metal foams is simulated using the present model. The melting front locations and the temperature distributions in the metal foams filled with PCM are obtained by the lattice Boltzmann method. The effects of the porosity and pore size on the melting are also investigated and discussed. The re-sults indicate that the effects of foam porosity play important roles in the overall heat transfer. For the lower porosity foams, the melting rate is comparatively greater than the higher porosity foams, due to greater heat conduction from metal foam with high heat conductivity. The foam pore size has a limited effect on the melting rate due to two counteracting effects between conduction and convection heat transfer.
deLisle, Lee
2009-01-01
"Creating Special Events" is organized as a systematic approach to festivals and events for students who seek a career in event management. This book looks at the evolution and history of festivals and events and proceeds to the nuts and bolts of event management. The book presents event management as the means of planning, organizing, directing,…
Dig-event: let's socialize around events
Zhao, Zhenzhen; Liu, Ji; Crespi, Noel
2012-01-01
International audience Traditional social networks socialize around the contents that have uploaded to these sites and discover interesting contents uploaded by others. In this demo we aim to explore the idea of activity-oriented social networks. We design a novel social networking site called Dig-Event (Do-it-together Event), where people are able to share events through calendar, while discover interesting events shared by others. Our demo has been inspired by previous research on calend...
Angeli, C.; Cimiraglia, R.; Dallo, F.; Guareschi, R.; Tenti, L.
2013-01-01
The dependence on the temperature of the population of the ith state, Pi, in the Boltzmann distribution is analyzed by studying its derivative with respect to the temperature, T. A simple expression is found, involving Pi, the energy of the state, Ei, and the average energy, âŸ̈EâŸ©. This relation i
Salomons, E.M.; Lohman, W.J.A.; Zhou, H.
2016-01-01
Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-fi
Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems
Directory of Open Access Journals (Sweden)
Emre eNeftci
2014-01-01
Full Text Available Restricted Boltzmann Machines (RBMs and Deep Belief Networks have been demonstrated to perform efficiently in variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The reverberating activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP carries out the weight updates in an online, asynchronous fashion.We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.
Institute of Scientific and Technical Information of China (English)
XIA Yong; LU De-Tang; LIU Yang; XU You-Sheng
2009-01-01
The multiple-relaxation-time lattice Boltzmann method (MRT-LBM) is implemented to numerically simulate the cross flow over a longitudinal vibrating circular cylinder.This research is carried out on a three-dimensional (3D) finite cantilevered cylinder to investigate the effect of forced vibration on the wake characteristics and the 319 effect of a cantilevered cylinder.To meet the accuracy of this method,the present calculation is carried out at a low Reynolds number Re = 100,as well as to make the vibration obvious,we make the vibration strong enough.The calculation results indicate that the vibration has significant influence on the wake characteristics. When the vibrating is big enough,our early works show that the 2D vortex shedding would be locked up by vibration.Contrarily,this phenomenon would not appear in the present 313 case because of the end effect of the cantilevered cylinder.
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; LIU Yang; HUANG Guo-Xiang
2004-01-01
@@ Digital images (DI) and lattice Boltzmann method (LBM) are used to characterize the threshold dynamic parameters of porous media. Two-dimensional representations of the porous structure are reconstructed from segmentation of digital images obtained from a series of tiny samples. The threshold pressure gradients and threshold Péclet numbers are researched on seven test samples by using LBM. Numerical results are in agreement with that obtained by integrating Darcy's law. The results also indicate that fluids can flow through porous media only if the fluid force is large enough to overcome threshold pressure gradient in porous media. One synthetic case is used to further illustrate the applicability of the proposed technique. In addition, the dynamical rules in our model are local, therefore it can be run on parallel computers with well computational efficiency.
A dynamic mesh refinement technique for Lattice Boltzmann simulations on octree-like grids
Neumann, Philipp
2012-04-27
In this contribution, we present our new adaptive Lattice Boltzmann implementation within the Peano framework, with special focus on nanoscale particle transport problems. With the continuum hypothesis not holding anymore on these small scales, new physical effects - such as Brownian fluctuations - need to be incorporated. We explain the overall layout of the application, including memory layout and access, and shortly review the adaptive algorithm. The scheme is validated by different benchmark computations in two and three dimensions. An extension to dynamically changing grids and a spatially adaptive approach to fluctuating hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest, is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated separately in simulations of particle transport problems. The application of this scheme to an oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such setups. © 2012 Springer-Verlag.
Sailfish: a flexible multi-GPU implementation of the lattice Boltzmann method
Januszewski, Michal
2013-01-01
We present Sailfish, an open source fluid simulation package implementing the lattice Boltzmann method (LBM) on modern Graphics Processing Units (GPUs) using CUDA/OpenCL. We take a novel approach to GPU code implementation and use run-time code generation techniques and a high level programming language (Python) to achieve state of the art performance, while allowing easy experimentation with different LBM models and tuning for various types of hardware. We discuss the general design principles of the code, scaling to multiple GPUs in a distributed environment, as well as the GPU implementation and optimization of many different LBM models, both single component (BGK, MRT, ELBM) and multicomponent (Shan-Chen, free energy). The paper also presents results of performance benchmarks spanning the last three NVIDIA GPU generations (Tesla, Fermi, Kepler), which we hope will be useful for researchers working with this type of hardware and similar codes.
A shallow water model for the propagation of tsunami via Lattice Boltzmann method
International Nuclear Information System (INIS)
An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory
Demand Forecasting at Low Aggregation Levels using Factored Conditional Restricted Boltzmann Machine
DEFF Research Database (Denmark)
Mocanu, Elena; Nguyen, Phuong H.; Gibescu, Madeleine;
2016-01-01
approaches have been proposed in the literature. As an evolution of neural network-based prediction methods, deep learning techniques are expected to increase the prediction accuracy by allowing stochastic formulations and bi-directional connections between neurons. In this paper, we investigate a newly...... developed deep learning model for time series prediction, namely Factored Conditional Restricted Boltzmann Machine (FCRBM), and extend it for electrical demand forecasting. The assessment is made on the EcoGrid dataset, originating from the Bornholm island experiment in Denmark, consisting of aggregated......The electrical demand forecasting problem can be regarded as a nonlinear time series prediction problem depending on many complex factors since it is required at various aggregation levels and at high temporal resolution. To solve this challenging problem, various time series and machine learning...
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Zheng, Lin; Zhai, Qinglan
2014-01-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface fore (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter visa Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is also solved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and a two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then ...