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.
Stable Equilibrium Based on Lévy Statistics:A Linear Boltzmann Equation Approach
Barkai, Eli
2004-06-01
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, we consider stochastic collision models. The models are a generalization of the Rayleigh collision model, for a heavy one dimensional particle M interacting with ideal gas particles with a mass mlaw equilibrium. We show, under certain conditions, that the velocity distribution function of the heavy particle is Lévy stable, the Maxwellian distribution being a special case. We demonstrate our results with numerical examples. The relation of the power law equilibrium obtained here to thermodynamics is discussed. In particular we compare between two models: a thermodynamic and an energy scaling approaches. These models yield insight into questions like the meaning of temperature for power law equilibrium, and into the issue of the universality of the equilibrium (i.e., is the width of the generalized Maxwellian distribution functions obtained here, independent of coupling constant to the bath).
Serov, S A
2013-01-01
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.
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).
Distributional Monte Carlo Methods for the Boltzmann Equation
2013-03-01
become the first to possess non - Maxwellian distributions, and therefore become the only location where 112 collisions are required to be calculated... Maxwellian . . . . . . . . . . . . . . . . . 16 fMB Maxwell-Boltzmann Density . . . . . . . . . . . . . . . . . . . . . . . . 16 nMB Maxwell-Boltzmann...is equivalent to assuming that millions of actual particles all share the exact velocity vector. This assumption is non -physical in the sense that
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...
Lindner, Manfred
2007-01-01
Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by Kadanoff-Baym equations is severely restricted in th...
Boltzmann-Gibbs Distribution of Fortune and Broken Time-Reversible Symmetry in Econodynamics
Ao, P
2005-01-01
Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential distributions can be accommodated by it. The demonstration is based on a mathematical structure discovered during a study in gene regulatory network dynamics. Further possible analogy between equilibrium economy and thermodynamics is explored.
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.
Directory of Open Access Journals (Sweden)
Juan Frausto-Solis
2016-01-01
Full Text Available 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.
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 ...
The Boltzmann Equation for a Multi-species Mixture Close to Global Equilibrium
Briant, Marc; Daus, Esther S.
2016-12-01
We study the Cauchy theory for a multi-species mixture, where the different species can have different masses, in a perturbative setting on the three dimensional torus. The ultimate aim of this work is to obtain the existence, uniqueness and exponential trend to equilibrium of solutions to the multi-species Boltzmann equation in {L^1_vL^∞_x(m)}, where {m˜ (1+ |v|^k)} is a polynomial weight. We prove the existence of a spectral gap for the linear multi-species Boltzmann operator allowing different masses, and then we establish a semigroup property thanks to a new explicit coercive estimate for the Boltzmann operator. Then we develop an {L^2-L^∞} theory à la Guo for the linear perturbed equation. Finally, we combine the latter results with a decomposition of the multi-species Boltzmann equation in order to deal with the full equation. We emphasize that dealing with different masses induces a loss of symmetry in the Boltzmann operator which prevents the direct adaptation of standard mono-species methods (for example Carleman representation, Povzner inequality). Of important note is the fact that all methods used and developed in this work are constructive. Moreover, they do not require any Sobolev regularity and the {L^1_vL^∞_x} framework is dealt with for any {k > k_0}, recovering the optimal physical threshold of finite energy {k_0=2} in the particular case of a multi-species hard spheres mixture with the same masses.
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.
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.
Equilibrium Tail Distribution Due to Touschek Scattering
Energy Technology Data Exchange (ETDEWEB)
Nash,B.; Krinsky, S.
2009-05-04
Single large angle Coulomb scattering is referred to as Touschek scattering. In addition to causing particle loss when the scattered particles are outside the momentum aperture, the process also results in a non-Gaussian tail, which is an equilibrium between the Touschek scattering and radiation damping. Here we present an analytical calculation for this equilibrium distribution.
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.
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.
Liu, Q
2016-01-01
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding source terms into the temperature-based MRT-LB equations. Moreover, the discrete lattice effects are considered in the introduction of source terms into the temperature-based MRT-LB equations. The source terms accounting for the thermal non-equilibrium effects are simple and the model retains the inherent features of the standard LB method. Numerical results demonstrate that the proposed model can be served as an accura...
On equilibrium charge distribution above dielectric surface
Directory of Open Access Journals (Sweden)
Yu.V. Slyusarenko
2009-01-01
Full Text Available The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated. We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium distributions of charges and the electric field, which is generated by these charges in the system in the case of ideally plane dielectric surface, are obtained. The solution of electrostatic equations of the system under consideration in case of small spatial heterogeneities caused by the dielectric surface, is also obtained. These spatial inhomogeneities can be caused both by the inhomogeneities of the surface and by the inhomogeneous charge distribution upon it. In particular, the case of the "wavy" spatially periodic surface is considered taking into account the possible presence of the surface charges.
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.
Energy Distributions in Small Populations: Pascal versus Boltzmann
Kugel, Roger W.; Weiner, Paul A.
2010-01-01
The theoretical distributions of a limited amount of energy among small numbers of particles with discrete, evenly-spaced quantum levels are examined systematically. The average populations of energy states reveal the pattern of Pascal's triangle. An exact formula for the probability that a particle will be in any given energy state is derived.…
Bergeron, H.; Curado, E. M. F.; Gazeau, J. P.; Rodrigues, Ligia M. C. S.
2016-02-01
Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies is studied through three examples. The first one has the q-exponential as the generating function, the second one involves the modified Abel polynomials, and the third one has Hermite polynomials. We prove analytically that the Rényi entropy is extensive for these three cases, i.e., it is proportional (asymptotically) to the number n of events and that q-exponential and Hermite cases have also extensive Boltzmann-Gibbs. The Abel case is exceptional in the sense that its Boltzmann-Gibbs entropy is not extensive and behaves asymptotically as the square root of n. This result is obtained numerically and also confirmed analytically, under reasonable assumptions, by using a regularization of the beta function and its derivative. Probabilistic urn and genetic models are presented for illustrating this remarkable case.
Equilibrium of global amphibian species distributions with climate
DEFF Research Database (Denmark)
Munguía, Mariana; Rahbek, Carsten; Rangel, Thiago F.
2012-01-01
A common assumption in bioclimatic envelope modeling is that species distributions are in equilibrium with contemporary climate. A number of studies have measured departures from equilibrium in species distributions in particular regions, but such investigations were never carried out for a compl...
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.
Equilibrium of global amphibian species distributions with climate.
Munguía, Mariana; Rahbek, Carsten; Rangel, Thiago F; Diniz-Filho, Jose Alexandre F; Araújo, Miguel B
2012-01-01
A common assumption in bioclimatic envelope modeling is that species distributions are in equilibrium with contemporary climate. A number of studies have measured departures from equilibrium in species distributions in particular regions, but such investigations were never carried out for a complete lineage across its entire distribution. We measure departures of equilibrium with contemporary climate for the distributions of the world amphibian species. Specifically, we fitted bioclimatic envelopes for 5544 species using three presence-only models. We then measured the proportion of the modeled envelope that is currently occupied by the species, as a metric of equilibrium of species distributions with climate. The assumption was that the greater the difference between modeled bioclimatic envelope and the occupied distribution, the greater the likelihood that species distribution would not be at equilibrium with contemporary climate. On average, amphibians occupied 30% to 57% of their potential distributions. Although patterns differed across regions, there were no significant differences among lineages. Species in the Neotropic, Afrotropics, Indo-Malay, and Palaearctic occupied a smaller proportion of their potential distributions than species in the Nearctic, Madagascar, and Australasia. We acknowledge that our models underestimate non equilibrium, and discuss potential reasons for the observed patterns. From a modeling perspective our results support the view that at global scale bioclimatic envelope models might perform similarly across lineages but differently across regions.
Capitelli, M.; Colonna, G.; D’Ammando, G.; Laricchiuta, A.; Pietanza, L. D.
2017-03-01
Non-equilibrium vibrational distributions (vdf) and non-equilibrium electron energy distribution functions (eedf) in a nitrogen plasma at low pressure (mtorr) have been calculated by using a time-dependent plasma physics model coupled to the Boltzmann equation and heavy particle kinetics. Different case studies have been selected showing the non-equilibrium character of both vdf and eedf under discharge and post-discharge conditions in the presence of large concentrations of electrons. Particular attention is devoted to the electron-molecule resonant vibrational excitation cross sections acting in the whole vibrational ladder. The results in the post-discharge conditions show the interplay of superelastic vibrational and electronic collisions in forming structures in the eedf. The link between the present results in the mtorr afterglow regime with the existing eedf in the torr and atmospheric regimes is discussed.
Total variation approximation for quasi-equilibrium distributions, II
Barbour, A D
2011-01-01
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In an earlier paper, we gave biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute. In this paper, we consider conditions under which the quasi-stationary distribution, if it exists, need not be unique, but an apparent stochastic equilibrium can nonetheless be identified and computed; we call such a distribution a quasi-equilibrium distribution.
Equilibrium distribution of heavy quarks in fokker-planck dynamics
Walton; Rafelski
2000-01-01
We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We provide a complete characterization of the equilibrium distribution in terms of the drag and diffusion transport coefficients. We apply this analysis to charm quark dynamics in a thermal quark-gluon plasma for the case of collisional equilibration.
Boltzmann-Machine Learning of Prior Distributions of Binarized Natural Images
Obuchi, Tomoyuki; Koma, Hirokazu; Yasuda, Muneki
2016-11-01
Prior distributions of binarized natural images are learned by using a Boltzmann machine. According the results of this study, there emerges a structure with two sublattices in the interactions, and the nearest-neighbor and next-nearest-neighbor interactions correspondingly take two discriminative values, which reflects the individual characteristics of the three sets of pictures that we process. Meanwhile, in a longer spatial scale, a longer-range, although still rapidly decaying, ferromagnetic interaction commonly appears in all cases. The characteristic length scale of the interactions is universally up to approximately four lattice spacings ξ ≈ 4. These results are derived by using the mean-field method, which effectively reduces the computational time required in a Boltzmann machine. An improved mean-field method called the Bethe approximation also gives the same results, as well as the Monte Carlo method does for small size images. These reinforce the validity of our analysis and findings. Relations to criticality, frustration, and simple-cell receptive fields are also discussed.
Gyrokinetic simulations with a general equilibrium distribution function
Wilkie, George; Highcock, Edmund; Abel, Ian; Dorland, William
2013-10-01
Applying the gyrokinetic framework to study the dynamics of fast particles requires a transport-scale equilibrium distribution that is not Maxwellian, and whose functional form may not be known a priori. The GS2 gyrokinetics code has been modified to accommodate an arbitrary equilibrium distribution and this capability has been validated. The need to resolve the tail of the distribution for fast particles introduces numerical challenges that are resolved by implementing a generalized quadrature scheme that retains spectral accuracy of velocity-space integrals. Preliminary simulation results are presented.
Q Value-Based Dynamic Programming with Boltzmann Distribution in Large Scale Road Network
Yu, Shanqing; Xu, Yelei; Mabu, Shingo; Mainali, Manoj Kanta; Shimada, Kaoru; Hirasawa, Kotaro
In this paper, a global optimal traffic assignment strategy, i.e., Q value-based Dynamic Programming with Boltzmann Distribution is applied to the Kitakyushu City traffic system. The main idea of the proposed traffic assignment strategy is to calculate the expected traveling time for each origin-destination pair and the probability of selecting the next section, then to generate a considerable number of route candidates for the drivers based on the calculated probability. In the simulation, how to select the temperature parameter and the number of the route candidates is discussed in detail. The comparison between the proposed method and the shortest path algorithms indicates that the proposed method could reduce the risk of the traffic congestion occurrence and save the traveling cost effectively. In addition, the computation time is given to reveal the feasibility of the proposed method in large scale networks.
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
Tovar-Pescador, J.; Pozo-Vázquez, D.; Batlles, J.; López, G.; Rubio, M. A.
2003-04-01
To obtain simple correlations for the estimation of the performance of biological systems, which transform the solar energy by photosynthesis, and to generate synthetic data, it is necessary to know the frequency distributions of photosynthetically active radiation (PAR). In this work we carried out an analysis of the properties of hourly values of PAR data collected in southern Spain. Its dependence on the optical mass for all type of skies, including cloudy skies, is analyzed. Results show that, for a given value of the optical mass, the PAR density distributions are not symmetrical and have certain degree of bimodality. The increment in the optical mass value has two effects on the PAR distributions, the first one is a shift toward lower values of the maximum and the second one is a decrease in the range of PAR values. A model of the frequency distribution of PAR values, based on a new kind of functions related to the Boltzmann´s statistic, is proposed. The parameters of these functions depend just on the optical mass. Results show a very good agreement between the data and the model proposed
Thermodynamic Derivation of the Equilibrium Distribution Functions of Statistical Mechanics.
Stoeckly, Beth
1979-01-01
Presents a simplified derivation of the equilibrium distribution functions. The derivation proceeds from the change in the Helmholtz free energy when a particle is added to a system of fixed temperature, volume, and chemical potential. The derivations show the relationship between statistical mechanics and macroscopic thermodynamics. (Author/GA)
The Equilibrium Distribution of Income and the Market for Status.
Becker, Gary S.; Murphy, Kevin M.; Werning, Ivan
2005-01-01
This paper explores the implications for risk-taking behavior and the equilibrium distribution of income of assuming that the desire for status positions is a powerful motive and that it raises the marginal utility of consumption. In contrast to previous analyses, we consider the case in which status positions are sold in a hedonic market. We show…
Total variation approximation for quasi-equilibrium distributions
Barbour, A D
2010-01-01
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In this paper, we give biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute.
Cervantes-Sanchez, Fernando; Hernandez-Aguirre, Arturo; Solorio-Meza, Sergio; Ornelas-Rodriguez, Manuel; Torres-Cisneros, Miguel
2016-01-01
This paper presents a novel method for improving the training step of the single-scale Gabor filters by using the Boltzmann univariate marginal distribution algorithm (BUMDA) in X-ray angiograms. Since the single-scale Gabor filters (SSG) are governed by three parameters, the optimal selection of the SSG parameters is highly desirable in order to maximize the detection performance of coronary arteries while reducing the computational time. To obtain the best set of parameters for the SSG, the area (Az) under the receiver operating characteristic curve is used as fitness function. Moreover, to classify vessel and nonvessel pixels from the Gabor filter response, the interclass variance thresholding method has been adopted. The experimental results using the proposed method obtained the highest detection rate with Az = 0.9502 over a training set of 40 images and Az = 0.9583 with a test set of 40 images. In addition, the experimental results of vessel segmentation provided an accuracy of 0.944 with the test set of angiograms. PMID:27738422
Directory of Open Access Journals (Sweden)
Fernando Cervantes-Sanchez
2016-01-01
Full Text Available This paper presents a novel method for improving the training step of the single-scale Gabor filters by using the Boltzmann univariate marginal distribution algorithm (BUMDA in X-ray angiograms. Since the single-scale Gabor filters (SSG are governed by three parameters, the optimal selection of the SSG parameters is highly desirable in order to maximize the detection performance of coronary arteries while reducing the computational time. To obtain the best set of parameters for the SSG, the area (Az under the receiver operating characteristic curve is used as fitness function. Moreover, to classify vessel and nonvessel pixels from the Gabor filter response, the interclass variance thresholding method has been adopted. The experimental results using the proposed method obtained the highest detection rate with Az=0.9502 over a training set of 40 images and Az=0.9583 with a test set of 40 images. In addition, the experimental results of vessel segmentation provided an accuracy of 0.944 with the test set of angiograms.
Distributions of Hardy-Weinberg equilibrium test statistics.
Rohlfs, R V; Weir, B S
2008-11-01
It is well established that test statistics and P-values derived from discrete data, such as genetic markers, are also discrete. In most genetic applications, the null distribution for a discrete test statistic is approximated with a continuous distribution, but this approximation may not be reasonable. In some cases using the continuous approximation for the expected null distribution may cause truly null test statistics to appear nonnull. We explore the implications of using continuous distributions to approximate the discrete distributions of Hardy-Weinberg equilibrium test statistics and P-values. We derive exact P-value distributions under the null and alternative hypotheses, enabling a more accurate analysis than is possible with continuous approximations. We apply these methods to biological data and find that using continuous distribution theory with exact tests may underestimate the extent of Hardy-Weinberg disequilibrium in a sample. The implications may be most important for the widespread use of whole-genome case-control association studies and Hardy-Weinberg equilibrium (HWE) testing for data quality control.
Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots
Energy Technology Data Exchange (ETDEWEB)
Rudd, R E; Briggs, G D; Sutton, A P; Medeiros-Ribeiro, G; Williams, R S
2006-05-01
We present in detail a thermodynamic equilibrium model for the growth of nanostructures on semiconductor substrates in heteroepitaxy and its application to germanium deposition on silicon. Some results of this model have been published previously, but the details of the formulation of the model are given here for the first time. The model allows the computation of the shape and size distributions of the surface nanostructures, as well as other properties of the system. We discuss the results of the model, and their incorporation into a nanostructure diagram that summarizes the relative stability of domes and pyramids in the bimodal size distributions.
Equilibrium distribution from distributed computing (simulations of protein folding).
Scalco, Riccardo; Caflisch, Amedeo
2011-05-19
Multiple independent molecular dynamics (MD) simulations are often carried out starting from a single protein structure or a set of conformations that do not correspond to a thermodynamic ensemble. Therefore, a significant statistical bias is usually present in the Markov state model generated by simply combining the whole MD sampling into a network whose nodes and links are clusters of snapshots and transitions between them, respectively. Here, we introduce a depth-first search algorithm to extract from the whole conformation space network the largest ergodic component, i.e., the subset of nodes of the network whose transition matrix corresponds to an ergodic Markov chain. For multiple short MD simulations of a globular protein (as in distributed computing), the steady state, i.e., stationary distribution determined using the largest ergodic component, yields more accurate free energy profiles and mean first passage times than the original network or the ergodic network obtained by imposing detailed balance by means of symmetrization of the transition counts.
Management Model of Resources Equilibrium Distribution among Overlapping-Generations
Institute of Scientific and Technical Information of China (English)
Jiang Xuemin; Li Ling
2004-01-01
The overlapping generation models the western scholars have designed from various perspectives to address different kinds of issues do not reflect Chinese emerging political and economic problems, and cannot be entirely and blindly applied to Chinese practical situation. In this paper the authors endeavor to incorporate some western scholars' research results into their own research findings to present overlapping generations model theory in a new perspective through establishing an overlapping generations theory on population including articulation of concepts and theorems of biological generation, economic generation and social generation and the overlapping periods in biological generation and two overlapping periods in economic generation among three generations. This management model with equilibrium distribution of resource wealth includes overlapping generations length model (δ),equilibrium transfer model (θ) and a complete model on equilibrium distribution among generations (δ-θ).The model provides quantitative basis for the creation of resource management system, and fills in a theoretical gap in this discipline in China. Besides,it furnishes a new methodology and manipulable tool for Chinese government to establish a comprehensive management information bank for many sectors such as economic trade, population, science and technology, education, human resource, natural resource and environment, agriculture, forestry,industry, mining and energy.
NHPP-Based Software Reliability Models Using Equilibrium Distribution
Xiao, Xiao; Okamura, Hiroyuki; Dohi, Tadashi
Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.
Nauenberg, Michael
2005-03-01
In 1916 Einstein published a remarkable paper entitled ``On the Quantum Theory of Radiation''ootnotetextA. Einstein ``On the Quantum theory of Radiation,'' Phys. Zeitschrift 18 (1917) 121. First printed in Mitteilungender Physikalischen Gesellschaft Zurich. No 18, 1916. Translated into English in Van der Waerden ``Sources of Quantum Mechanics'' (North Holland 1967) pp. 63-77. in which he obtained Planck's formula for black-body radiation by introducing a new statistical hypothesis for the emmision and absorption of electromagneic radiation based on discrete bundles of energy and momentum which are now called photons. Einstein radiation theory replaced Maxwell's classical theory by a stochastic process which, when properly interpreted, also gives well known statistics of massless particles with even spin.^2 This quantum distribution, however, was not discovered by Einstein but was communicated to him by Bose in 1924. Like Boltzmann's classical counterpart, Einstein's statistical theory leads to an irreversible approach to thermal equilibrium, but because this violates time reversal, Einstein theory can not be regarded as a fundamental theory of physical process.ootnotetextM. Nauenberg ``The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of statistical mechanics,'' American Journal of Physics 72 (2004) 313 Apparently Einstein and his contemporaries were unaware of this problem, and even today this problem is ignored in contemporary discussions of Einstein's treatment of the black-body spectrum.
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.
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.
Sels, Dries; Brosens, Fons
2013-10-01
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.
Learning thermodynamics with Boltzmann machines
Torlai, Giacomo; Melko, Roger G.
2016-10-01
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.
A non-slip boundary condition for lattice Boltzmann simulations
Inamuro, T; Ogino, F; Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru
1995-01-01
A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.
On the full Boltzmann equations for Leptogenesis
Garayoa, J; Pinto, T; Rius, N; Vives, O
2009-01-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous...
On the full Boltzmann equations for leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O., E-mail: garayoa@ific.uv.es, E-mail: pastor@ific.uv.es, E-mail: teguayco@gmail.com, E-mail: nuria@ific.uv.es, E-mail: vives@ific.uv.es [Depto. de Física Teórica and IFIC, Universidad de Valencia-CSIC, Edificio de Institutos de Paterna, Apt. 22085, 46071 Valencia (Spain)
2009-09-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.
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
Lattice Boltzmann simulation for the spiral waves in the excitable medium
Institute of Scientific and Technical Information of China (English)
GuangwuYAN; LiYUAN
2000-01-01
We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov reactions with scratching mark, i. e. using a scratching mark pacemaker, obtained one classical spiral waves.
Energy Technology Data Exchange (ETDEWEB)
Imai, M., E-mail: imai@nucleng.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, Nishikyo, Kyoto 615-8540 (Japan); Sataka, M.; Matsuda, M.; Okayasu, S. [Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195 (Japan); Kawatsura, K. [Kansai Gaidai University, Hirakata, Osaka 573-1001 (Japan); Takahiro, K. [Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Sakyo, Kyoto 606-8585 (Japan); Komaki, K. [Atomic Physics Laboratory, RIKEN, Wako, Saitama 351-0198 (Japan); Shibata, H. [Department of Nuclear Engineering, Kyoto University, Nishikyo, Kyoto 615-8540 (Japan); Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047 (Japan); Nishio, K. [Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195 (Japan)
2015-07-01
Both equilibrium and non-equilibrium charge-state distributions were studied experimentally for 2.0 MeV/u carbon ions after passing through carbon foils. Measured charge-state distribution established the equilibrium at a target thickness of 10 μg/cm{sup 2} and this remained unchanged until a maximum target thickness of 98 μg/cm{sup 2}. The equilibrium charge-state distribution, the equilibrium mean charge-state, and the width and skewness of the equilibrium distribution were compared with predictions using existing semi-empirical formulae as well as simulation results, including the ETACHA code. It was found that charge-state distributions, mean charge states, and distribution widths for C{sup 2+}, C{sup 3+}, and C{sup 4+} incident ions merged into quasi-equilibrium values at a target thickness of 5.7 μg/cm{sup 2} in the pre-equilibrium region and evolved simultaneously to the ‘real equilibrium’ values for all of the initial charge states, including C{sup 5+} and C{sup 6+} ions, as previously demonstrated for sulfur projectile ions at the same velocity (Imai et al., 2009). Two kinds of simulation, ETACHA and solution of rate equations taking only single electron transfers into account, were used, and both of them reproduced the measured charge evolution qualitatively. The quasi-equilibrium behavior could be reproduced with the ETACHA code, but not with solution of elementary rate equations.
Lattice Boltzmann model for nanofluids
Energy Technology Data Exchange (ETDEWEB)
Xuan Yimin; Yao Zhengping [Nanjing University of Science and Technology, School of Power Engineering, Nanjing (China)
2005-01-01
A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. 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 is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles. (orig.)
Hu, Kainan; Geng, Shaojuan
2016-01-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e. the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion...
Boltzmann transport calculation of collinear spin transport on short timescales
Nenno, Dennis M.; Kaltenborn, Steffen; Schneider, Hans Christian
2016-09-01
A spin-dependent Boltzmann transport equation is used to describe charge and spin dynamics resulting from the excitation of hot electrons in a ferromagnet/normal metal heterostructure. As the microscopic Boltzmann equation works with k -dependent distribution functions, it can describe far-from-equilibrium excitations, which are outside the scope of drift-diffusion theories. We study different scenarios for spin-dependent carrier injection into a nonmagnetic metal using an effectively two-dimensional phase space. While the charge signal is robust for various excitation schemes, the shape of the resulting spin current/density depends critically on the interplay between transport and scattering, and on the energetic distribution of the injected carriers. Our results imply that the energy dependence of the injected hot electrons has a decisive effect on the spin dynamics.
Randomness as an Equilibrium. Potential and Probability Density
2002-01-01
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field than provides a way of viewing probability density from a perspective of forces/potentials, hidden behind it.
The Approach to Equilibrium: Detailed Balance and the Master Equation
Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.
2011-01-01
The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…
Equilibrium circulation and stress distribution in viscoelastic creeping flow
Biello, Joseph A
2015-01-01
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both, as an asymptotic parameter and a regularization parameter. The structure of the singular part of polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed $\\delta$-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number and, although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this...
Wang, Huimin
2017-01-01
In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.
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.
Equilibrium distribution of the wave energy in a carbyne chain
Kovriguine, D. A.; Nikitenkova, S. P.
2016-03-01
The steady-state energy distribution of thermal vibrations at a given ambient temperature has been investigated based on a simple mathematical model that takes into account central and noncentral interactions between carbon atoms in a one-dimensional carbyne chain. The investigation has been performed using standard asymptotic methods of nonlinear dynamics in terms of the classical mechanics. In the first-order nonlinear approximation, there have been revealed resonant wave triads that are formed at a typical nonlinearity of the system under phase matching conditions. Each resonant triad consists of one longitudinal and two transverse vibration modes. In the general case, the chain is characterized by a superposition of similar resonant triplets of different spectral scales. It has been found that the energy equipartition of nonlinear stationary waves in the carbyne chain at a given temperature completely obeys the standard Rayleigh-Jeans law due to the proportional amplitude dispersion. The possibility of spontaneous formation of three-frequency envelope solitons in carbyne has been demonstrated. Heat in the form of such solitons can propagate in a chain of carbon atoms without diffusion, like localized waves.
Green, B. I.; Vedula, Prakash
2013-07-01
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework.
Energy Technology Data Exchange (ETDEWEB)
Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp
2012-01-15
A Boltzmann plot for many iron ionic lines having excitation energies of 4.7-9.1 eV was investigated in an argon glow discharge plasma when the discharge parameters, such as the voltage/current and the gas pressure, were varied. A Grimm-style radiation source was employed in a DC voltage range of 400-800 V at argon pressures of 400-930 Pa. The plot did not follow a linear relationship over a wide range of the excitation energy, but it yielded a normal Boltzmann distribution in the range of 4.7-5.8 eV and a large overpopulation in higher-lying excitation levels of iron ion. A probable reason for this phenomenon is that excitations for higher excited energy levels of iron ion would be predominantly caused by non-thermal collisions with argon species, the internal energy of which is received by iron atoms for the ionization. Particular intense ionic lines, which gave a maximum peak of the Boltzmann plot, were observed at an excitation energy of ca. 7.7 eV. They were the Fe II 257.297-nm and the Fe II 258.111-nm lines, derived from the 3d{sup 5}4s4p {sup 6}P excited levels. The 3d{sup 5}4s4p {sup 6}P excited levels can be highly populated through a resonance charge transfer from the ground state of argon ion, because of good matching in the excitation energy as well as the conservation of the total spin before and after the collision. An enhancement factor of the emission intensity for various Fe II lines could be obtained from a deviation from the normal Boltzmann plot, which comprised the emission lines of 4.7-5.8 eV. It would roughly correspond to a contribution of the charge transfer excitation to the excited levels of iron ion, suggesting that the charge-transfer collision could elevate the number density of the corresponding excited levels by a factor of ca.10{sup 4}. The Boltzmann plots give important information on the reason why a variety of iron ionic lines can be emitted from glow discharge plasmas.
Lattice Boltzmann model for incompressible flows through porous media.
Guo, Zhaoli; Zhao, T S
2002-09-01
In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.
CMB spectral distortions as solutions to the Boltzmann equations
Ota, Atsuhisa
2016-01-01
We newly re-interpret cosmic microwave background spectral distortions as solutions to the Boltzmann equation at second order. This approach makes it possible to solve the equation of the momentum dependent temperature perturbations explicitly. In addition, we define higher order spectral distortions systematically, assuming that the collision term is linear in the photon distribution functions. For example, we find the linear Sunyaev-Zel'dovich effect whose momentum shape is different from the usual $y$ distortion, and show that the higher order spectral distortions are also generated as a result of the diffusion process in a language of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.
Institute of Scientific and Technical Information of China (English)
王伟; 孙会君; 吴建军
2015-01-01
The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value (CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities. Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.
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.
Di Troia, Claudio
2015-01-01
A class of parametric distribution functions has been proposed in [C.DiTroia, Plasma Physics and Controlled Fusion,54,2012] as equilibrium distribution functions (EDFs) for charged particles in fusion plasmas, representing supra-thermal particles in anisotropic equilibria for Neutral Beam Injection, Ion Cyclotron Heating scenarios. Moreover, the EDFs can also represent nearly isotropic equilibria for Slowing-Down $alpha$ particles and core thermal plasma populations. These EDFs depend on constants of motion (COMs). Assuming an axisymmetric system with no equilibrium electric field, the EDF depends on the toroidal canonical momentum $P_\\phi$, the kinetic energy $w$ and the magnetic moment \\mu. In the present work, the EDFs are obtained from first principles and general hypothesis. The derivation is probabilistic and makes use of the Bayes' Theorem. The bayesian argument allows us to describe how far from the prior probability distribution function (pdf), e.g. Maxwellian, the plasma is, based on the information...
Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks
DEFF Research Database (Denmark)
Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj;
2015-01-01
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potent......We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non......-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have...
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).
Xiao, Zhiyong
2016-12-01
Accumulation of impact craters is the major reason causing equilibrium of crater populations on airless planetary surfaces. Besides primary craters, the effect of widespread secondaries on the equilibrium of local crater populations is little studied. Here the different secondary crater populations formed by the Hokusai crater on Mercury are systematically studied, and they are compared with those on the Moon to investigate their contribution to the evolution of local crater populations. Self-secondaries cause equilibrium on continuous ejecta deposits in a short time, and the equilibrium crater population has a differential size-frequency distribution (SFD) slope of about -3. Background secondaries are abundant on Mercury, and equilibrium caused by a combination of primaries and potential background secondaries follows the same pattern on the Moon and Mercury. The spatial dispersion of fragments that form both near-field and distant secondaries is the major factor affecting the degree of mutual destruction and thus the final crater SFD. Some clustered distant secondaries on Mercury are likely formed by individual fragments considering their large spatial dispersion and identical morphology with same-sized primaries, and the SFD rollovers of these secondaries possibly reflect the inherent SFD rollovers of the impact fragments. Near-field secondaries and many other distant secondaries have morphology and spatial distribution that are consistent with being formed by clustered fragments, and mutual destruction of secondaries may be the major reason causing the observed SFD rollovers. Heterogeneous secondary impacts are a potential explanation for both different crater densities within the equilibrium diameter range and different regolith thicknesses on coeval surfaces.
Saksena, Radhika S; Mazzeo, Marco D; Zasada, Stefan J; Coveney, Peter V
2010-08-28
We present very large-scale rheological studies of self-assembled cubic gyroid liquid crystalline phases in ternary mixtures of oil, water and amphiphilic species performed on petascale supercomputers using the lattice-Boltzmann method. These nanomaterials have found diverse applications in materials science and biotechnology, for example, in photovoltaic devices and protein crystallization. They are increasingly gaining importance as delivery vehicles for active agents in pharmaceuticals, personal care products and food technology. In many of these applications, the self-assembled structures are subject to flows of varying strengths and we endeavour to understand their rheological response with the objective of eventually predicting it under given flow conditions. Computationally, our lattice-Boltzmann simulations of ternary fluids are inherently memory- and data-intensive. Furthermore, our interest in dynamical processes necessitates remote visualization and analysis as well as the associated transfer and storage of terabytes of time-dependent data. These simulations are distributed on a high-performance grid infrastructure using the application hosting environment; we employ a novel parallel in situ visualization approach which is particularly suited for such computations on petascale resources. We present computational and I/O performance benchmarks of our application on three different petascale systems.
Institute of Scientific and Technical Information of China (English)
AlbertC.J.LUO; C.D.MOTE,Jr.
2000-01-01
The exact, closed-form solution for equilibrium of traveling, sagged, elastic cables under uniformly-distributed loading is derived. Three components of displacement describing two equilibria of an extensible, traveling, elastic cable are also obtained. Illustrations of equilibrium configuration, tension distribution and displacements of cables are given.
Mazumder, Surasree; Alam, Jan-e
2014-01-01
The effects of gluon radiation by charm quarks on the transport coefficients {\\it e.g.} drag, longitudinal and transverse diffusion and shear viscosity have been studied within the ambit of perturbative quantum chromodynamics (pQCD) and kinetic theory. We found that while the soft gluon radiation has substantial effects on the transport coefficients of the charm quarks in the quark gluon plasma its effects on the equilibrium distribution function is insignificant.
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...
Energy Technology Data Exchange (ETDEWEB)
Koyama, T.; Kinoshita, K.; Inoue, T. [Central Research Inst. of Electric Power Industry, Tokyo (Japan); Ougier, M.; Malmbeck, R.; Glatz, J.P. [Joint Research Centre, Karlsruhe (Germany). Inst. for Transuranium Elements
2008-07-01
Equilibrium distribution of actinides both in molten LiCl-KCl eutectic and liquid cadmium were measured from the concentration data obtained in electrorefining tests and reductive extraction tests. Separation factors for U, Np, Am, Cm against Pu were derived in the practical temperature range of 700 K to 783 K. The derived separation factors are consistent with the reported values measured at 773 K and 723 K. The temperature dependence for Cm is different compared to the other actinides (U, Np and Am). This behavior remains unclear and additional experimental measurements of distribution coefficient of Cm are required before ruling on the real behavior. (orig.)
Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks.
Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj; Wiuf, Carsten
2015-09-01
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
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.
Directory of Open Access Journals (Sweden)
Xiliang Zheng
2015-04-01
Full Text Available We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity, the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.
Zheng, Xiliang; Wang, Jin
2015-01-01
We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics. PMID:25885453
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.
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.
Institute of Scientific and Technical Information of China (English)
ZHOU Hai-jun
2007-01-01
At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state.The system is able to visit all spin configurations of the same macroscopic state, while it can not spontaneously jump between two different macroscopic states.Ergodicity of the whole configurational phase space of the system, however, can be recovered if a temperatureannealing process is repeated an infinite number of times.In a heating-annealing cycle, the environmental temperature is first elevated to a high level and then decreased extremely slowly until a final low temperature T is reached.Different macroscopic states may be reached in different rounds of the annealing experiment; while the probability of finding the system in macroscopic state a decreases exponentially with the free energy Fa(T) of this state.For finite-connectivity spin glass systems, we use this free energy Boltzmann disParisi [Eur.Phys.J.B, 2001, 20: 217] in a slightly different form.For the ±J spin-glass model on a random regular graph of degree K=6, the predictions of the present work agree with earlier simulational and theoretical results.
Li, Zhihui; Wu, Junlin; Ma, Qiang; Jiang, Xinyu; Zhang, Hanxin
2014-12-01
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Energy Technology Data Exchange (ETDEWEB)
Li, Zhihui; Ma, Qiang [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000, China and National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China); Wu, Junlin; Jiang, Xinyu [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000 (China); Zhang, Hanxin [National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China)
2014-12-09
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Chakraborty, P.; Kapusta, J. I.
2017-01-01
In simulations of high energy heavy ion collisions that employ viscous hydrodynamics, single particle distributions are distorted from their thermal equilibrium form due to gradients in the flow velocity. These are closely related to the formulas for the shear and bulk viscosities in the quasiparticle approximation. Distorted single particle distributions are now commonly used to calculate the emission of photons and dilepton pairs, and in the late stage to calculate the conversion of a continuous fluid to individual particles. We show how distortions of the single particle distribution functions due to both shear and bulk viscous effects can be done rigorously in the quasiparticle approximation and illustrate it with the linear σ model at finite temperature.
Dzifcakova, Elena
2013-01-01
New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian kappa-distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The kappa-distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII--XIV. The results are supplied in electronic form compatible with the CHIANTI database.
Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges
Energy Technology Data Exchange (ETDEWEB)
Baker, D.A.; Mann, L.W.; Schoenberg, K.F.
1982-04-01
A comparison between the analytic formulae of Shafranov for equilibrium in axisymmetric toroidal reversed field pinch (RFP) systems and fully toroidal numerical solutions of the Grad-Shafranov equation is presented as a function of poloidal beta, internal plasma inductance, and aspect ratio. The Shafranov formula for the equilibrium poloidal field distribution is accurate to within 5% for aspect ratios greater than 2, poloidal betas less than 50%, and for plasma current channels that exceed one-third of the minor toroidal radius. The analytic description for the center shift of the innermost flux surface that encloses the plasma current (the Shafranov shift) is accurate to within 15% for aspect ratios greater than 2 and poloidal betas below 50%, provided the shift does not exceed one-tenth of the minor conducting boundary radius. The behavior of the magnetic axis shift as a function of plasma parameters is included. The Shafranov formulae provide a convenient method for describing the equilibrium behavior of an RFP discharge. Examples illustrating the application of the analytic formulae to the Los Alamos ZT-40M RFP experiment are given.
Diffusion and near-equilibrium distribution of MRI and CT contrast agents in articular cartilage
Silvast, Tuomo S.; Kokkonen, Harri T.; Jurvelin, Jukka S.; Quinn, Thomas M.; Nieminen, Miika T.; Töyräs, Juha
2009-11-01
Charged contrast agents have been used both in vitro and in vivo for estimation of the fixed charge density (FCD) in articular cartilage. In the present study, the effects of molecular size and charge on the diffusion and equilibrium distribution of several magnetic resonance imaging (MRI) and computed tomography (CT) contrast agents were investigated. Full thickness cartilage disks (Ø = 4.0 mm, n = 64) were prepared from fresh bovine patellae. Contrast agent (gadopentetate: Magnevist®, gadodiamide: Omniscan™, ioxaglate: Hexabrix™ or sodium iodide: NaI) diffusion was allowed either through the articular surface or through the deep cartilage. CT imaging of the samples was conducted before contrast agent administration and after 1, 5, 9, 16, 25 and 29 h (and with three samples after 2, 3, 4 and 5 days) diffusion using a clinical peripheral quantitative computed tomography (pQCT) instrument. With all contrast agents, the diffusion through the deep cartilage was slower when compared to the diffusion through the articular surface. With ioxaglate, gadopentetate and gadodiamide it took over 29 h for diffusion to reach the near-equilibrium state. The slow diffusion of the contrast agents raise concerns regarding the validity of techniques for FCD estimation, as these contrast agents may not reach the equilibrium state that is assumed. However, since cartilage composition, i.e. deep versus superficial, had a significant effect on diffusion, imaging of the nonequilibrium diffusion process might enable more accurate assessment of cartilage integrity.
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.
Bazow, D.; Denicol, G. S.; Heinz, U.; Martinez, M.; Noronha, J.
2016-12-01
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-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 nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic 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. However, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.
Energy Technology Data Exchange (ETDEWEB)
Bihani, Abhishek [University of Texas at Austin; Daigle, Hugh [University of Texas at Austin; Cook, Ann [Ohio State University; Glosser, Deborah [Ohio State University; Shushtarian, Arash [University of Texas at Austin
2015-12-15
Coexistence of three methane phases (liquid (L), gas (G), hydrate (H)) in marine gas hydrate systems may occur according to in-situ pressure, temperature, salinity and pore size. In sediments with salinity close to seawater, a discrete zone of three-phase (3P) equilibrium may occur near the base of the regional hydrate stability zone (RHSZ) due to capillary effects. The existence of a 3P zone influences the location of the bottom-simulating reflection (BSR) and has implications for methane fluxes at the base of the RHSZ. We studied hydrate stability conditions in two wells, WR313-G and WR313-H, at Walker Ridge Block 313 in the northern Gulf of Mexico. We determined pore size distributions (PSD) by constructing a synthetic nuclear magnetic resonance (NMR) relaxation time distribution. Correlations were obtained by non-linear regression on NMR, gamma ray, and bulk density logs from well KC-151 at Keathley Canyon. The correlations enabled construction of relaxation time distributions for WR313-G and WR313-H, which were used to predict PSD through comparison with mercury injection capillary pressure measurements. With the computed PSD, L+H and L+G methane solubility was determined from in-situ pressure and temperature. The intersection of the L+G and L+H curves for various pore sizes allowed calculation of the depth range of the 3P equilibrium zone. As in previous studies at Blake Ridge and Hydrate Ridge, the top of the 3P zone moves upwards with increasing water depth and overlies the bulk 3P equilibrium depth. In clays at Walker Ridge, the predicted thickness of the 3P zone is approximately 35 m, but in coarse sands it is only a few meters due to the difference in absolute pore sizes and the width of the PSD. The thick 3P zone in the clays may explain in part why the BSR is only observed in the sand layers at Walker Ridge, although other factors may influence the presence or absence of a BSR.
Bihani, A. D.; Daigle, H.; Cook, A.; Glosser, D.; Shushtarian, A.
2015-12-01
Coexistence of three methane phases (liquid (L), gas (G), hydrate (H)) in marine gas hydrate systems may occur according to in-situ pressure, temperature, salinity and pore size. In sediments with salinity close to seawater, a discrete zone of three-phase (3P) equilibrium may occur near the base of the regional hydrate stability zone (RHSZ) due to capillary effects. The existence of a 3P zone influences the location of the bottom-simulating reflection (BSR) and has implications for methane fluxes at the base of the RHSZ. We studied hydrate stability conditions in two wells, WR313-G and WR313-H, at Walker Ridge Block 313 in the northern Gulf of Mexico. We determined pore size distributions (PSD) by constructing a synthetic nuclear magnetic resonance (NMR) relaxation time distribution. Correlations were obtained by non-linear regression on NMR, gamma ray, and bulk density logs from well KC-151 at Keathley Canyon. The correlations enabled construction of relaxation time distributions for WR313-G and WR313-H, which were used to predict PSD through comparison with mercury injection capillary pressure measurements. With the computed PSD, L+H and L+G methane solubility was determined from in-situ pressure and temperature. The intersection of the L+G and L+H curves for various pore sizes allowed calculation of the depth range of the 3P equilibrium zone. As in previous studies at Blake Ridge and Hydrate Ridge, the top of the 3P zone moves upwards with increasing water depth and overlies the bulk 3P equilibrium depth. In clays at Walker Ridge, the predicted thickness of the 3P zone is approximately 35 m, but in coarse sands it is only a few meters due to the difference in absolute pore sizes and the width of the PSD. The thick 3P zone in the clays may explain in part why the BSR is only observed in the sand layers at Walker Ridge, although other factors may influence the presence or absence of a BSR.
Raut, L K
1991-01-01
A study is conducted in attempts to increase the understanding of the links between macroeconomic effects and causes of population growth in formulating policy. An overlapping generations general equilibrium model is employed aggregating household decisions about fertility, savings, and investment in the human capital of children with the objective of studying intertemporal relationships among population growth, income distribution, inter-generation social mobility, skill composition of the labor force, and household income. As a result of endogenous fertility, the equilibrium path attains steady state from the second generation. Income tax transfer, child taxation, and social security taxation policies are also examined in the paper. A structural explanation is given for the inverse household income-child quantity and negative child quality-quantity relationships seen in developing countries. In a Cobb-Douglas economy, these relationships hold in the short-run, potentially working over the long-run in other economies. Overall, the model shows that group interests may hinder emergence of perfect capital markets with private initiatives. Where developing countries are concerned, these results have strong implications for population policy. A policy mix of building good quality schools, or subsidizing rural education, introducing a formal social security program, and providing high-yield, risk-free investments, banking, and insurance services to the poor is recommended.
Acoustic equations of state for simple lattice Boltzmann velocity sets.
Viggen, Erlend Magnus
2014-07-01
The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.
The Kinetic and Equilibrium Cluster Size Distributions of Finite Bond Aggregation Processes
Sherman, Derin Andrew
Aggregation is a phenomenon central to many natural and synthetic processes. In this thesis, I explore in detail the phenomenon of antibody-induced colloidal aggregation. I use a new and novel system composed of highly charged uniform polystyrene microspheres to which antigens are covalently coupled. Bivalent antibodies in solution bind to the antigens on the spheres' surfaces and crosslink the spheres causing them to aggregate. As such, the bonds which form between the spheres are discrete and rigid. Using a single particle light scattering instrument developed in the Cohen laboratory, I have measured the temporal evolution of the cluster size distribution for the system of spheres and antibodies. The results show that the cluster size distribution exhibits dynamic scaling. Although antigen coated colloidal spheres have been used extensively in the past, the system I use is unique in that the bonds which form between the antibodies and the spheres are fragile making the aggregation process thermodynamically reversible. This effect causes the system to reach equilibrium in a finite amount of time. The classical theory which predicts the equilibrium cluster size distribution for a variety of aggregating systems is known as Flory -Stockmayer theory. Since each monomer possesses several antibodies and several antigens,m the colloidal system is expected to obey the statistics for the Flory A _{f}RB_{g} model where f,ggg 1. In Flory's model, the system is expected to gel. However, I see no evidence of gelation. I am able to resolve this discrepancy using the ideas of Ball and colleagues. I have also developed the theory by which this system may be used to measure the binding affinity between antibodies and antigens. I have used the light scattering instrument to measure the binding affinity between a monoclonal antibody and a number of different antigens covering a large range of binding affinities. I have demonstrated that the instrument is capable of detecting small
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.
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.
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.
Nicholls, David C; Sutherland, Ralph S; Kewley, Lisa J; Palay, Ethan
2013-01-01
In this paper we develop tools for observers to use when analysing nebular spectra for temperatures and metallicities, with two goals: to present a new, simple method to calculate equilibrium electron temperatures for collisionally excited line flux ratios, using the latest atomic data; and to adapt current methods to include the effects of possible non-equilibrium '{\\kappa}' electron energy distributions. Adopting recent collision strength data for [O iii], [S iii], [O ii], [S ii], and [N ii], we find that existing methods based on older atomic data seriously overestimate the electron temperatures, even when considering purely Maxwellian statistics. If {\\kappa} distributions exist in H ii regions and planetary nebulae as they do in solar system plasmas, it is important to investigate the observational consequences. This paper continues our previous work on the {\\kappa} distribution (Nicholls et al. 2012). We present simple formulaic methods that allow observers to (a) measure equilibrium electron temperature...
Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics
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.
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Directory of Open Access Journals (Sweden)
Ryan eBabbush
2013-10-01
Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán
2013-01-01
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
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.
Lattice Boltzmann methods for global linear instability analysis
Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis
2016-11-01
Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.
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...
Full Boltzmann equations for leptogenesis including scattering
Hahn-Woernle, F; Wong, Y Y Y
2009-01-01
We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/i...
Stary, J
1979-01-01
Critical Evaluation of Equilibrium Constants Involving 8-Hydroxyquinoline and Its Metal Chelates presents and evaluates the published data on the solubility, dissociation, and liquid-liquid distribution of oxine and its metal chelates to recommend the most reliable numerical data. This book explores the dissociation constants of oxine in aqueous solutions.Organized into four chapters, this book begins with an overview of the characteristics of 8-hydroxyquinoline (oxine). This text then examines the total solubility of oxine in aqueous solution at different pH values. Other chapters consider th
A stylized model for wealth distribution
Düring, Bertram; Scalas, Enrico
2016-01-01
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related Boltzmann-type kinetic equations. In this literature, the usual concept of equilibrium in Economics is either replaced or completed by statistical equilibrium. In order to illustrate this activity with a concrete example, we present a stylised random exchange model for the distribution of wealth. We first discuss a fully discrete version (a Markov chain with finite state space). We then study its discrete-time continuous-state-space version and we prove the existence of the equilibrium distribution. Finally, we discuss the connection of these models with Boltzmann-like kinetic equations for the marginal distribution of wealth. This paper shows in practice how it is possible to start from a fini...
Fission fragment mass and angular distributions: Probes to study non-equilibrium fission
Indian Academy of Sciences (India)
R G Thomas
2015-08-01
Synthesis of heavy and superheavy elements is severely hindered by fission and fission-like processes. The probability of these fission-like, non-equilibrium processes strongly depends on the entrance channel parameters. This article attempts to summarize the recent experimental findings and classify the signatures of these non-equilibrium processes based on macroscopic variables. The importance of the sticking time of the dinuclear complex with respect to the equilibration times of various degrees of freedom is emphasized.
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
Boltzmann-Electron Model in Aleph.
Energy Technology Data Exchange (ETDEWEB)
Hughes, Thomas Patrick; Hooper, Russell
2014-11-01
We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical "grid instability" that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model
Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan
2016-10-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.
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...
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.
Xu, Dazhi; Cao, Jianshu
2016-08-01
The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi's golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.
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.
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.
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.
Contact line dynamics in binary lattice Boltzmann simulations
Pooley, C M; Yeomans, J M; 10.1103/PhysRevE.78.056709
2008-01-01
We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.
Smolyansky, S A; Prozorkevich, A V; Vinnik, D V; Schmidt, S M; Toneev, V D
1999-01-01
We investigate some details of the back reaction (BR) problem formulated on the basis of the kinetic approach of authors to description of vacuum pair production in a strong electromagnetic field (Schwinger's mechanism). Here we study numerically an evolution on the distribution functions of strong non-equilibrium systems bosons and fermions. The realized analysis is shown the regular dynamics in an absence of BR mechanism is destroyed at its account. As the result some large-scale structure is arisen an a background of small-scale chaotic motions.
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
Gamba, I. M.; Panferov, V.; Villani, C.
2007-01-01
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.
Thomas, Drew M
2013-01-01
A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.
Haubold, H. J.; Mathai, A. M.; 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.
Relativistic rotating Boltzmann gas using the tetrad formalism
Ambrus, Victor E
2015-01-01
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 relativistic 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 flow four-vector and of the equilibrium stress-energy tensor.
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), 10.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015), 10.1103/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.
Bonnet-Lebrun, Anne-Sophie
2017-03-17
Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modelled communities - i.e., with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities - from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual-based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species-abundance distribution), consistent with gene flow being a key process in macro-evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in pre-equilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under pre-equilibrium conditions. This article is protected by copyright. All rights reserved.
Chakraborty, P
2016-01-01
In high energy heavy ion collisions, single particle distributions are distorted from their thermal equilibrium form due to gradients in the flow velocity. These are closely related to the formulas for the shear and bulk viscosities in the quasi-particle approximation. Distorted single particle distributions are now commonly used to calculate the emission of photons and dilepton pairs, and in the late stage to calculate the conversion of a continuous fluid to individual particles. In practice this is done only in a very approximate way. We show how it can be done rigorously in the quasi-particle approximation and illustrate it with the linear $\\sigma$ model at finite temperature for both the shear and bulk contributions.
Porter, Mark L.; Coon, E. T.; Kang, Q.; Moulton, J. D.; Carey, J. W.
2012-09-01
This work focuses on an improved multicomponent interparticle-potential lattice Boltzmann model. The model results in viscosity-independent equilibrium densities and is capable of simulating kinematic viscosity ratios greater than 1000. External forces are incorporated into the discrete Boltzmann equation, rather than through an equilibrium velocity shift as in the original Shan and Chen (hereafter, SC) model. The model also requires the derivation of a momentum conserving effective velocity, which is substituted into the equilibrium distribution function and applies to both the single- and multiple-relaxation-time formulations. Additionally, higher-order isotropy is used in the calculation of the fluid-fluid interaction forces to reduce the magnitude of spurious currents (i.e., numerical errors) in the vicinity of interfaces. First, we compare the model to the SC model for static bubble simulations. We demonstrate that the model results in viscosity-independent equilibrium bubble densities for a wide range of kinematic viscosities, which is not the case for the SC model. Furthermore, we show that the model is capable of simulating stable bubbles for kinematic viscosity ratios greater than 1000 (when higher-order isotropy is used), whereas the SC model is known to be limited to kinematic viscosity ratios on the order of 10. Next we verify the model for surface tension via Laplace's law and show that the model results in the same surface tension values for a range of kinematic viscosities and kinematic viscosity ratios of 10, 100, and 1000. The model is also verified for layered cocurrent flow though parallel plates. We show that the simulated velocity profiles preserve continuity at the interface for kinematic viscosity ratios ranging from 0.001 to 1000 and that the model accurately predicts nonwetting and wetting phase relative permeability for kinematic viscosity ratios of 0.01 to 100.
Energy Technology Data Exchange (ETDEWEB)
Lund, Steven M.; Friedman, Alex; Bazouin, Guillaume
2011-01-10
A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet beam model is then applied to analyze several problems of fundamental interest. A sheet beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- d three-dimensional thermal equilibrium models in terms of the equilibrium structure and Deybe screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability.
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.
Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.
Guo, Zhaoli; Zhao, T S
2003-06-01
In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Kaita, R.; Kozub, T.; Logan, N.; Majeski, R.; Menard, J.; Zakharov, L.
2010-12-10
The lithium tokamak experiment LTX is a modest-sized spherical tokamak R0=0.4 m and a =0.26 m designed to investigate the low-recycling lithium wall operating regime for magnetically confined plasmas. LTX will reach this regime through a lithium-coated shell internal to the vacuum vessel, conformal to the plasma last-closed-flux surface, and heated to 300-400 oC. This structure is highly conductive and not axisymmetric. The three-dimensional nature of the shell causes the eddy currents and magnetic fields to be three-dimensional as well. In order to analyze the plasma equilibrium in the presence of three-dimensional eddy currents, an extensive array of unique magnetic diagnostics has been implemented. Sensors are designed to survive high temperatures and incidental contact with lithium and provide data on toroidal asymmetries as well as full coverage of the poloidal cross-section. The magnetic array has been utilized to determine the effects of nonaxisymmetric eddy currents and to model the start-up phase of LTX. Measurements from the magnetic array, coupled with two-dimensional field component modeling, have allowed a suitable field null and initial plasma current to be produced. For full magnetic reconstructions, a three-dimensional electromagnetic model of the vacuum vessel and shell is under development.
Directory of Open Access Journals (Sweden)
William T Bean
Full Text Available Species distributions are known to be limited by biotic and abiotic factors at multiple temporal and spatial scales. Species distribution models, however, frequently assume a population at equilibrium in both time and space. Studies of habitat selection have repeatedly shown the difficulty of estimating resource selection if the scale or extent of analysis is incorrect. Here, we present a multi-step approach to estimate the realized and potential distribution of the endangered giant kangaroo rat. First, we estimate the potential distribution by modeling suitability at a range-wide scale using static bioclimatic variables. We then examine annual changes in extent at a population-level. We define "available" habitat based on the total suitable potential distribution at the range-wide scale. Then, within the available habitat, model changes in population extent driven by multiple measures of resource availability. By modeling distributions for a population with robust estimates of population extent through time, and ecologically relevant predictor variables, we improved the predictive ability of SDMs, as well as revealed an unanticipated relationship between population extent and precipitation at multiple scales. At a range-wide scale, the best model indicated the giant kangaroo rat was limited to areas that received little to no precipitation in the summer months. In contrast, the best model for shorter time scales showed a positive relation with resource abundance, driven by precipitation, in the current and previous year. These results suggest that the distribution of the giant kangaroo rat was limited to the wettest parts of the drier areas within the study region. This multi-step approach reinforces the differing relationship species may have with environmental variables at different scales, provides a novel method for defining "available" habitat in habitat selection studies, and suggests a way to create distribution models at spatial and
The temperature and size distribution of large water clusters from a non-equilibrium model
Energy Technology Data Exchange (ETDEWEB)
Gimelshein, N. [Gimel, Inc., San Jose, California 95124 (United States); Gimelshein, S., E-mail: gimelshe@usc.edu [University of Southern California, Los Angeles, California 90089 (United States); Pradzynski, C. C.; Zeuch, T., E-mail: tzeuch1@gwdg.de [Institut für Physikalische Chemie, Universität Göttingen, Tammanstr. 6, D-37077 Göttingen (Germany); Buck, U., E-mail: ubuck@gwdg.de [Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen (Germany)
2015-06-28
A hybrid Lagrangian-Eulerian approach is used to examine the properties of water clusters formed in neon-water vapor mixtures expanding through microscale conical nozzles. Experimental size distributions were reliably determined by the sodium doping technique in a molecular beam machine. The comparison of computed size distributions and experimental data shows satisfactory agreement, especially for (H{sub 2}O){sub n} clusters with n larger than 50. Thus validated simulations provide size selected cluster temperature profiles in and outside the nozzle. This information is used for an in-depth analysis of the crystallization and water cluster aggregation dynamics of recently reported supersonic jet expansion experiments.
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.
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.)
Wickholm, D.; Bickel, W. S.
1976-01-01
The paper describes an experiment consisting of the acceleration of N(+) and N2(+) ions to energies between 0.25 and 1.75 MeV and their injection through a thin carbon foil, whereupon they were charge-state analyzed with an electrostatic analyzer. A foil-covered electrically suppressed Faraday cup, connected to a stepping motor, moved in the plane of the dispersed beams. The Faraday cup current, which was proportional to the number of incident ions, was sent to a current digitizer and computer programmed as a multiscaler. The energy-dependent charge-state fractions, the mean charge and the distribution width were calculated. It was shown that for incident atoms, the charge state distribution appeared to be spread over more charge states, while for the incident molecules, there was a greater fraction of charge states near the mean charge.
1979-01-01
ELECTE! Mg++ and K+ Distribution in Frog Muscle and Egg: B A Disproof of the Donnan Theory of Membrane B Equilibrium Applied to the Living Cells GILBERT...19107 J ABSTRACT 1. We studied the equilibrium distribution of Mg** in the form of chlo- ride and pulfate at two temperatures (5* and 25°C) in frog ...vicinity of 90 jmoles/g/ fresh muscle cells. 4. We observed a similar rectilinear distribution of Mg** in frog ovarian eggs. As in muscle tissues, no major
Tovbin, Yu. K.
2006-10-01
The possibility of unified self-consistent calculations of equilibrium distributions of molecules in three states of aggregation within the framework of the lattice gas model is considered. The corresponding approach was generalized to arbitrary pressures with including the compressibility of lattice structures. Closed equations were obtained for calculating thermodynamic functions (including an equation for the chemical potential of mixture components) in the continuum quasi-chemical approximation. Their use ensures equally accurate calculations of interphase equilibria in gas-liquid-solid systems and the determination of the triple and critical points. Possibilities for simplifying the equations by passing to the effective pair interaction potential, which takes into account averaged vibrations and volume accessible to the translational motion of molecules of commensurate sizes, are considered.
Koga, S; Shibata, T; Terasaki, R; Kameyama, N; Hatayama, A; Bacal, M; Tsumori, K
2012-02-01
In negative ion sources for the neutral beam injection, it is important to calculate H atom flux onto the plasma grid (PG) surface for the evaluation of H(-) production on the PG surface. We have developed a neutral (H(2) molecules and H atoms) transport code. In the present study, the neutral transport code is applied to the analysis of the H(2) and H transport in a NIFS-R&D ion source in order to calculate the flux onto the PG surface. Taking into account non-equilibrium feature of the electron energy distribution function (EEDF), i.e., the fast electron component, we have done the neutral transport simulation. The results suggest that the precise evaluation of the EEDF, especially in the energy range 15 eV < E < 30 eV is important for the dissociation rate of H(2) molecules by the electron impact collision and the resultant H atom flux on the PG.
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
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.
Noronha, Jorge
2015-01-01
In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime $\\mathrm{AdS}_{2}\\otimes \\mathrm{S}_{2}$. We further derive explicit analytic expressions for the momentum dependence of the single particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The non-equilibrium contribution to the entropy density is shown to be due to higher order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Thus, in this system the slowly moving hydrodynamic d...
de Avillez, M A; Breitschwerdt, D; Spitoni, E
2012-01-01
Using three-dimensional non-equilibrium ionization (NEI) hydrodynamical simulation of the interstellar medium (ISM), we study the electron density, $n_{e}$, in the Galactic disk and compare it with the values derived from dispersion measures towards pulsars with known distances located up to 200 pc on either side of the Galactic midplane. The simulation results, consistent with observations, can be summarized as follows: (i) the DMs in the simulated disk lie between the maximum and minimum observed values, (ii) the log derived from lines of sight crossing the simulated disk follows a Gaussian distribution centered at \\mu=-1.4 with a dispersion \\sigma=0.21, thus, the Galactic midplane =0.04\\pm 0.01$ cm$^{-3}$, (iii) the highest electron concentration by mass (up to 80%) is in the thermally unstable regime (200
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.
On the moments of the Boltzmann's collision operator arising from chemical reactions
Sarna, Neeraj; Torrilhon, Manuel
2016-11-01
For any study of microflows it is crucial to understand the collision dynamics of the molecules involved. In the present work we will discuss the collision dynamics of chemically reacting hard spheres(CRHS). The inability of the classical smooth inelastic hard spheres, which have been extensively used in the past to study granular gases, to describe the collision dynamics of chemically reacting hard spheres has been discussed. Using the model of rough inelastic hard spheres as a motivation, a new model has been proposed for chemically reacting hard spheres which has been further used to derive certain useful velocity transformations. A methodology to compute the moments of the Boltzmann's collision operator arising from chemical reactions, using Grad's distribution function, has been discussed in detail. Finally explicit expressions for the rates of the reaction have been obtained which contain contributions from higher order moment and thus can be used for non-equilibrium chemically reacting flows.
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.
Search for a Lorentz invariant velocity distribution of a relativistic gas
Curado, Evaldo M F; Soares, Ivano Damiao
2016-01-01
We examine numerically and analytically the problem of the relativistic velocity distribution in a 1-dim relativistic gas in thermal equilibrium. Our derivation is based on the special theory of relativity, the central limit theorem and the Lobachevsky structure of the velocity space of the theory, where the rapidity variable plays a crucial role. For v^2/c^2 << 1 and 1/\\beta = k_B T/ m_0 c^2 << 1 the distribution tends to the Maxwell-Boltzmann distribution.
Lanthaler, S.; Pfefferlé, D.; Graves, J. P.; Cooper, W. A.
2017-04-01
An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for guiding-centre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving the correspondence between guiding-centre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guiding-centre’s parallel velocity via the so-called Baños drift. The correct treatment of the guiding-centre push-forward with the Baños term leads to an anisotropic shift in the phase-space distribution of guiding-centres, consistent with the well-known magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guiding-centre equations: (1) neutral beam injection in a MAST-like low aspect-ratio spherical equilibrium where the fast ion driven current is significantly larger with respect to previous calculations, (2) fast ion losses due to resonant magnetic perturbations where a lower lost fraction and a better confinement is confirmed, (3) alpha particles in the ripple field of the European DEMO where the effect is found to be marginal.
Energy Technology Data Exchange (ETDEWEB)
Koga, S.; Shibata, T.; Terasaki, R.; Kameyama, N.; Hatayama, A. [Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522 (Japan); Bacal, M. [LPP, Ecole Polytechnique, Palaiseau, UPMC, Universite PARIS-SUD 11, UMR CNRS 7648 (France); Tsumori, K. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292 (Japan)
2012-02-15
In negative ion sources for the neutral beam injection, it is important to calculate H atom flux onto the plasma grid (PG) surface for the evaluation of H{sup -} production on the PG surface. We have developed a neutral (H{sub 2} molecules and H atoms) transport code. In the present study, the neutral transport code is applied to the analysis of the H{sub 2} and H transport in a NIFS-R and D ion source in order to calculate the flux onto the PG surface. Taking into account non-equilibrium feature of the electron energy distribution function (EEDF), i.e., the fast electron component, we have done the neutral transport simulation. The results suggest that the precise evaluation of the EEDF, especially in the energy range 15 eV < E < 30 eV is important for the dissociation rate of H{sub 2} molecules by the electron impact collision and the resultant H atom flux on the PG.
Discretization of the velocity space in solution of the Boltzmann equation
Shan, X; Shan, Xiaowen; He, Xiaoyi
1998-01-01
We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature.
Nomura, Yasunori
2015-01-01
Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except possibly the one imposed by the Poincare recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.
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...
Nagapetyan, Tigran
2011-01-01
In this work we widespread statistical physics (chemical kinetic stochastic) approach to the investigation of macrosystems, arise in economic, sociology and traffic flow theory. The main line is a definition of equilibrium of macrosystem as most probable macrostate of invariant measure of Markov dynamic (corresponds to the macrosystem). We demonstrate new dynamical interpretations for the well known static model of correspondence matrix calculation. Based on this model we propose a best response dynamics for the Beckmann's traffic flow distribution model. We prove that this "natural" dynamic under quite general conditions converges to the Nash-Wardrop's equilibrium. After that we consider two interesting demonstration examples.
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.
Lattice Boltzmann solver of Rossler equation
Institute of Scientific and Technical Information of China (English)
GuangwuYAN; LiRUAN
2000-01-01
We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the diffusion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numerical results show the method can be used to simulate Rossler equation.
Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach
Song, Huichao; Heinz, Ulrich W
2010-01-01
A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the non-equilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles for further propagation with the Boltzmann cascade we test the ability of the macroscopic hydrodynamic approach to emulate the microscopic evolution during the hadronic stage and extract the temperature dependence of the effective shear viscosity of the hadron resonance gas produced in the collision. We find that the extracted values depend...
Directory of Open Access Journals (Sweden)
Monique Florenzano
2008-09-01
Full Text Available General equilibrium is a central concept of economic theory. Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause “ceteris paribus” that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model
KOMPUTASI DISTRIBUSI NEUTRON DALAM STATISTIK MAXWELL BOLTZMANN
Directory of Open Access Journals (Sweden)
Tuti Purwoningsih
2013-03-01
Full Text Available The migration of neutron is arranged by some probability distributions such as probability of spread distribution, probability of distance distribution, probability of energy distribution and probability of flux distribution. One application of these pattern distributions is modelling the reaction between neutron and elements which compose the tissue related to the absorption of neutron in brain cancer tissues. This article explores computation analysis of pattern of distribution of neutron flux in a reactor system. Variables were the amount of neutron simulated and the depth of cylindrical reactor system. Simulations showed that 20-120 minutes was needed in executing 100,000 neutrons to build the distribution pattern of neutrons flux. This pattern was also depended on the depth of the system. In all depths, the peak of neutron flux distribution pattern was in the 3rd bin. Comparison between this simulations and experiment results in literatures showed that by analyzing the simulation of the distribution of neutron flux, a Poisson distribution which follows the Maxwell-Boltzmann was resulted. Perpindahan neutron diatur dengan beberapa peluang distribusi, seperti peluang distribusi sudut hamburan, peluang distribusi jarak perpindahan, peluang distribusi energi transfer, serta peluang distribusi fluks neutron. Salah satu aplikasi dari pola distribusi ini adalah pemodelan reaksi antara neutron dengan elemen-elemen penyusun jaringan yang terkait dengan serapan neutron dan dosis yang terserap oleh jaringan tumor otak pada terapi BNCT (Boron Neutron Capture Therapy. Dalam penelitian ini dibahas analisis komputasi tentang pola distribusi fluks neutron dalam suatu sistem reaktor. Variabel dalam penelitian ini adalah banyaknya neutron yang disimulasikan, serta kedalaman sistem reaktor yang dalam penelitian ini menggunakan sistem reaktor berbentuk silinder. Hasil simulasi menunjukkan bahwa dengan neutron sebanyak 100.000 diperlukan waktu eksekusi sekitar
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.
Directory of Open Access Journals (Sweden)
Gian Paolo Beretta
2008-08-01
Full Text Available A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Numerical solution of Boltzmann's equation
Energy Technology Data Exchange (ETDEWEB)
Sod, G.A.
1976-04-01
The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig.
2009-09-01
and Fe hydroxides) until an approximate equilibrium is achieved between particulate and aqueous phases as: 2dC (2) where Cp2 = the soil...adsorbed inorganic P pool (M·M-1; Barrow 1983; Van Riemsdijk et al. 1984). In general, Cp2 represents a small fraction of the total adsorbed inorganic P...3) where ρ = the soil density (M·L-3). Cd2 and Cp2 are related to an equilibrium partition coefficient as: 2 2p dC k C (4) where kd2 = the
F. Wania; Lei, Y. D.; Wang, C.; Abbatt, J. P. D.; Goss, K.-U.
2015-01-01
Many atmospheric and chemical variables influence the partitioning equilibrium between gas phase and condensed phases of compounds implicated in the formation of secondary organic aerosol (SOA). The large number of factors and their interaction makes it often difficult to assess their relative importance and concerted impact. Here we introduce a two-dimensional space which maps regions of dominant atmospheric phase distribution within a coordinate system defined by equilibri...
F. Wania; Lei, Y. D.; Wang, C.; Abbatt, J. P. D.; K.-U. Goss
2014-01-01
Many atmospheric and chemical variables influence the partitioning equilibrium between gas phase and condensed phases of compounds implicated in the formation of secondary organic aerosol (SOA). The large number of factors and their interaction makes it often difficult to assess their relative importance and concerted impact. Here we introduce a two-dimensional space, which maps regions of dominant atmospheric phase distribution within a coordinate system de...
Bagchi, Debarshee; Tsallis, Constantino
2017-04-01
The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.
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.
Beelen P van; Verbruggen EMJ; Peijnenburg WJGM; ECO
2002-01-01
The equilibrium partitioning method (EqP-method) can be used to derive environmental quality standards (like the Maximum Permissible Concentration or the intervention value) for soil or sediment, from aquatic toxicity data and a soil/water or sediment/water partitioning coefficient. The validity of
Lattice Boltzmann modeling of water entry problems
Zarghami, A.; Falcucci, G.; Jannelli, E.; Succi, S.; Porfiri, M.; Ubertini, S.
2014-12-01
This paper deals with the simulation of water entry problems using the lattice Boltzmann method (LBM). The dynamics of the free surface is treated through the mass and momentum fluxes across the interface cells. A bounce-back boundary condition is utilized to model the contact between the fluid and the moving object. The method is implemented for the analysis of a two-dimensional flow physics produced by a symmetric wedge entering vertically a weakly-compressible fluid at a constant velocity. The method is used to predict the wetted length, the height of water pile-up, the pressure distribution and the overall force on the wedge. The accuracy of the numerical results is demonstrated through comparisons with data reported in the literature.
Training Restricted Boltzmann Machines on Word Observations
Dahl, George E; Larochelle, Hugo
2012-01-01
The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language processing applications, words are naturally modeled by K-ary discrete distributions, where K is determined by the vocabulary size and can easily be in the hundred thousands. The conventional approach to training RBMs on word observations is limited because it requires sampling the states of K-way softmax visible units during block Gibbs updates, an operation that takes time linear in K. In this work, we address this issue by employing a more general class of Markov chain Monte Carlo operators on the visible units, yielding updates with computational complexity independent of K. We demonstrate the success of our approach by training RBMs on hundreds of millions of word n-grams using larger vocabularies than previously feasible with RBMs and using the learned features to improve p...
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 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.
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...
Are there Boltzmann brains in the vacuum
Davenport, Matthew
2010-01-01
"Boltzmann brains" are human brains that arise as thermal or quantum fluctuations and last at least long enough to think a few thoughts. In many scenarios involving universes of infinite size or duration, Boltzmann brains are infinitely more common than human beings who arise in the ordinary way. Thus we should expect to be Boltzmann brains, in contradiction to observation. We discuss here the question of whether Boltzmann brains can arise as quantum fluctuations in the vacuum. Such Boltzmann brains pose an even worse problem than those arising as fluctuations in the thermal state of an exponentially expanding universe. We give several arguments for and against inclusion of vacuum Boltzmann brains in the anthropic reference class, but find neither choice entirely satisfactory.
Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows
Meng, Jianping
2009-01-01
In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is proved to be equivalent to the linearized Bhatnagar-Gross-Krook (BGK) equation. Therefore, when the same Gauss-Hermite quadrature is used, LB method closely assembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be correlated with the approximation order in terms of the Knudsen number to the BGK equation, which was previously suggested by \\cite{2006JFM...550..413S}. Furthermore, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equili...
Directory of Open Access Journals (Sweden)
Wei-Bin Zhang
2014-01-01
Full Text Available This paper proposes a growth model of heterogeneous households with economic structure, wealth accumulation, endogenous labour supply, and tax rates. The paper is focused on effects of redistribution policies on income and wealth distribution, economic structure and economic growth. The paper integrates the Walrasian general equilibrium theory and neoclassical economic growth within a comprehensive framework. We overcome the controversial features in the two traditional theories by applying an alternative approach to households. We build an analytical framework for a disaggregated and microfounded general theory of economic growth with endogenous wealth accumulation. We simulate the model to identify equilibrium, stability and to plot the motion of the dynamic system with three groups. We also carry out comparative dynamic analysis with regard to the lump tax, human capital and propensity to use leisure time.
Gamma-distribution and wealth inequality
Indian Academy of Sciences (India)
A Chakraborti; M Patriarca
2008-08-01
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann entropy and a microscopic analysis of the collision dynamics of molecules in a gas. In various relevant cases, the equilibrium distribution is well-approximated by a gamma-distribution with suitably defined temperature and number of dimensions. This in turn allows one to quantify the inequalities observed in the wealth distributions and suggests that their origin should be traced back to very general underlying mechanisms, for instance, the fact that smaller the fraction of the relevant quantity (e.g. wealth) that agent can exchange during an interaction, the closer the corresponding equilibrium distribution is to a fair distribution.
Huang, Rongzong; Wu, Huiying
2015-08-01
In this paper, phase interface effects, including the differences in thermophysical properties between solid and liquid phases and the numerical diffusion across phase interface, are investigated for the recently developed total enthalpy-based lattice Boltzmann model for solid-liquid phase change, which has high computational efficiency by avoiding iteration procedure and linear equation system solving. For the differences in thermophysical properties (thermal conductivity and specific heat) between solid and liquid phases, a novel reference specific heat is introduced to improve the total enthalpy-based lattice Boltzmann model, which makes the thermal conductivity and specific heat decoupled. Therefore, the differences in thermal conductivity and specific heat can be handled by the dimensionless relaxation time and equilibrium distribution function, respectively. As for the numerical diffusion across phase interface, it is revealed for the first time and found to be induced by solid-liquid phase change. To reduce such numerical diffusion, multiple-relaxation-time collision scheme is exploited, and a special value (one fourth) for the so-called "magic" parameter, a combination of two relaxation parameters, is found. Numerical tests show that the differences in thermophysical properties can be correctly handled and the numerical diffusion across phase interface can be dramatically reduced. Finally, theoretical analyses are carried out to offer insights into the roles of the reference specific heat and "magic" parameter in the treatments of phase interface effects.
LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES
Institute of Scientific and Technical Information of China (English)
Sun Chenghai
2000-01-01
We present an adaptive lattice Boltzmann model to simulate super sonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation.As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions.The velocity distributions are compared with the analytical solution and the mea sured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection.
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.
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
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.
Energy Technology Data Exchange (ETDEWEB)
Ainsworth, Nathan G [ORNL; Grijalva, Prof. Santiago [Georgia Institute of Technology, Atlanta
2013-01-01
This paper discusses a proposed frequency restoration controller which operates as an outer loop to frequency droop for voltage-source inverters. By quasi-equilibrium analysis, we show that the proposed controller is able to provide arbitrarily small steady-state frequency error while maintaing power sharing between inverters without need for communication or centralized control. We derive rate of convergence, discuss design considerations (including a fundamental trade-off that must be made in design), present a design procedure to meet a maximum frequency error requirement, and show simulation results verifying our analysis and design method. The proposed controller will allow flexible plug-and-play inverter-based networks to meet a specified maximum frequency error requirement.
An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium
Eppard, W. M.; Grossman, B.
1993-01-01
We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.
Non-Boltzmann Ensembles and Monte Carlo Simulations
Murthy, K. P. N.
2016-10-01
Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble and for calculating macroscopic properties of a closed system at desired temperatures. An estimate of a mechanical property, like energy, of an equilibrium system, is made by averaging over a large number microstates generated by Boltzmann Monte Carlo methods. This is possible because we can assign a numerical value for energy to each microstate. However, a thermal property like entropy, is not easily accessible to these methods. The reason is simple. We can not assign a numerical value for entropy, to a microstate. Entropy is not a property associated with any single microstate. It is a collective property of all the microstates. Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo technique called Umbrella sampling was proposed some forty years ago. Umbrella sampling has since undergone several metamorphoses and we have now, multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc. This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated as follows. First un-weight a microstates of the entropic ensemble; then re-weight it to the desired physical ensemble. Carry out weighted average over the entropic ensemble to estimate physical quantities. In this talk I shall tell you of the most recent non- Boltzmann Monte Carlo method and show how to calculate free energy for a few systems. We first consider estimation of free energy as a function of energy at different temperatures to characterize phase transition in an hairpin DNA in the presence of an unzipping force. Next we consider free energy as a function of order parameter and to this end we estimate density of states g(E, M), as a function of both energy E, and order parameter M. This is carried out in two stages. We estimate g(E) in the first stage. Employing g
Analysis of Jeans instability from the Boltzmann equation
Kremer, Gilberto M.
2016-11-01
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. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.
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.
Morgan, George; London, David
2002-12-01
This study examines the effects of increasing supersaturation, attained by single-step liquidus undercooling (ΔT), on the partitioning of barium and cesium between potassic alkali feldspar (Afs) and hydrous granitic liquid at 200 MPa. The investigation is motivated by trace-element distribution patterns in granitic pegmatites which cannot be simulated by fractionation models using "equilibrium" partition coefficients, and thus its purpose is to assess if, how, and why partition coefficients for compatible and incompatible trace elements may vary when crystal growth commences far from the crystal-melt equilibrium boundary. Barium expands the liquidus stability field of potassic feldspar to higher temperatures, such that liquidi for the Ba-rich ( 0.5 wt% BaO) compositions used are 100 °C higher than for Ba-absent analogues. At low degrees of undercooling (ΔT 50 °C), values of DBaAfs/m. ( 10-20) fall within the range of previous investigations, as do values of DCsAfs/m. (=100 °C) are heterogeneous, such that DBaAfs/m. versus K/K+Na varies linearly between the average value at 850 °C and the equilibrium value appropriate to the temperature of growth. Hence, high supersaturation accompanying undercooling produces feldspar compositions by isothermal growth which record a vestige of the liquid line of descent (i.e., an ontogeny within zoned crystals which approximately tracks the feldspar liquidus from high temperature to the final low temperature of actual crystal growth). Such zoning patterns may mimic normal patterns produced by fractionation with decreasing temperature under near-equilibrium (near-liquidus) conditions. Increasing fluorine contents tend to exacerbate the effects of undercooling by inhibiting feldspar nucleation, causing both K/K+Na ratios and compatible trace-element partitioning behavior in feldspar to deviate from equilibrium values. This effect continues until nucleation lag is overcome, whereupon a period of rapid growth from supersaturated
Distribution Equilibrium of o-Phthalic Acid and trans-Butenedioic in Water and Di-n-butyl Phthalate
Institute of Scientific and Technical Information of China (English)
GAO Zhenghong; YANG Xiaorui; HU Chaoquan; LI Jiang
2006-01-01
The organic dissolvent(di-n-butyl phthalate)needs to be washed by water to recycle itself in the process of recovering maleic anhydride by organic dissolvent. The design and optimization of the extraction process require the distribution coefficients of the organic solutes, o-phthalic acid and trans-butenedioic in water and di-n-butyl phthalate, on which the extraction efficiency depends. In this study, the distribution coefficients of o-phthalic acid and trans-butenedioic in water and di-n-bu-tyl phthalate(DBP)at 298.15 K, 318.15 K and 333.15 K were determined respectively by acid-alkali titration. The dissociation constants of o-phthalic acid and trans-butenedioic at those temperatures were obtained by fitting the measured hydrogen-ion concentrations and the known solute concentrations in the aqueous solution containing the two organic solutes. Then the distribution constants were calculated. Both the distribution coefficients and the distribution constants increase along with the temperature increasing. And the distribution coefficients at 333.15 K are large enough to ensure the efficiency of extraction process. In addition, the mutual solubility of water and di-n-butyl phthalate at 298.15 K, 318.15 K and 333.15 K was also measured respectively by High Performance Liquid Chromatography and Karl Fischer Watertitration, which was not more than 0.5%(mass fraction).
Roussel-Dupre, R.
1979-01-01
Non-Maxwellian electron velocity distribution functions, previously computed for Dupree's model of the solar transition region are used to calculate ionization rates for ions of carbon, nitrogen, and oxygen. Ionization equilibrium populations for these ions are then computed and compared with similar calculations assuming Maxwellian distribution functions for the electrons. The results show that the ion populations change (compared to the values computed with a Maxwellian) in some cases by several orders of magnitude depending on the ion and its temperature of formation.
An Infinite Restricted Boltzmann Machine.
Côté, Marc-Alexandre; Larochelle, Hugo
2016-07-01
We present a mathematical construction for the restricted Boltzmann machine (RBM) that does not require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, with a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behavior of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size.
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
van der Burg, W.; van Willigenburg, T.
1998-01-01
The basic idea of reflective equilibrium, as a method for theory construction and decision making in ethics, is that we should bring together a broad variety of moral and non-moral beliefs and, through a process of critical scrutiny and mutual adjustment, combine these into one coherent belief syste
Study on Equilibrium of Supply Chain Network with Uncertain Demand Distribution%需求分布不定的供应链网络均衡
Institute of Scientific and Technical Information of China (English)
李增强; 胡劲松; 胡小根; 张桂涛
2012-01-01
In this paper we studied the equilibrium of a supply chain network composed of multiple mutually competing manufacturers and re tailers and the latter were faced with uncertain demand distribution.Using variational inequality theory, we depicted the optimal behaviour of the manufacturers, retailers and consumers, established the supply chain network equilibrium model and designed its solution algorithm. Then we used a numerical example to study the influence of the distributional uncertainty and price ceiling on the network equilibrium and found that as compared with stochastic demand, when the demand distribution was uncertain, the profit of the retailers would be diminished while that of the manufacturers would be increased and they also would produce more; when where was a price ceiling, the consumer market would experience commodity shortage and the total profit of the manufacturers and retailers would decrease.%研究了由多个相互竞争制造商以及多个相互竞争零售商组成且零售商面临分布不定的需求的供应链网络均衡.借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型并设计网络均衡的求解算法.数值分析了分布不定和限制性价格上限对网络均衡的影响.结果表明:与随机需求相比较,需求分布不定情形下的零售商利润将减少,制造商利润将增多且生产量更大；当存在限制性价格上限时,消费市场可能出现商品短缺,且制造商和零售商的总利润减少.
Uranium-Radium Equilibrium Coefficient Distribution in Pingxiashui Area%坪下水地区铀矿石铀镭平衡系数变化特征
Institute of Scientific and Technical Information of China (English)
王家跃
2014-01-01
Uranium-radium equilibrium coefficient is an important parameter in uranium exploration. Correctly measuring and analyzing the parameter is significance to guide the uranium exploration and research of uranium metal ogenic regularity. Used of analyze data of dril core samples in PINGXIASHUI area analyzing distribution characteristics of U-Ra equilibrium coefficient that could providing references for uranium exploration in this area.%铀镭平衡系数是铀矿勘查的重要参数，正确测量、分析该参数，对指导铀矿勘查、研究铀成矿规律有重要意义，利用坪下水地区钻探岩矿心样品分析结果，综合分析研究该地区铀镭平衡系数分布特征，为坪下水地区今后铀矿勘查提供参考。
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.
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
A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
Denicol, Gabriel S; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael
2014-01-01
We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to 1st- and 2nd-order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. This novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.
Filter-matrix lattice Boltzmann model for microchannel gas flows.
Zhuo, Congshan; Zhong, Chengwen
2013-11-01
The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.
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.
Boltzmann and the art of flying
Dahmen, Silvio R
2007-01-01
One of the less known facets of Ludwig Boltzmann was that of an advocate of Aviation, one of the most challenging technological problems of his times. Boltzmann followed closely the studies of pioneers like Otto Lilienthal in Berlin, and during a lecture on a prestigious conference he vehemently defended further investments in the area. In this article I discuss his involvement with Aviation, his role in its development and his correspondence with two flight pioneers, Otto Lilienthal e Wilhelm Kress.
Chau, Nancy H.
2009-01-01
This paper presents a capability-augmented model of on the job search, in which sweatshop conditions stifle the capability of the working poor to search for a job while on the job. The augmented setting unveils a sweatshop equilibrium in an otherwise archetypal Burdett-Mortensen economy, and reconciles a number of oft noted yet perplexing features of sweatshop economies. We demonstrate existence of multiple rational expectation equilibria, graduation pathways out of sweatshops in complete abs...
Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation
Ren, Feng; Song, Baowei; Sukop, Michael C.; Hu, Haibao
2016-08-01
The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015), 10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014), 10.1103/PhysRevE.89.053320]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.
Lattice Boltzmann method simulations of Stokes number effects on particle motion in a channel flow
Zhang, Lenan; Jebakumar, Anand Samuel; Abraham, John
2016-06-01
In a recent experimental study by Lau and Nathan ["Influence of Stokes number on the velocity and concentration distributions in particle-laden jets," J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (effects on particle trajectories in a wall-bounded flow," Comput. Fluids 124, 208 (2016)] have carried out simulations of a particle in a laminar channel flow to investigate this behavior. In their work, they report a similar behavior where particles with low St migrate toward the wall and oscillate about a mean position near the wall while those with high St oscillate about the channel center plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.
Non-equilibrium cation distribution and enhanced spin disorder in hollow CoFe2O4 nanoparticles.
Jaffari, G Hassnain; Ceylan, A; Bui, Holt P; Beebe, Thomas P; Ozcan, S; Shah, S Ismat
2012-08-22
We present magnetic properties of hollow and solid CoFe(2)O(4) nanoparticles that were obtained by annealing of Co(33)Fe(67)/CoFe(2)O(4) (core/shell) nanoparticles. Hollow nanoparticles were polycrystalline whereas the solid nanoparticles were mostly single crystal. Electronic structure studies were performed by photoemission which revealed that particles with hollow morphology have a higher degree of inversion compared to solid nanoparticles and the bulk counterpart. Electronic structure and the magnetic measurements show that particles have uncompensated spins. Quantitative comparison of saturation magnetization (M(S )), assuming bulk Néel type spin structure with cationic distribution, calculated from quantitative XPS analysis, is presented. The thickness of uncompensated spins is calculated to be significantly large for particles with hollow morphology compared to solid nanoparticles. Both morphologies show a lack of saturation up to 7 T. Moreover magnetic irreversibility exists up to 7 T of cooling fields for the entire temperature range (10-300 K). These effects are due to the large bulk anisotropy constant of CoFe(2)O(4) which is the highest among the cubic spinel ferrites. The effect of the uncompensated spins for hollow nanoparticles was investigated by cooling the sample in large fields of up to 9 T. The magnitude of horizontal shift resulting from the unidirectional anisotropy was more than three times larger than that of solid nanoparticles. As an indication signature of uncompensated spin structure, 11% vertical shift for hollow nanoparticles is observed, whereas solid nanoparticles do not show a similar shift. Deconvolution of the hysteresis response recorded at 300 K reveals the presence of a significant paramagnetic component for particles with hollow morphology which further confirms enhanced spin disorder.
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...
Institute of Scientific and Technical Information of China (English)
段雅丽; 陈先进; 孔令华
2015-01-01
We develop a lattice Boltzmann model for compound Burgers-Korteweg-de Vries ( cBKdV) equation. By properly treating dispersive term uxxx and applying Chapman-Enskog expansion, the governing equation is recovered correctly from lattice Boltzmann equation and local equilibrium distribution functions are obtained. Numerical experiments show that our results agree well with exact solutions and have better numerical accuracy compared with previous numerical results. This hence indicates that the model is satisfactory and efficient.%针对Burgers-Korteweg-de Vries ( cBKdV)复合方程提出一种格子Boltzmann模型。通过恰当地处理色散项uxxx 并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程，从而得到联系微观量与宏观量的局部平衡分布函数。对不同微分方程进行数值实验，数值解与解析解非常吻合，相比于其它数值结果，该格子Boltzmann模型的数值结果更精确，说明该数值模型的高效性。
A tightly coupled non-equilibrium model for inductively coupled radio-frequency plasmas
Energy Technology Data Exchange (ETDEWEB)
Munafò, A., E-mail: munafo@illinois.edu; Alfuhaid, S. A., E-mail: alfuhai2@illinois.edu; Panesi, M., E-mail: mpanesi@illinois.edu [Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Talbot Laboratory, 104 S. Wright St., Urbana, Illinois 61801 (United States); Cambier, J.-L., E-mail: jean-luc.cambier@us.af.mil [Edwards Air Force Base Research Laboratory, 10 E. Saturn Blvd., Edwards AFB, California 93524 (United States)
2015-10-07
The objective of the present work is the development of a tightly coupled magneto-hydrodynamic model for inductively coupled radio-frequency plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State approach. A multi-temperature formulation is used to account for thermal non-equilibrium between translation of heavy-particles and vibration of molecules. Excited electronic states of atoms are instead treated as separate pseudo-species, allowing for non-Boltzmann distributions of their populations. Free-electrons are assumed Maxwellian at their own temperature. The governing equations for the electro-magnetic field and the gas properties (e.g., chemical composition and temperatures) are written as a coupled system of time-dependent conservation laws. Steady-state solutions are obtained by means of an implicit Finite Volume method. The results obtained in both LTE and NLTE conditions over a broad spectrum of operating conditions demonstrate the robustness of the proposed coupled numerical method. The analysis of chemical composition and temperature distributions along the torch radius shows that: (i) the use of the LTE assumption may lead to an inaccurate prediction of the thermo-chemical state of the gas, and (ii) non-equilibrium phenomena play a significant role close the walls, due to the combined effects of Ohmic heating and macroscopic gradients.
Oliveira, Mário J
2013-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This textbo...
de Oliveira, Mário J
2017-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This new edit...
Adaptive Lattice Boltzmann Model for Compressible Flows
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new lattice Boltzmann model for compressible flows is presented. The main difference from the standard lattice Boltzmann model is that the particle velocities are no longer constant, but vary with the mean velocity and internal energy. The adaptive nature of the particle velocities permits the mean flow to have a high Mach number. The introduction of a particle potential energy makes the model suitable for a perfect gas with arbitrary specific heat ratio. The Navier-Stokes (N-S) equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. Two kinds of simulations have been carried out on the hexagonal lattice to test the proposed model. One is the Sod shock-tube simulation. The other is a strong shock of Mach number 5.09 diffracting around a corner.
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
General Search Market Equilibrium
Albrecht, James W.; Axell, Bo
1982-01-01
In this paper we extend models of “search market equilibrium” to incorporate general equilibrium considerations. The model we treat is one with a single product market and a single labor market. Imperfectly informed individuals follow optimal strategies in searching for a suitably low price and high wage. For any distribution of price and wage offers across firms these optimal strategies generate product demand and labor supply schedules. Firms then choose prices and wages to maximize expecte...
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.
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
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.
Energy Technology Data Exchange (ETDEWEB)
Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)
2011-04-08
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.
Hong, Y.; Zhang, K.; Gourley, J. J.
2015-12-01
Floods and landslides account for the large number of natural hazards and affect more people than many other types of natural disasters around the world. This study proposed a coupled hydrological-geotechnical model iCRESLIDE (Integration of Coupled Routing and Excess Storage and SLope-Infiltration-Distributed Equilibrium). The iCRESLIDE is designed to remedy the discrepancy of the original landslide model (SLIDE) by coupling with a hydrological model (CREST) and building an integrated system for predicting cascading storm-flood-landslides using remote sensing and geospatial datasets. This coupled system is implemented and evaluated in Macon County, North Carolina, where Hurricane Ivan triggered widespread landslides in September 2004 during the hurricane season. Model simulations from iCRESLIDE show its reliability to predict landslides occurrence (location and time). Receiver Operating Characteristic (ROC) analysis demonstrate that the iCRESLIDE has higher global accuracy (0.750) and higher sensitivity (11.36%) compared to the original SLIDE model. Such improved predictive performance demonstrates the advantage of coupling hydrological-geotechnical models, which calls more attentions and deserves further investigations in order to develop a not only geotechnical sound but also hydrological sensitive system for landslides early warning at regional scale. This talk will also present early results of the NFL (National-Flash-Landslide) Monitoring and Prediction system under development at the NOAA/OU National Weather Center.
Ahmed, Khaliq; Fӧger, Karl
2017-03-01
The SOFC is well-established as a high-efficiency energy conversion technology with demonstrations of micro-CHP systems delivering 60% net electrical efficiency [1]. However, there are key challenges in the path to commercialization. Foremost among them is stack durability. Operating at high temperatures, the SOFC invariably suffers from thermally induced material degradation. This is compounded by thermal stresses within the SOFC stack which are generated from a number of interacting factors. Modelling is used as a tool for predicting undesirable temperature and current density gradients. For an internal reforming SOFC, fidelity of the model is strongly linked to the representation of the fuel reforming reactions, which dictate species concentrations and net heat release. It is critical for simulation of these profiles that the set of reaction rate expressions applicable for the particular anode catalyst are chosen in the model. A relatively wide spectrum of kinetic correlations has been reported in the literature. This work presents a comparative analysis of the internal distribution of temperature, current, voltage and compositions on a SOFC anode, using various combinations of reaction kinetics and equilibrium expressions for the reactions. The results highlight the significance of the fuel reforming chemistry and kinetics in the prediction of cell performance.
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
Master equation for a chemical wave front with perturbation of local equilibrium
Dziekan, P.; Lemarchand, A.; Nowakowski, B.
2011-08-01
In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.
Energy Technology Data Exchange (ETDEWEB)
Capitelli, Mario [Dipartimento di Chimica, Universitá di Bari, Via Orabona 4, 70125 Bari (Italy); CNR-IMIP, Via Amendola 122/D, 70126 Bari (Italy); Colonna, Gianpiero; D' Ammando, Giuliano; Laricchiuta, Annarita [CNR-IMIP, Via Amendola 122/D, 70126 Bari (Italy); Laporta, Vincenzo [Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom)
2013-10-15
Electron energy distribution functions have been calculated by a self-consistent model which couples the electron Boltzmann equation with vibrationally and electronically excited state kinetics and plasma chemistry. Moderate pressure nitrogen gas discharges in the E/N range from 30 to 60 Townsend are investigated comparing an electron-impact cross section set considering transitions starting from all the vibrational states, with reduced models, taking into account only collisions involving the ground vibrational level. The results, while confirming the important role of second kind collisions in affecting the eedf, show a large dependence of the eedf on the set of inelastic processes involving vibrationally and electronically excited molecules, pointing out the need of using a cross section database including processes linking excited states in non-equilibrium plasma discharge models.
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.
A Boltzmann Transport Simulation Using Open Source Physics
Hasbun, Javier
2004-03-01
The speed of a charged particle, under an applied electric field, in a conducting media, is, usually, simply modelled by writing Newton's 2nd law in the form mfrac ddtv=qE-mfrac vτ ; (1), where v is the speed, E is the applied electric field, q is the charge, m is the mass, and τ is the scattering time between collisions. Here, we simulate a numerical solution of the Boltzmann transport equation,frac partial partial tf+ vot nabla _rf+Fot nabla _pf=frac partial partial tf|_coll (2), where in general the Boltzmann distribution function f=f(r,p,t) depends on position, momentum, and time. Our numerical solution is made possible by neglecting the 2nd term on the LHS, and by modelling the RHS collision term as fracpartial partial tf|_coll=-frac 1τ . With these approximations, in addition to considering only one dimension, we find, our numerical solution of (2). The average velocity numerically obtained through the resulting distribution is compared to that obtained by the analytic solution of (1). An efficient method of carrying out the numerical solution of (2) due to P. Drallos and M. Wadehra [Journal of Applied Physics 63, 5601(1988)] is incorporated here. A final version of an applet that performs the full Java simulation will be located at http://www.westga.edu/ jhasbun/osp/osp.htm.
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.
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.
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.
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...
From Newton's Law to the Linear Boltzmann Equation Without Cut-Off
Ayi, Nathalie
2017-01-01
We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. More particularly, we will describe the motion of a tagged particle in a gas close to global equilibrium. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated with the long-range interaction, leading to some explicit weak estimates.
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...
From Newton's Law to the Linear Boltzmann Equation Without Cut-Off
Ayi, Nathalie
2017-03-01
We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. More particularly, we will describe the motion of a tagged particle in a gas close to global equilibrium. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated with the long-range interaction, leading to some explicit weak estimates.
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 ...
Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Directory of Open Access Journals (Sweden)
Ramon F. Álvarez-Estrada
2014-03-01
Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not
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...
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.
Geometric variations of the Boltzmann entropy
Kalogeropoulos, Nikos
2008-01-01
We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.
Boltzmann und das Ende des mechanistischen Weltbildes
Renn, Jürgen
2007-01-01
Der Wissenschaftshistoriker und Physiker Jürgen Renn untersucht die Rolle des österreichischen Physikers und Philosophen Ludwig Boltzmann (18441906) bei der Entwicklung der modernen Physik. Boltzmann war einer der letzen Vertreter des mechanistischen Weltbildes und stand somit am Ende eines Zeitalters. Renn porträtiert den Wissenschaftler aber als einen Pionier der modernen Physik, dessen Beschäftigung mit den inneren Spannungen der klassischen Physik ihn visionär zukünftige Fragestellungen aufgreifen ließ. So befasste sich Boltzmann etwa mit den Grenzproblemen zwischen Mechanik und Thermodynamik, die ihn zur Entwicklung immer raffinierterer Instrumente der statistischen Physik antrieb, die schließlich zu Schlüsselinstrumenten der modernen Physik wurden. Boltzmanns Werk steht somit am Übergang vom mechanistischen Weltbild zur Relativitäts- und Quantentheorie. Der Aussage des viel bekannteren Physikers Albert Einstein, dass Fantasie wichtiger sei als Wissen, hält Jürgen Renn im Hinblick auf Leben ...
Entropic lattice Boltzmann model for Burgers's equation.
Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey
2004-08-15
Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
Stefan-Boltzmann law for massive photons
Moreira, E S
2015-01-01
Thirty years ago a paper appeared in the literature generalizing the Stefan-Boltzmann law to include massive photons. The paper suffers from a flaw though: it assumes that a massive photon travels at the speed of (massless) light. The present work fixes the mistake and presents the correct formula for the radiance.
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.
Boltzmann Samplers for Colored Combinatorial Objects
Bodini, Olivier
2009-01-01
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary generating function.
The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation
Frank, Martin; Larsen, Edward W; Vasques, Richard
2014-01-01
We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo, with only statistical errors - no truncation errors.
Nicholls, David C; Sutherland, Ralph S
2012-01-01
The measurement of electron temperatures and metallicities in H ii regions and Planetary Nebulae (PNe) has-for several decades-presented a problem: results obtained using different techniques disagree. What it worse, they disagree consistently. There have been numerous attempts to explain these discrepancies, but none has provided a satisfactory solution to the problem. In this paper, we explore the possibility that electrons in H ii regions and PNe depart from a Maxwell-Boltzmann equilibrium energy distribution. We adopt a "kappa-distribution" for the electron energies. Such distributions are widely found in Solar System plasmas, where they can be directly measured. This simple assumption is able to explain the temperature and metallicity discrepancies in H ii regions and PNe arising from the different measurement techniques. We find that the energy distribution does not need to depart dramatically from an equilibrium distribution. From an examination of data from Hii regions and PNe it appears that kappa ~ ...
Far-from-equilibrium processes without net thermal exchange via energy sorting.
Vilar, Jose M G; Rubi, J Miguel
2012-02-14
Many important processes at the microscale require far-from-equilibrium conditions to occur, as in the functioning of mesoscopic bioreactors, nanoscopic rotors, and nanoscale mass conveyors. Achieving such conditions, however, is typically based on energy inputs that strongly affect the thermal properties of the environment and the controllability of the system itself. Here, we present a general class of far-from-equilibrium processes that suppress the net thermal exchange with the environment by maintaining the Maxwell-Boltzmann velocity distribution intact. This new phenomenon, referred to as ghost equilibrium, results from the statistical cancellation of superheated and subcooled nonequilibrated degrees of freedom that are autonomously generated through a microscale energy sorting process. We provide general conditions to observe this phenomenon and study its implications for manipulating energy at the microscale. The results are applied explicitly to two mechanistically different cases, an ensemble of rotational dipoles and a gas of trapped particles, which encompass a great variety of common situations involving both rotational and translational degrees of freedom.
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.
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.
Application of Lattice Boltzmann Methods in Complex Mass Transfer Systems
Sun, Ning
Lattice Boltzmann Method (LBM) is a novel computational fluid dynamics method that can easily handle complex and dynamic boundaries, couple local or interfacial interactions/reactions, and be easily parallelized allowing for simulation of large systems. While most of the current studies in LBM mainly focus on fluid dynamics, however, the inherent power of this method makes it an ideal candidate for the study of mass transfer systems involving complex/dynamic microstructures and local reactions. In this thesis, LBM is introduced to be an alternative computational method for the study of electrochemical energy storage systems (Li-ion batteries (LIBs) and electric double layer capacitors (EDLCs)) and transdermal drug design on mesoscopic scale. Based on traditional LBM, the following in-depth studies have been carried out: (1) For EDLCs, the simulation of diffuse charge dynamics is carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). Steric effect of concentrated solutions is considered by using modified Poisson-Nernst-Plank (MPNP) equations and compared with regular Poisson-Nernst-Plank (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. (2) For the study of dendrite formation on the anode of LIBs, it is shown that the Lattice Boltzmann model can capture all the experimentally observed features of microstructure evolution at the anode, from smooth to mossy to dendritic. The mechanism of dendrite formation process in mesoscopic scale is discussed in detail and compared with the traditional Sand's time theories. It shows that dendrite formation is closely related to the inhomogeneous reactively at the electrode-electrolyte interface
Determining equilibrium constants for dimerization reactions from molecular dynamics simulations.
De Jong, Djurre H; Schäfer, Lars V; De Vries, Alex H; Marrink, Siewert J; Berendsen, Herman J C; Grubmüller, Helmut
2011-07-15
With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form ΔG ∝ ln(P(1) /P(0) ). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics.
Non-equilibrium Warm Dense Gold: Experiments and Simulations
Ng, Andrew
2015-11-01
This talk is an overview of a series of studies of non-equilibrium Warm Dense Matter using a broad range of measured properties of a single material, namely Au, as comprehensive benchmarks for theory. The measurements are made in fs-laser pump-probe experiments. For understanding lattice stability, our investigation reveals a solid phase at high energy density. This leads to the calculation of lattice dynamics using MD simulations and phonon hardening in DFT-MD simulations. For understanding electron transport in two-temperature states, AC conductivity is used to evaluate DFT-MD and Kubo-Greenwood calculations while DC conductivity is used to test Ziman calculations in a DFT average atom model. The electron density is also used to assess electronic structure calculations in DFT simulations. In our latest study of electron kinetics in states with a non-Fermi-Dirac distribution, three-body recombination is found to have a significant effect on electron thermalizaiton time. This is driving an effort to develop electron kinetics simulations using the Boltzmann equation method.
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
Boltzmann equations for neutrinos with flavor mixings
Yamada, Shoichi
2000-01-01
With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained ...
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.
Energy flow in non-equilibrium conformal field theory
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
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.
Feigin, Alexander; Belikovich, Mikhail; Kulikov, Mikhail
2016-04-01
Atomic oxygen and hydrogen are known to be among key components for the photochemistry and energy balance of the Earth's atmosphere between approximately 80 and 100 km altitude (mesopause region). Therefore, obtaining information about the vertical distributions of O and H concentrations is an important task in studies of this region. Solving of this problem is rather difficult due to the absence of regular methods which allow one to direct measurements of distributions of these components in mesosphere. However, indirect methods used to retrieve O and H distributions from the satellite-based measurements of the OH and O2(1D) airglow emission, as well as the data of IR and microwave O3 measurements have a sufficiently long development history. These methods are rooted in the use of the condition of photochemical equilibrium of ozone density in the range of altitudes from 50 to 100 km. A significant factor is that an insufficient volume of such measurement data forces researchers to use approximate ("truncated") photochemical-equilibrium conditions. In particular, it is assumed that in the daytime the ozone production reaction is perfectly balanced by ozone photodissociation, whereas during the night the only ozone sink is the reaction of ozone with atomic hydrogen, which, in its turn, leads to formation of excited OH and airglow emission of the latter. The presentation analyzes applicability of the photochemical-equilibrium conditions both in the total and truncated forms for description of the spatio-temporal evolution of mesospheric ozone during a year. The analysis is based on year-long time series generated by a 3D chemical transport model, which reproduces correctly various types of atmosphere dynamics in the range of altitudes from 50 to 100 km. These data are used to determine statistics of the ratio between the correct (calculated dynamically) distributions of the O3 density and its uncontracted and truncated equilibrium values for the conditions of the
Huang, Rongzong; Wu, Huiying
2016-06-01
A total enthalpy-based lattice Boltzmann (LB) method with adaptive mesh refinement (AMR) is developed in this paper to efficiently simulate solid-liquid phase change problem where variables vary significantly near the phase interface and thus finer grid is required. For the total enthalpy-based LB method, the velocity field is solved by an incompressible LB model with multiple-relaxation-time (MRT) collision scheme, and the temperature field is solved by a total enthalpy-based MRT LB model with the phase interface effects considered and the deviation term eliminated. With a kinetic assumption that the density distribution function for solid phase is at equilibrium state, a volumetric LB scheme is proposed to accurately realize the nonslip velocity condition on the diffusive phase interface and in the solid phase. As compared with the previous schemes, this scheme can avoid nonphysical flow in the solid phase. As for the AMR approach, it is developed based on multiblock grids. An indicator function is introduced to control the adaptive generation of multiblock grids, which can guarantee the existence of overlap area between adjacent blocks for information exchange. Since MRT collision schemes are used, the information exchange is directly carried out in the moment space. Numerical tests are firstly performed to validate the strict satisfaction of the nonslip velocity condition, and then melting problems in a square cavity with different Prandtl numbers and Rayleigh numbers are simulated, which demonstrate that the present method can handle solid-liquid phase change problem with high efficiency and accuracy.
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
Directory of Open Access Journals (Sweden)
Rudolf A. Treumann
2014-08-01
Full Text Available 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.
Emergence of Compositional Representations in Restricted Boltzmann Machines
Tubiana, Jérôme
2016-01-01
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for this purpose, and to be able to generate distributed and graded representations of the data. We characterize the structural conditions (sparsity of the weights, low effective temperature, nonlinearities in the activation functions of hidden units, and adaptation of fields maintaining the activity in the visible layer) allowing RBM to operate in such a compositional phase. Evidence is provided by the replica analysis of an adequate statistical ensemble of random RBMs and by RBM trained on the handwritten digits dataset MNIST.
Simulating High Reynolds Number Flow 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
@@ A two-dimensional channel flow with different Reynolds numbers is tested by using the lattice Boltzmann method under different pressure and velocity boundary conditions. The results show that the simulation error increases,and the pressure and the flow rate become unstable under a high Reynolds number. To improve the simulation precision under a high Reynolds number, the number of fluid nodes should be enlarged. For a higher Reynoldsnumber flow, the velocity boundary with an approximately parabolic velocity profile is found to be more adaptive.Blood flow in an artery with cosine shape symmetrical narrowing is then simulated under a velocity boundary condition. Its velocity, pressure and wall shear stress distributions are consistent with previous studies.
Lattice Boltzmann simulations of convection heat transfer in porous media
Liu, Qing; He, Ya-Ling
2017-01-01
A non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed to study convection heat transfer in porous media at the representative elementary volume scale based on the generalized non-Darcy model. In the method, two different LB models are constructed: one is constructed in the framework of the double-distribution-function approach, and the other is constructed in the framework of the hybrid approach. In particular, the transformation matrices used in the MRT-LB models are non-orthogonal matrices. The present method is applied to study mixed convection flow in a porous channel and natural convection flow in a porous cavity. It is found that the numerical results are in good agreement with the analytical solutions and/or other results reported in previous studies. Furthermore, the non-orthogonal MRT-LB method shows better numerical stability in comparison with the BGK-LB method.
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.
Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
Das, Santosh K; Greco, Vincenzo
2013-01-01
The propagation of heavy quarks through the quark-gluon plasma (QGP) has been often treated within the framework of Langevin equation (LV), i.e. assuming the heavy flavor momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a thorough study of the approximations involved in Langevin dynamics by mean of a direct comparison with the solution of the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_q/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra with time and consequently on the so-called nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but the estimate of the underlying diffusion coefficient can differ by about $\\sim 15-50\\%$ depending on t...
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao
2013-10-01
The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases
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.
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.
Gao, Y.-Q.; Liu, F.-H.
2016-03-01
The transverse momentum spectra of charged particles produced in Au + Au collisions at the relativistic heavy ion collider and in Pb + Pb collisions at the large hadron collider with different centrality intervals are described by the multisource thermal model which is based on different statistic distributions for a singular source. Each source in the present work is described by the Tsallis distribution and the Boltzmann distribution, respectively. Then, the interacting system is described by the (two-component) Tsallis distribution and the (two-component) Boltzmann distribution, respectively. The results calculated by the two distributions are in agreement with the experimental data of the Solenoidal Tracker At Relativistic heavy ion collider, Pioneering High Energy Nuclear Interaction eXperiment, and A Large Ion Collider Experiment Collaborations. The effective temperature parameters extracted from the two distributions on the descriptions of heavy-ion data at the relativistic heavy ion collider and large hadron collider are obtained to show a linear correlation.
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.
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...
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.
A new way to measure the departure from thermodynamic equilibrium in stellar atmospheres
Institute of Scientific and Technical Information of China (English)
Zhong-Quan Qu; Long-Fei Hao; Xiao-Li Yan; Cheng-Lin Xu
2009-01-01
A new way to measure the departure from thermodynamic equilibrium is proposed based on the departure factor which evaluates the deviation from a Boltzmann level distribution, used by Short and Hauschildt (2005) and others. The way is based on an explicit relationship describing the departure factor as a function of line to continuum source, dynamic temperature and line photon frequency, under three assumptions that the scattering can be neglected, the background continuum can be treated as a Planck function, and finally the complete redistribution can be true. It has the advantage that the departure can be very conveniently evaluated from the spectral analysis with only the radiative transfer involved. Some physical insights are recovered for some extreme cases.Some example calculations of the departure are presented for the quiet Sun, faint solar flare and strong solar flare for the generally used solar chromospheric lines: Hα, Hβ,CaII H, K and triplet. It is revealed that in the case of solar flares, the departure is less than thermodynamic equilibrium along the larger depth range than in the quiet sun due to chromospheric condensation. It becomes hard to distinguish the departures for the different lines of the same atom or ion. It is expected that this investigation can be constructive for studying stellar atmospheres in cases where the three assumptions are close to reality.
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.
Hot electrons in superlattices: quantum transport versus Boltzmann equation
DEFF Research Database (Denmark)
Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.;
1999-01-01
A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...
Soluble Boltzmann equations for internal state and Maxwell models
Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.
1980-01-01
We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions. In the continuous variable version these models can equally be interpreted as Boltzmann equations for Ma
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati
Axisymmetric multiphase lattice Boltzmann method for generic equations of state
Reijers, S.A.; Gelderblom, H.; Toschi, F.
2016-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
Entropic Lattice Boltzmann Methods for Fluid Mechanics
Chikatamarla, Shyam; Boesch, Fabian; Sichau, David; Karlin, Ilya
2013-11-01
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. Our 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. We review here recent advances in ELBM as a practical, modeling-free tool for simulation of turbulent flows in complex geometries. We shall present recent simulations including turbulent channel flow, flow past a circular cylinder, knotted vortex tubes, and flow past a surface mounted cube. ELBM listed all admissible lattices supporting a discrete entropy function and has classified them in hierarchically increasing order of accuracy. Applications of these higher-order lattices to simulations of turbulence and thermal flows shall also be presented. This work was supported CSCS grant s437.
Williams, Samuel; Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA; NERSC, Lawrence Berkeley National Laboratory; Computer Science Department, University of California, Irvine, CA
2009-01-01
We apply auto-tuning to a hybrid MPI-pthreads lattice Boltzmann computation running on the Cray XT4 at National Energy Research Scientific Computing Center (NERSC). Previous work showed that multicore-specific auto-tuning can improve the performance of lattice Boltzmann magnetohydrodynamics (LBMHD) by a factor of 4x when running on dual- and quad-core Opteron dual-socket SMPs. We extend these studies to the distributed memory arena via a hybrid MPI/pthreads implementation. In addition to con...
The Geometry of Finite Equilibrium Datasets
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...
The geometry of finite equilibrium sets
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
2009-01-01
We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...
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.
Ion exchange equilibrium constants
Marcus, Y
2013-01-01
Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and
Quantum-statistical equilibrium and the ``law'' of constant Fermi potential
Le Coz, Yannick L.
2003-02-01
We apply the general quantum-statistical density-matrix formalism to an independent-electron gas within a space-dependent external electric potential, under equilibrium conditions. This problem is analogous to an ideal semiconductor homojunction diode. We solve the resulting equilibrium density-matrix equation using a perturbation theory. Next, we derive a first-order quantum correction to the classical Maxwell-Boltzmann density-potential formula. The correction appears as an added curvature term in external potential. It represents expected quantum-mechanical scattering against a spatially varying potential. Our results indicate that the commonly encountered thermodynamic or statistical-mechanical "law" of constant, equilibrium Fermi potential—with Fermi potential a parameter in the Maxwell-Boltzmann density-potential formula—is not fundamentally exact. In a general space-dependent potential, this "law," we prove, is simply a classical approximation.
Ambrus, Victor E
2016-01-01
We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.
Munafò, A; Panesi, M; Magin, T E
2014-02-01
A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.
Energy Technology Data Exchange (ETDEWEB)
Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M. [KU Leuven, Department of Mechanical Engineering, Celestijnenlaan 300A, 3001 Leuven (Belgium); Dekeyser, W. [ITER Organization, route de Vinon-sur-Verdon, 13067 St. Paul lez Durance Cedex (France); Samaey, G. [KU Leuven, Department of Computer Science, Celestijnenlaan 200A, 3001 Leuven (Belgium)
2016-01-15
We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assuming equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed
2013-06-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
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.
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 ...
Analytical solution of the Boltzmann-Poisson equation and its application to MIS tunneling junctions
Institute of Scientific and Technical Information of China (English)
Zhang Li-Zhi; Wang Zheng-Chuan
2009-01-01
In order to consider quantum transport under the influence of an electron-electron (e-e) interaction in a mesoscopic conductor, the Boltzmann equation and Poisson equation are investigated jointly. The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e-e interaction are obtained, and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation. Then we apply these results to the tunneling junctions of a metal-insulatorsemiconductor (MIS) in which the electrons are accumulated near the interface of the semiconductor, and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density, electric current as well as screening Coulombic potential in this case are studied, and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
Allen, Rebecca
2016-06-29
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.
Non-Boltzmann sampling and Bennett's acceptance ratio method: how to profit from bending the rules.
König, Gerhard; Boresch, Stefan
2011-04-30
The exact computation of free energy differences requires adequate sampling of all relevant low energy conformations. Especially in systems with rugged energy surfaces, adequate sampling can only be achieved by biasing the exploration process, thus yielding non-Boltzmann probability distributions. To obtain correct free energy differences from such simulations, it is necessary to account for the effects of the bias in the postproduction analysis. We demonstrate that this can be accomplished quite simply with a slight modification of Bennett's Acceptance Ratio method, referring to this technique as Non-Boltzmann Bennett. We illustrate the method by several examples and show how a creative choice of the biased state(s) used during sampling can also improve the efficiency of free energy simulations.
Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.
Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew
2014-12-26
Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.
The stationary non-equilibrium plasma of cosmic-ray electrons and positrons
Tomaschitz, Roman
2016-06-01
The statistical properties of the two-component plasma of cosmic-ray electrons and positrons measured by the AMS-02 experiment on the International Space Station and the HESS array of imaging atmospheric Cherenkov telescopes are analyzed. Stationary non-equilibrium distributions defining the relativistic electron-positron plasma are derived semi-empirically by performing spectral fits to the flux data and reconstructing the spectral number densities of the electronic and positronic components in phase space. These distributions are relativistic power-law densities with exponential cutoff, admitting an extensive entropy variable and converging to the Maxwell-Boltzmann or Fermi-Dirac distributions in the non-relativistic limit. Cosmic-ray electrons and positrons constitute a classical (low-density high-temperature) plasma due to the low fugacity in the quantized partition function. The positron fraction is assembled from the flux densities inferred from least-squares fits to the electron and positron spectra and is subjected to test by comparing with the AMS-02 flux ratio measured in the GeV interval. The calculated positron fraction extends to TeV energies, predicting a broad spectral peak at about 1 TeV followed by exponential decay.
1978-09-01
general equilibrium model of an economy with market fritions. A market is said to have frictions if buyers and sellers have trouble finding each other, if it is costly for them to search for each other, and if it is costly to wait to buy or sell. Equilibrium is a stationary probability distribution over the set of possible time paths of states of the economy. This equilibrium reflects rational expectations if all agents know the stationary distribution of the variables they observe and if they exploit this information. Prices are fixed and are not necessarily equilibrium
Classification of Sets using Restricted Boltzmann Machines
Louradour, Jérôme
2011-01-01
We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have been pre-segmented into smaller regions. We propose generalizations of the restricted Boltzmann machine (RBM) that are appropriate in this context and explore how to incorporate different assumptions about the relationship between the input sets and the target class within the RBM. In experiments on standard multiple-instance learning datasets, we demonstrate the competitiveness of approaches based on RBMs and apply the proposed variants to the problem of incoming mail classification.
Lattice Boltzmann Model for Numerical Relativity
Ilseven, E
2015-01-01
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with well-established tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
A lattice Boltzmann model for adsorption breakthrough
Energy Technology Data Exchange (ETDEWEB)
Agarwal, Saurabh; Verma, Nishith [Indian Institute of Technology Kanpur, Department of Chemical Engineering, Kanpur (India); Mewes, Dieter [Universitat Hannover, Institut fur Verfahrenstechnik, Hannover (Germany)
2005-07-01
A lattice Boltzmann model is developed to simulate the one-dimensional (1D) unsteady state concentration profiles, including breakthrough curves, in a fixed tubular bed of non-porous adsorbent particles. The lattice model solves the 1D time dependent convection-diffusion-reaction equation for an ideal binary gaseous mixture, with solute concentrations at parts per million levels. The model developed in this study is also able to explain the experimental adsorption/desorption data of organic vapours (toluene) on silica gel under varying conditions of temperature, concentrations and flowrates. Additionally, the programming code written for simulating the adsorption breakthrough is modified with minimum changes to successfully simulate a few flow problems, such as Poiseuille flow, Couette flow, and axial dispersion in a tube. The present study provides an alternative numerical approach to solving such types of mass transfer related problems. (orig.)
The Lattice Boltzmann method principles and practice
Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus
2017-01-01
This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...
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...
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.
Ordinal Boltzmann Machines for Collaborative Filtering
Truyen, Tran The; Venkatesh, Svetha
2012-01-01
Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper explores and extends a probabilistic model known as Boltzmann Machine for collaborative filtering tasks. It seamlessly integrates both the similarity and co-occurrence in a principled manner. In particular, we study parameterisation options to deal with the ordinal nature of the preferences, and propose a joint modelling of both the user-based and item-based processes. Experiments on moderate and large-scale movie recomm...
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 simulations of multiple-droplet interaction dynamics
Zhou, Wenchao; Loney, Drew; Fedorov, Andrei G.; Degertekin, F. Levent; Rosen, David W.
2014-03-01
A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface
Flow visualisation of downhill skiers using the lattice Boltzmann method
Asai, Takeshi; Hong, Sungchan; Ijuin, Koichi
2017-03-01
In downhill alpine skiing, skiers often exceed speeds of 120 km h-1, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s-1, increasing to 185.8 N at 40 m s-1. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.
Quantum statistical theory of semiconductor junctions in thermal equilibrium
Von Roos, O.
1977-01-01
Free carrier and electric field distributions of one-dimensional semiconductor junctions are evaluated using a quantum mechanical phase-space distribution and its corresponding Boltzmann equation. Attention is given to quantum and exchange corrections in cases of high doping concentrations when carrier densities become degenerate. Quantitative differences between degenerate and classical junction characteristics, e.g., maximum electric field and built-in voltage and carrier concentration within the transition region, are evaluated numerically.
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 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.
Numerical simulation of bubbly two-phase flow using the lattice Boltzmann method
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Tadashi; Ebihara, Kenichi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2000-09-01
The two-component two-phase lattice Boltzmann method, in which two distribution functions are used to represent two phases, is used to simulate bubbly flows as one of the fundamental two-phase flow phenomena in nuclear application fields. The inlet flow condition is proposed to simulate steady-state flow fields. The time variation and the spatial distribution of the volume fraction and the interfacial area are measured numerically. The simulation program is parallelized in one direction by the domain decomposition method using the MPI (Message Passing Interface) libraries, and parallel computations are performed on a workstation cluster. (author)
ON VECTOR NETWORK EQUILIBRIUM PROBLEMS
Institute of Scientific and Technical Information of China (English)
Guangya CHEN
2005-01-01
In this paper we define a concept of weak equilibrium for vector network equilibrium problems.We obtain sufficient conditions of weak equilibrium points and establish relation with vector network equilibrium problems and vector variational inequalities.
Energy Technology Data Exchange (ETDEWEB)
Dewar, K.M.; Montreuil, B.; Grondin, L.; Reader, T.A. (Universite de Montreal, Quebec (Canada))
1989-08-01
The binding properties of the substituted benzamide raclopride to dopamine D2 receptors were studied with membrane preparations from rat and rabbit neostriatum. An analysis of the association kinetics suggested a single binding site but the data from the dissociation experiments were better described by a two-site model. Examination of saturation curves at equilibrium revealed a single class of binding sites in the neostriatum from both species (rat: maximum binding capacity (Bmax) = 247 fmol/mg of protein; rabbit: Bmax = 337 fmol/mg of protein). In cortical regions known to possess a distinct dopaminergic innervation (piriform-entorhinal areas and cingulate cortex) the Bmax values ranged between 9 and 22 fmol/mg of protein. ({sup 3}H)Raclopride binding sites (less than 12 fmol/mg of protein) were also detectable in the dorsal and ventral hippocampus as well as in the somatosensory and visual cortices. The selectivity in the neostriatum was examined by competition experiments with dopaminergic drugs. The rank of potency of agonists and antagonists to displace ({sup 3}H)raclopride binding revealed its selectivity for the dopamine D2 receptor and was essentially the same for both species. Antagonist competition curves could be fitted to a single site but inhibition by agonists was better described assuming a two-site model. The stereospecificity of binding was demonstrated by the use of the enantiomer pairs. These results validate the utilization of the novel benzamide ({sup 3}H)raclopride as a selective marker of dopamine D2 receptors.
How accurate is Poisson-Boltzmann theory for monovalent ions near highly charged interfaces?
Bu, Wei; Vaknin, David; Travesset, Alex
2006-06-20
Surface sensitive synchrotron X-ray scattering studies were performed to obtain the distribution of monovalent ions next to a highly charged interface. A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at the air-water interface to control surface charge density. Using anomalous reflectivity off and at the L3 Cs+ resonance, we provide spatial counterion (Cs+) distributions next to the negatively charged interfaces. Five decades in bulk concentrations are investigated, demonstrating that the interfacial distribution is strongly dependent on bulk concentration. We show that this is due to the strong binding constant of hydronium H3O+ to the phosphate group, leading to proton-transfer back to the phosphate group and to a reduced surface charge. The increase of Cs+ concentration modifies the contact value potential, thereby causing proton release. This process effectively modifies surface charge density and enables exploration of ion distributions as a function of effective surface charge-density. The experimentally obtained ion distributions are compared to distributions calculated by Poisson-Boltzmann theory accounting for the variation of surface charge density due to proton release and binding. We also discuss the accuracy of our experimental results in discriminating possible deviations from Poisson-Boltzmann theory.
Brignole, Esteban Alberto
2013-01-01
Traditionally, the teaching of phase equilibria emphasizes the relationships between the thermodynamic variables of each phase in equilibrium rather than its engineering applications. This book changes the focus from the use of thermodynamics relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. Phase Equilibrium Engineering presents a systematic study and application of phase equilibrium tools to the development of chemical processes. The thermodynamic modeling of mixtures for process development, synthesis, simulation, design and
Buckling and Multiple Equilibrium States of Viscoelastic Rectangular Plates
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro-partial-differential equations is first presented by means of a structural function introduced in this paper. Then,by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro-partial-differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.
Niu, Xiao-Dong; Hyodo, Shi-Aki; Munekata, Toshihisa; Suga, Kazuhiko
2007-09-01
It is well known that the Navier-Stokes equations cannot adequately describe gas flows in the transition and free-molecular regimes. In these regimes, the Boltzmann equation (BE) of kinetic theory is invoked to govern the flows. However, this equation cannot be solved easily, either by analytical techniques or by numerical methods. Hence, in order to efficiently maneuver around this equation for modeling microscale gas flows, a kinetic lattice Boltzmann method (LBM) has been introduced in recent years. This method is regarded as a numerical approach for solving the BE in discrete velocity space with Gauss-Hermite quadrature. In this paper, a systematic description of the kinetic LBM, including the lattice Boltzmann equation, the diffuse-scattering boundary condition for gas-surface interactions, and definition of the relaxation time, is provided. To capture the nonlinear effects due to the high-order moments and wall boundaries, an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work [Guo et al., J. Appl. Phys. 99, 074903 (2006); Shan et al., J. Fluid Mech. 550, 413 (2006)]. The capability of the kinetic LBM of simulating microscale gas flows is illustrated based on the numerical investigations of micro Couette and force-driven Poiseuille flows.
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.
Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments
Jansen, H.P.; Sotthewes, K.; Swigchem, van J.; Zandvliet, H.J.W.; Kooij, E.S.
2013-01-01
Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results,
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...
Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields
Lindner, Manfred; Lindner, Manfred; Muller, Markus Michael
2006-01-01
Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Most notably, apart from quantitative discrepancies, on a qualitative level the universality observed for the Kadanoff-Baym equations is severely restricted in the case o...
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.
Boltzmann Samplers for v-balanced Colored Necklaces
Bodini, Olivier
2009-01-01
This paper is devoted to the random generation of particular colored necklaces for which the number of beads of a given color is constrained (these necklaces are called v-balanced). We propose an efficient sampler (its expected time complexity is linear) which satisfies the Boltzmann model principle introduced by Duchon, Flajolet, Louchard and Schaeffer. Our main motivation is to show that the absence of a decomposable specification can be circumvented by mixing the Boltzmann samplers with other types of samplers.
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...
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).
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...
Lattice Boltzmann Simulations of Evaporating Droplets with Nanoparticles
Zhao, Mingfei; Yong, Xin
2016-11-01
Elucidating the nanoparticle dynamics in drying droplets provides fundamental hydrodynamic insight into the evaporation-induced self-assembly, which is of great importance to materials printing and thin film processing. We develop a free-energy-based multiphase lattice Boltzmann model coupled with Lagrangian particle tracking to simulate evaporating particle-laden droplets on a solid substrate with specified wetting behavior. This work focuses on the interplay between the evaporation-driven advection and the self-organization of nanoparticles inside the droplet and at the droplet surface. For static droplets, the different parameters, fluid-particle interaction strength and particle number, governing the nanoparticle-droplet dynamics are systematically investigated, such as particle radial and circumferential distribution. We clarify the effect of nanoparticle presence on the droplet surface tension and wetting behavior. For evaporating droplets, we observe how droplet evaporation modulates the self-assembly of nanoparticles when the droplet has different static contact angles and hysteresis windows. We also confirm that the number of nanoparticles at the liquid-vapor interface influences the evaporation flux at the liquid-vapor interface.
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.
Equilibrium and Sudden Events in Chemical Evolution
Weinberg, David H; Freudenburg, Jenna
2016-01-01
We present new analytic solutions for one-zone (fully mixed) chemical evolution models and explore their implications. In contrast to existing analytic models, we incorporate a realistic delay time distribution for Type Ia supernovae (SNIa) and can therefore track the separate evolution of $\\alpha$-elements produced by core collapse supernovae (CCSNe) and iron peak elements synthesized in both CCSNe and SNIa. In generic cases, $\\alpha$ and iron abundances evolve to an equilibrium at which element production is balanced by metal consumption and gas dilution, instead of continuing to increase over time. The equilibrium absolute abundances depend principally on supernova yields and the outflow mass loading parameter $\\eta$, while the equilibrium abundance ratio [$\\alpha$/Fe] depends mainly on yields and secondarily on star formation history. A stellar population can be metal-poor either because it has not yet evolved to equilibrium or because high outflow efficiency makes the equilibrium abundance itself low. Sy...
Cartalade, Alain; Plapp, Mathis
2016-01-01
A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection-diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses t...
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.
Accurate lineshape spectroscopy and the Boltzmann constant.
Truong, G-W; Anstie, J D; May, E F; Stace, T M; Luiten, A N
2015-10-14
Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars and planets, and even constraining cosmological models. Reaching fundamental-noise limits permits optimal extraction of spectroscopic information from an absorption measurement. Here, we demonstrate a quantum-limited spectrometer that delivers high-precision measurements of the absorption lineshape. These measurements yield a very accurate measurement of the excited-state (6P1/2) hyperfine splitting in Cs, and reveals a breakdown in the well-known Voigt spectral profile. We develop a theoretical model that accounts for this breakdown, explaining the observations to within the shot-noise limit. Our model enables us to infer the thermal velocity dispersion of the Cs vapour with an uncertainty of 35 p.p.m. within an hour. This allows us to determine a value for Boltzmann's constant with a precision of 6 p.p.m., and an uncertainty of 71 p.p.m.
A new multiple-relaxation-time lattice Boltzmann model for incompressible flows in porous media
Liu, Qing; He, Chao
2013-01-01
In this paper, a two-dimensional eight-velocity (D2Q8) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy formulation. In the MRT-LB model, newly defined equilibrium moments are employed to account for the porosity of the porous media, and the linear and nonlinear drag forces of the media are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. The model is validated by simulating the 2D Poiseuille flow, Couette flow and lid-driven cavity flow in porous media. The numerical results are in excellent agreement with the analytical solutions and/or the well-documented data available in the literature.
Exponential Runge-Kutta schemes for inhomogeneous Boltzmann equations with high order of accuracy
Li, Qin
2012-01-01
We consider the development of exponential methods for the robust time discretization of space inhomogeneous Boltzmann equations in stiff regimes. Compared to the space homogeneous case, or more in general to the case of splitting based methods, studied in Dimarco Pareschi (SIAM J. Num. Anal. 2011) a major difficulty is that the local Maxwellian equilibrium state is not constant in a time step and thus needs a proper numerical treatment. We show how to derive asymptotic preserving (AP) schemes of arbitrary order and in particular using the Shu-Osher representation of Runge-Kutta methods we explore the monotonicity properties of such schemes, like strong stability preserving (SSP) and positivity preserving. Several numerical results confirm our analysis.
Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations
Di Staso, G.; Clercx, H. J. H.; Succi, S.; Toschi, F.
2016-11-01
Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier-Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Influence of state-to-state vibrational distributions on transport coefficients of a single gas
Kustova, Elena V.; Kremer, Gilberto M.
2016-11-01
In this work the influence of the size of vibrationally and rotationally excited molecules on the collision integrals required for the calculation of state-to-state transport coefficients is discussed. Several diatomic molecules are considered: N2, O2, NO, H2, Cl2. It is shown that whereas the molecular size is not affected by rotational excitation, it strongly depends on the vibrational state. Particular emphasis is given to the shear viscosity and thermal conductivity coefficients calculated in the temperature range 2 500-20 000 K for equilibrium Boltzmann vibrational distributions. It is shown that under conditions of local thermal equilibrium, the effect of vibrational excitation on the shear viscosity and thermal conductivity coefficients are found to be negligible for temperatures below 5 000 K, except for the case of Cl2 molecule where at 5 000 K the effect is about 10%. For T > 10 000 K, the contribution of excited states becomes important and reaches 10-25%.
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations
Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong
2016-06-01
where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.
Electric Current Equilibrium in the Corona
Filippov, Boris
2013-01-01
A hyperbolic flux-tube configuration containing a null point below the flux rope is considered as a pre-eruptive state of coronal mass ejections that start simultaneously with flares. We demonstrate that this configuration is unstable and cannot exist for a long time in the solar corona. The inference follows from general equilibrium conditions and from analyzing simple models of the flux-rope equilibrium. A direct consequence of the stable flux-rope equilibrium in the corona are separatrices in the horizontal-field distribution in the chromosphere. They can be recognized as specific "herring-bone structures" in a chromospheric fibril pattern.
Electric Current Equilibrium in the Corona
Filippov, Boris
2013-04-01
A hyperbolic flux-tube configuration containing a null point below the flux rope is considered as a pre-eruptive state of coronal mass ejections that start simultaneously with flares. We demonstrate that this configuration is unstable and cannot exist for a long time in the solar corona. The inference follows from general equilibrium conditions and from analyzing simple models of the flux-rope equilibrium. A direct consequence of the stable flux-rope equilibrium in the corona are separatrices in the horizontal-field distribution in the chromosphere. They can be recognized as specific "herring-bone structures" in a chromospheric fibril pattern.
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.
The Blood Flow at Arterial Bifurcations Simulated by the Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
JI Yu-Pin; KANG Xiu-Ying; LIU Da-He
2009-01-01
The Programmed model of non-Newtonian blood flow (the Casson model) at arterial bifurcations is established by the lattice Boltzmann method. The blood flow field under different Reynolds numbers is simulated, and distri-bution of dynamic factors such as flow velocity, shear stress, pressure and shear rate are presented. The existence of the fluid separation zone is analyzed. This provides a basis for further studies of the relationship between hemodynamic factors and pathogenesis, as well as a reference for a better understanding of the pathological changes and location of sediments, and the plague factor in arteries.
Institute of Scientific and Technical Information of China (English)
Zhen-Hua Chai; Tian-Shou Zhao
2012-01-01
In this paper,a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems.Unlike previous models in the literature,the present model not only enables the study of multicomponent flows with different molecular weights,different viscosities and different Schmidt numbers,but also ensures that the distribution function of each component evolves on the same square lattice without invoking additional interpolations.Furthermore,the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations,and satisfies the indifferentiability principle.The numerical validation exercises further demonstrate that the favorable performance of the present model.
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.
Heinz, U; Denicol, G S; Martinez, M; Nopoush, M; Noronha, J; Ryblewski, R; Strickland, M
2015-01-01
Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.
Chemical Principles Revisited: Chemical Equilibrium.
Mickey, Charles D.
1980-01-01
Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)
Thermodynamics "beyond" local equilibrium
Vilar, Jose; Rubi, Miguel
2002-03-01
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation considers only systems close to equilibrium, those satisfying the so-called local equilibrium hypothesis. Here we show that diffusion processes that occur far away from equilibrium can be viewed as at local equilibrium in a space that includes all the relevant variables in addition to the spatial coordinate. In this way, nonequilibrium thermodynamics can be used and the difficulties and ambiguities associated with the lack of a thermodynamic description disappear. We analyze explicitly the inertial effects in diffusion and outline how the main ideas can be applied to other situations. [J.M.G. Vilar and J.M. Rubi, Proc. Natl. Acad. Sci. USA 98, 11081-11084 (2001)].
Response reactions: equilibrium coupling.
Hoffmann, Eufrozina A; Nagypal, Istvan
2006-06-01
It is pointed out and illustrated in the present paper that if a homogeneous multiple equilibrium system containing k components and q species is composed of the reactants actually taken and their reactions contain only k + 1 species, then we have a unique representation with (q - k) stoichiometrically independent reactions (SIRs). We define these as coupling reactions. All the other possible combinations with k + 1 species are the coupled reactions that are in equilibrium when the (q - k) SIRs are in equilibrium. The response of the equilibrium state for perturbation is determined by the coupling and coupled equilibria. Depending on the circumstances and the actual thermodynamic data, the effect of coupled equilibria may overtake the effect of the coupling ones, leading to phenomena that are in apparent contradiction with Le Chatelier's principle.
Directory of Open Access Journals (Sweden)
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
Electrostatic interaction of two charged macroparticles in an equilibrium plasma
Energy Technology Data Exchange (ETDEWEB)
Filippov, A. V., E-mail: fav@triniti.ru; Pal’, A. F.; Starostin, A. N. [Russian State Research Center Troitsk Institute for Innovation and Fusion Research (TRINITI), Troitsk (Russian Federation)
2015-11-15
This article is a critical review of publications devoted to studying the electrostatic interaction of two charged macroparticles in an equilibrium plasma. It is shown from an analysis of the force of interaction based on the Maxwell stress tensor that two macroparticles with identical charges in the Poisson–Boltzmann model always repel each other both in isothermal and nonisothermal plasmas. At distances between macroparticles for which the Boltzmann exponents can be linearized, the interaction between macroparticles is completely described by the Debye–Hückel model. The correction to free energy due to the electrostatic interaction in the system of two macroparticles is determined by integrating the correction to the internal energy and by direct calculation of the correction for entropy. It is shown that the free energy coincides with the Yukawa potential. The coincidence of the interaction energy obtained by integrating the force of interaction with the free energy leads to the conclusion about the potential nature of the force of interaction between two macroparticles in an equilibrium plasma. The effect of the outer boundary on the electrostatic interaction force is analyzed; it is shown that the type of interaction depends on the choice of the boundary conditions at the outer boundary. It is also shown that the accumulation of space charge near the outer boundary can lead to the attraction of similarly charged particles at distances comparable with the radius of the outer boundary.
Equilibrium statistical mechanics
Mayer, J E
1968-01-01
The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t
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.
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.
On the core-halo distribution of dark matter in galaxies
Ruffini, Remo; Rueda, Jorge Armando
2014-01-01
We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. The most general solutions present, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) a decreasing density distribution $\\rho\\propto r^{-2}$ leading to flat rotation curves fulfilling the classical Boltzmann statistics. The mass of the inos is determined as an eigenfunction of the mass of the inner quantum cores. We compare and contrast this mass value with the lower limit on the particle mass by Tremaine and Gunn (1979), and show that the latter is approached for the less degenerate quantum cores in agreement with the fixed halo observa...
Acoustic limit of the Boltzmann equation: classical solutions
Jang, Juhi; Jiang, Ning
2009-01-01
We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution $F_\\varepsilon=\\mu +\\varepsilon \\sqrt{\\mu}f_\\varepsilon$ to the rescaled Boltzmann equation in the acoustic time scaling \\partial_t F_\\varepsilon +\\vgrad F_\\varepsilon =\\frac{1}{\\varepsilon} \\Q(F_\\varepsilon,F_\\varepsilon), inside a periodic box $\\mathbb{T}^3$, we establish the global-in-time uniform energy estimates of $f_\\varepsilon$ in $\\varepsilon$ and prove that $f_\\varepsilon$...
Axisymmetric multiphase Lattice Boltzmann method for generic equations of state
Reijers, Sten A; Toschi, Federico
2015-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.
Two-dimensional lattice Boltzmann model for magnetohydrodynamics.
Schaffenberger, Werner; Hanslmeier, Arnold
2002-10-01
We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.
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.
Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method
Bogner, Simon; Rüde, Ulrich
2014-01-01
In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.
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.
Li, Angsheng; Zhang, Xiaohui; Pan, Yicheng; Peng, Pan
2014-12-01
It seems a universal phenomenon of networks that the attacks on a small number of nodes by an adversary player Alice may generate a global cascading failure of the networks. It has been shown (Li et al., 2013) that classic scale-free networks (Barabási and Albert, 1999, Barabási, 2009) are insecure against attacks of as small as O(logn) many nodes. This poses a natural and fundamental question: Can we introduce a second player Bob to prevent Alice from global cascading failure of the networks? We proposed a game in networks. We say that a network has an equilibrium game if the second player Bob has a strategy to balance the cascading influence of attacks by the adversary player Alice. It was shown that networks of the preferential attachment model (Barabási and Albert, 1999) fail to have equilibrium games, that random graphs of the Erdös-Rényi model (Erdös and Rényi, 1959, Erdös and Rényi, 1960) have, for which randomness is the mechanism, and that homophyly networks (Li et al., 2013) have equilibrium games, for which homophyly and preferential attachment are the underlying mechanisms. We found that some real networks have equilibrium games, but most real networks fail to have. We anticipate that our results lead to an interesting new direction of network theory, that is, equilibrium games in networks.
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
Martín-Hernández, G; Mastinu, P F; Praena, J; Dzysiuk, N; Capote Noy, R; Pignatari, M
2012-08-01
The need of neutron capture cross section measurements for astrophysics motivates present work, where calculations to generate stellar neutron spectra at different temperatures are performed. The accelerator-based (7)Li(p,n)(7)Be reaction is used. Shaping the proton beam energy and the sample covering a specific solid angle, neutron activation for measuring stellar-averaged capture cross section can be done. High-quality Maxwell-Boltzmann neutron spectra are predicted. Assuming a general behavior of the neutron capture cross section a weighted fit of the spectrum to Maxwell-Boltzmann distributions is successfully introduced.
d'Eon, Eugene
2013-01-01
We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing medium with isotropic scattering. We consider both classical transport theory with exponentially-distributed free paths in arbitrary dimensions as well as a number of non-classical transport theories (non-exponential random flights) that describe a broader class of transport processes within partially-correlated random media. New rigorous asymptotic diffusion approximations are derived where possible. We also generalize Grosjean's moment-preserving approach of separating the first (or uncollided) distribution from the collided portion and approximating only the latter using diffusion. We find that for any spatial dimension and for many free-path distributions Grosjean's approach produces compact, analytic approximations that are, overall, more accurate for high absorption and f...
Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows
Li, Q; Gao, Y J
2011-01-01
The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions, one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this brief report, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional interfacial force is included in the recovered momentum equation. The effects of the additional force are investigated by numerical simulations of droplet splashing on a thin liquid film and falling droplet under gravity. In the former test, it is found that the formation and evolution of secondary droplets are greatly affected, while in the latter the additional force is found to increase the falling velocity and limit the stretch of the droplet.
Hu, Kainan; Zhang, Hongwu
2016-01-01
A lattice Boltzmann scheme associated with flexible Prandtl number and specific heat ratio is proposed, which is based on the polyatomic ellipsoidal statistics model(ES-BGK). The Prandtl number can be modified by a parameter of the Gaussian distribution and the specific heat ratio can be modified by additional free degrees. For the sake of constructing the scheme proposed, the Gaussian distribution is expanded on the Hermite polynomials and the general term formula for the Hermite coefficients of the Gaussian distribution is deduced. Benchmarks are carried out to verify the scheme proposed. The numerical results are in good agreement with the the analytical solutions.
Energy Technology Data Exchange (ETDEWEB)
Neuman, M.W.
1982-01-01
The conundrum of blood undersaturation with respect to bone mineralization and its supersaturation with respect to bone's homeostatic function has acquired a new equation. On the supply side, Ca/sup 2 +/ is pumped in across bone cells to provide the needed Ca/sup 2 +/ x P/sub i/ for brushite precipitation. On the demand side, blood is in equilibrium with bone fluid, which is in equilibrium with a mineral more soluble than apatite. The function of potassium in this equation is yet to be found.
Non-Equilibrium Transitions of Heliospheric plasma
Livadiotis, G.; McComas, D. J.
2011-12-01
Recent advances in Space Physics theory have established the connection between non-extensive Statistical Mechanics and space plasmas by providing a theoretical basis for the empirically derived kappa distributions commonly used to describe the phase space distribution functions of these systems [1]. The non-equilibrium temperature and the kappa index that govern these distributions are the two independent controlling parameters of non-equilibrium systems [1-3]. The significance of the kappa index is primarily given by its role in identifying the non-equilibrium stationary states, and measuring their "thermodynamic distance" from thermal equilibrium [4], while its physical meaning is connected to the correlation between the system's particles [5]. For example, analysis of the IBEX high Energetic Neutral Atom spectra [6] showed that the vast majority of measured kappa indices are between ~1.5 and ~2.5, consistent with the far-equilibrium "cavity" of minimum entropy discovered by Livadiotis & McComas [2]. Spontaneous procedures that can increase the entropy, move the system gradually toward equilibrium, that is the state with the maximum (infinite) kappa index. Other external factors that may decrease the entropy, move the system back to states further from equilibrium where the kappa indices are smaller. Newly formed pick-up ions can play this critical role in the solar wind and other space plasmas. We have analytically shown that their highly ordered motion can reduce the average entropy in the plasma beyond the termination shock, inside the inner heliosheath [7]. Non-equilibrium transitions have a key role in understanding the governing thermodynamical processes of space plasmas. References 1. Livadiotis, G., & McComas, D. J. 2009, JGR, 114, 11105. 2. Livadiotis, G., & McComas, D. J. 2010a, ApJ, 714, 971. 3. Livadiotis, G., & McComas, D. J. 2010c, in AIP Conf. Proc. 9, Pickup Ions Throughout the Heliosphere and Beyond, ed. J. LeRoux, V. Florinski, G. P. Zank, & A
Mei, Ren-Wei; Shyy, Wei; Yu, Da-Zhi; Luo, Li-Shi; Rudy, David (Technical Monitor)
2001-01-01
The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is
Performance evaluation of a parallel sparse lattice Boltzmann solver
Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A.G.
2008-01-01
We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and
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…
EXTERNAL BODY FORCE IN FINITE DIFFERENCE LATTICE BOLTZMANN METHOD
Institute of Scientific and Technical Information of China (English)
CHEN Sheng; LIU Zhao-hui; SHI Bao-chang; ZHENG Chu-guang
2005-01-01
A new finite difference lattice Boltzmann scheme is developed. Because of analyzing the influence of external body force roundly, the correct Navier-Stokes equations with the external body force are recovered, without any additional unphysical terms. And some numerical results are presented. The result which close agreement with analytical data shows the good performance of the model.
Lattice Boltzmann simulations of droplet formation during microchannel emulsification
Zwan, van der E.A.; Sman, van der R.G.M.; Schroën, C.G.P.H.; Boom, R.M.
2009-01-01
In this study, we compared microchannel droplet formation in a microfluidics device with a two phase lattice Boltzmann simulation. The droplet formation was found to be qualitatively described, with a slightly smaller droplet in the simulation. This was due to the finite thickness of the interface i
The lattice Boltzmann method and the problem of turbulence
Energy Technology Data Exchange (ETDEWEB)
Djenidi, L. [School of Engineering The University of Newcastle, Callaghan NSW 2308 (Australia)
2015-03-10
This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.
Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation
García-Perciante, A L; García-Colin, L S
2007-01-01
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to the thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are briefly explored.
Lattice Boltzmann method for linear oscillatory noncontinuum flows
Shi, Yong; Yap, Ying Wan; Sader, John E.
2014-03-01
Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.
Analytical solutions of the lattice Boltzmann BGK model
Zou, Q; Doolen, G D; Zou, Qisu; Hou, Shuling; Doolen, Gary D.
1995-01-01
Abstract: Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time representation of these two flows without any approximation.
Determining Planetary Temperatures with the Stefan-Boltzmann Law
LoPresto, Michael C.; Hagoort, Nichole
2011-01-01
What follows is a description of several activities involving the Stefan-Boltzmann radiation law that can provide laboratory experience beyond what is normally found in traditional introductory thermodynamics experiments on thermal expansion, specific heat, and heats of transformation. The activities also provide more extensive coverage of and…
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.
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.
Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions
Allegrini, Paolo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo; West, Bruce J.
2005-03-01
We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.
Reis, Tim
2012-01-01
We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.
Demaison, Jean; Császár, Attila G.
2012-09-01
Based on a sample of 38 molecules, 47 accurate equilibrium CO bond lengths have been collected and analyzed. These ultimate experimental (reEX), semiexperimental (reSE), and Born-Oppenheimer (reBO) equilibrium structures are compared to reBO estimates from two lower-level techniques of electronic structure theory, MP2(FC)/cc-pVQZ and B3LYP/6-311+G(3df,2pd). A linear relationship is found between the best equilibrium bond lengths and their MP2 or B3LYP estimates. These (and similar) linear relationships permit to estimate the CO bond length with an accuracy of 0.002 Å within the full range of 1.10-1.43 Å, corresponding to single, double, and triple CO bonds, for a large number of molecules. The variation of the CO bond length is qualitatively explained using the Atoms in Molecules method. In particular, a nice correlation is found between the CO bond length and the bond critical point density and it appears that the CO bond is at the same time covalent and ionic. Conditions which permit the computation of an accurate ab initio Born-Oppenheimer equilibrium structure are discussed. In particular, the core-core and core-valence correlation is investigated and it is shown to roughly increase with the bond length.
Energy Technology Data Exchange (ETDEWEB)
Molaeimanesh, Gholam Reza; Akbari, Mohammad Hadi [Shiraz University, Shiraz (Iran, Islamic Republic of)
2015-03-15
A pore-scale model based on the lattice Boltzmann method (LBM) is proposed for the cathode electrode of a PEM fuel cell with heterogeneous and anisotropic porous gas diffusion layer (GDL) and interdigitated flow field. An active approach is implemented to model multi-component transport in GDL, which leads to enhanced accuracy, especially at higher activation over-potentials. The core of the paper is the implementation of an electrochemical reaction with an active approach in a multi-component lattice Boltzmann model for the first time. After model validation, the capability of the presented model is demonstrated through a parametric study. Effects of activation over-potential, pressure differential between inlet and outlet gas channels, land width to channel width ratio, and channel width are investigated. The results show the significant influence of GDL microstructure on the oxygen distribution and current density profile.
Regulski, Wojciech; Szumbarski, Jacek
2016-01-01
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared in terms of spatial convergence and their behaviour in transient and inertial flows. The choice of lattice and the presence of Burnett stresses was found to influence the results of both models, however the latter did not significantly degrade the velocity field. Using Bingham flows in ducts and synthetic porous media, it was found that the implicitly-regularised model was superior in capturing transient and inertial fl...
Institute of Scientific and Technical Information of China (English)
周溪召
2001-01-01
Because the randomness of transportation information has not been considered in present practical transportation planning ,the accuracy or efficiency of transportation planning is depreciated.In order to overcome this drawback,the combinatorial model simulaneously involving OD distribution of trips in a transportation network and stochastic user equilibrium assignment(SUEA) of trips to routes in each OD pairs was developped on the basis of analysis on random ness in choices of route and destination for a given mode. It was proved that the solution of the combinatorial model was unique and it satisfied Wardropian principle of SUEA and requirement of OD distribution by introducing Langrangian function.Finally,the algorithm of model was given by using the direction hunting method.%目前交通规划实践缺乏考虑交通信息的随机性，从而降低了它所得结果的准确性.为此，通过分析出行路径选择和目标选择的随机性，建立了交通网络OD分布与随机平衡（或均衡）分配的组合模型，通过引入拉格朗日函数，证明了模型最优解满足随机用户平衡条件和OD分布的要求且最优解是唯一的;最后给出了模型的方向搜索算法.
Equilibrium molecular thermodynamics from Kirkwood sampling.
Somani, Sandeep; Okamoto, Yuko; Ballard, Andrew J; Wales, David J
2015-05-21
We present two methods for barrierless equilibrium sampling of molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys. 2009, 130, 134102). Kirkwood sampling employs low-order correlations among internal coordinates of a molecule for random (or non-Markovian) sampling of the high dimensional conformational space. This is a geometrical sampling method independent of the potential energy surface. The first method is a variant of biased Monte Carlo, where Kirkwood sampling is used for generating trial Monte Carlo moves. Using this method, equilibrium distributions corresponding to different temperatures and potential energy functions can be generated from a given set of low-order correlations. Since Kirkwood samples are generated independently, this method is ideally suited for massively parallel distributed computing. The second approach is a variant of reservoir replica exchange, where Kirkwood sampling is used to construct a reservoir of conformations, which exchanges conformations with the replicas performing equilibrium sampling corresponding to different thermodynamic states. Coupling with the Kirkwood reservoir enhances sampling by facilitating global jumps in the conformational space. The efficiency of both methods depends on the overlap of the Kirkwood distribution with the target equilibrium distribution. We present proof-of-concept results for a model nine-atom linear molecule and alanine dipeptide.
Institute of Scientific and Technical Information of China (English)
邱欣; 杨青; 游庆龙
2013-01-01
The space distribution characteristics of equilibrium moisture of non-saturated clay subgrade were surveyed along the road cross-section by the in-situ and laboratory tests. Based on the basic theory of unsaturated soil mechanics, matric suctions of soil samples with different kinds of moisture condition were determined and the soil-water characteristic curve model was calibrated to reflect a single-valued function relationship between water content and matric suction of clay soils. Combining the above results, an estimation method of the equilibrium moisture of the unsaturated clay subgrade outside the affected zone of atmospheric precipitation/evaporation was established. The results show that the atmospheric precipitation/evaporation has significant effect on moisture condition of the subgrade soil located in the upper part of the subgrade near the central reserve and hard shoulders. However, equilibrium moisture of subgrade soil outside the affected zone of atmospheric precipitation/evaporation is mainly controlled by the impact of the groundwater table. Fredlund & Xing model can be used to characterize the relationship between the unsaturated clay soil moisture and matric suction, and the fitting results of model parameters have high reliability. A consistency between the predictive results and the experimental data shows the presented model is accurate and credible.%通过室内外试验探讨了非饱和粘土路基平衡湿度沿道路横断面的空间分布特征,并基于非饱和土力学基本理论,采用滤纸法测定了不同含水量土样的基质吸力,标定了反映含水量与基质吸力单值函数关系的土水特征曲线模型,建立了大气降水/蒸发影响区以外非饱和粘土路基平衡湿度的预估方法.研究结果表明,近中央分隔带和路肩处的上部路基土的平衡湿度受大气降水/蒸发的影响显著；大气降水/蒸发影响区以外的路基土平衡湿度主要受控于地下水位的影响
Analysis of droplet jumping phenomenon with lattice Boltzmann simulation of droplet coalescence
Peng, Benli; Wang, Sifang; Lan, Zhong; Xu, Wei; Wen, Rongfu; Ma, Xuehu
2013-04-01
Droplet jumping from condensing surfaces induced by droplet coalescence during dropwise condensation of mixed steam on a superhydrophobic surface can significantly enhance condensation heat transfer of mixed steam with non-condensable gas. This phenomenon was visually observed and theoretically analyzed in the present paper. The dynamic evolution of droplet and the velocity distribution inside the droplet during coalescence were simulated using multiphase lattice Boltzmann method. The energy distribution released by droplet coalescence was calculated statistically, and the jumping height induced by droplet coalescence on a superhydrophobic surface was predicted based on the energy conservation method. The theoretical predictions obtained by the modified model proposed in this paper agree well with the experimental observations.
Lattice Boltzmann technique for heat transport phenomena coupled with melting process
Ibrahem, A. M.; El-Amin, M. F.; Mohammadein, A. A.; Gorla, Rama Subba Reddy
2017-01-01
In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar-Gross-Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.
Bayramoglu, Beste; Faller, Roland
2011-03-01
We present systematic coarse-graining of several polystyrene models and test their performance under confinement and eventually in brush systems. The structural properties of a dilute polystyrene solution, a polystyrene melt and a confined concentrated polystyrene solution at 450K, 1 bar were investigated in detail by atomistic molecular dynamics simulations of these systems. Coarse-graining of the models was performed by Iterative Boltzmann Inversion Technique (IBI), in which the interaction potentials are optimized against the structure of the corresponding atomistically simulated systems. Radial distribution functions, bond, angle and dihedral angle probability distributions were calculated and compared to characterize the structure of the systems. Good agreement between the simulation results of the coarse-grained and atomistic models was observed.
Lattice Boltzmann technique for heat transport phenomena coupled with melting process
Ibrahem, A. M.; El-Amin, M. F.; Mohammadein, A. A.; Gorla, Rama Subba Reddy
2016-04-01
In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar-Gross-Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.
Li, Zheng; Zhang, Yuwen
2016-01-01
Three-dimensional melting problems are investigated numerically with Lattice Boltzmann method (LBM). Regarding algorithm's accuracy and stability, Multiple-Relaxation-Time (MRT) models are employed to simplify the collision term in LBM. Temperature and velocity fields are solved with double distribution functions, respectively. 3-D melting problems are solved with double MRT models for the first time in this article. The key point for the numerical simulation of a melting problem is the methods to obtain the location of the melting front and this article uses interfacial tracking method. The interfacial tracking method combines advantages of both deforming and fixed grid approaches. The location of the melting front was obtained by calculating the energy balance at the solid-liquid interface. Various 3-D conduction controlled melting problems are solved firstly to verify the numerical method. Liquid fraction tendency and temperature distribution obtained from numerical methods agree with the analytical result...
Chen, Li; Zhang, Lei; Tao, Wenquan
2014-01-01
Size, morphology and distributions of pores in organic matters of shale matrix are discussed based on high resolution images from experiments in the literature. 150 nanoscale structures of the organic matters are then reconstructed by randomly placing pore spheres with different diameters and overlap tolerances. Effects of porosity, the mean diameter and the overlap tolerance on void space connectivity and pore size distribution are studied. Further, a pore-scale model based on the Lattice Boltzmann method is developed to predict the Knudsen diffusivity and permeability of the reconstructed organic matters. The simulation results show that the mean pore diameter and overlap tolerance significantly affect the transport properties. The predicted Knudsen effective diffusivity is compared with Bruggeman equation and it is found that this equation underestimate the tortuosity. A modified Bruggeman equation is proposed based on the simulation results. The predicted intrinsic permeability is in acceptable agreement ...
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Bounded Computational Capacity Equilibrium
Hernandez, Penelope
2010-01-01
We study repeated games played by players with bounded computational power, where, in contrast to Abreu and Rubisntein (1988), the memory is costly. We prove a folk theorem: the limit set of equilibrium payoffs in mixed strategies, as the cost of memory goes to 0, includes the set of feasible and individually rational payoffs. This result stands in sharp contrast to Abreu and Rubisntein (1988), who proved that when memory is free, the set of equilibrium payoffs in repeated games played by players with bounded computational power is a strict subset of the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded computational power.
Equilibrium statistical mechanics
Jackson, E Atlee
2000-01-01
Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t
Tourism Equilibrium Price Trends
Directory of Open Access Journals (Sweden)
Mohammad Mohebi
2012-01-01
Full Text Available Problem statement: A review of the tourism history shows that tourism as an industry was virtually unknown in Malaysia until the late 1960s. Since then, it has developed and grown into a major industry, making an important contribution to the country's economy. By allocating substantial funds to the promotion of tourism and the provision of the necessary infrastructure, the government has played an important role in the impressive progress of the Malaysian tourism industry. One of the important factors which can attract tourists to Malaysia is the tourism price. Has the price of tourism decreased? To answer this question, it is necessary to obtain the equilibrium prices as well as the yearly trend for Malaysia during the sample period as it will be useful for analysis of the infrastructure situation of the tourism industry in this country. The purpose of the study is to identify equilibrium tourism price trends in Malaysian tourism market. Approach: We use hotel room as representative of tourism market. Quarterly data from 1995-2009 are used and a dynamic model of simultaneous equation is employed. Results: Based on the result during the period of 1995 until 2000, the growth rate of the equilibrium price was greater than consumer price index and producer price index. Conclusion: In the Malaysian tourism market, new infrastructure during this period had not been developed to keep pace with tourist arrivals.
Bhakta, Subrata; Ghosh, Uttam; Sarkar, Susmita
2017-02-01
In this paper, we have investigated the effect of secondary electron emission on nonlinear propagation of dust acoustic waves in a complex plasma where equilibrium dust charge is negative. The primary electrons, secondary electrons, and ions are Boltzmann distributed, and only dust grains are inertial. Electron-neutral and ion-neutral collisions have been neglected with the assumption that electron and ion mean free paths are very large compared to the plasma Debye length. Both adiabatic and nonadiabatic dust charge variations have been separately taken into account. In the case of adiabatic dust charge variation, nonlinear propagation of dust acoustic waves is governed by the KdV (Korteweg-de Vries) equation, whereas for nonadiabatic dust charge variation, it is governed by the KdV-Burger equation. The solution of the KdV equation gives a dust acoustic soliton, whose amplitude and width depend on the secondary electron yield. Similarly, the KdV-Burger equation provides a dust acoustic shock wave. This dust acoustic shock wave may be monotonic or oscillatory in nature depending on the fact that whether it is dissipation dominated or dispersion dominated. Our analysis shows that secondary electron emission increases nonadiabaticity induced dissipation and consequently increases the monotonicity of the dust acoustic shock wave. Such a dust acoustic shock wave may accelerate charge particles and cause bremsstrahlung radiation in space plasmas whose physical process may be affected by secondary electron emission from dust grains. The effect of the secondary electron emission on the stability of the equilibrium points of the KdV-Burger equation has also been investigated. This equation has two equilibrium points. The trivial equilibrium point with zero potential is a saddle and hence unstable in nature. The nontrivial equilibrium point with constant nonzero potential is a stable node up to a critical value of the wave velocity and a stable focus above it. This critical
Dellar, Paul
2016-11-01
We present discrete kinetic and lattice Boltzmann formulations for reaction cross-diffusion systems, as commonly used to model microbiological chemotaxis and macroscopic predator-prey interactions, and their hyperbolic extensions with fluid-like persistence terms. For example, the canonical Patlak-Keller-Segal model for chemotaxis involves a flux of cells up the gradient of a chemical secreted by the cells, in addition to the usual down-gradient diffusive fluxes. Existing lattice Boltzmann approaches for such systems use finite difference approximations to compute the flux of cells due to the chemical gradient. The resulting coupling between, and necessary synchronisation of the evolution of, adjacent grid points greatly complicates boundary conditions, and efficient implementation on graphical processing units (GPUs). We present a kinetic formulation using cross-collisions between bases of moments for the two sets of distribution functions to couple the fluxes of the two species, from which we construct lattice Boltzmann algorithms using second-order Strang splitting. We demonstrate an efficient GPU implementation, and verify second-order spatial convergence towards spectral solutions for benchmark problems such as the finite-time blow-up in the Patlak-Keller-Segal model.
Lattice Boltzmann Methods for Fluid Structure Interaction
2012-09-01
all of the devices are physically located on the same machine, it is convenient to use the shared-memory paradigms of OpenMP rather than explicitly...The standard programming paradigm for programs of this type is to use a distributed parallel programming model based on MPI. When developing a program...presented in this work only accommodate flows for Reynolds number up to approximately 10,000. Current research in entropic and thermal LBM along with
Noncompact Equilibrium Points and Applications
Directory of Open Access Journals (Sweden)
Zahra Al-Rumaih
2012-01-01
Full Text Available We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.
Dynamics of annihilation. I. Linearized Boltzmann equation and hydrodynamics.
García de Soria, María Isabel; Maynar, Pablo; Schehr, Grégory; Barrat, Alain; Trizac, Emmanuel
2008-05-01
We study the nonequilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of ballistic annihilation therefore constantly loses particles. The dynamics of perturbations around the free decay regime is investigated using the spectral properties of the linearized Boltzmann operator, which characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of molecular dynamics simulations that validate the theoretical predictions.
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.
Lattice Boltzmann Numerical Simulation of a Circular Cylinder
Institute of Scientific and Technical Information of China (English)
冯士德; 赵颖; 郜宪林; 季仲贞
2002-01-01
The lattice Boltzmann equation (LBE) model based on the Boltzmann equation is suitable for the numerical simulation of various flow fields. The fluid dynamics equation can be recovered from the LBE model. However,compared to the Navier-Stokes transport equation, the fluid dynamics equation derived from the LBE model is somewhat different in the viscosity transport term, which contains not only the Navier-Stokes transport equation but also nonsteady pressure and momentum flux terms. The two nonsteady terms can produce the same function as the random stirring force term introduced in the direct numerical or large-eddy vortex simulation of turbulence.Through computation of a circular cylinder, it is verified that the influence of the two nonsteady terms on flow field stability cannot be ignored, which is helpful for the study of turbulence.
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...
Accelerated Monte Carlo simulations with restricted Boltzmann machines
Huang, Li; Wang, Lei
2017-01-01
Despite their exceptional flexibility and popularity, 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 feed-forward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine to propose efficient Monte Carlo updates to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate an improved acceptance ratio and autocorrelation time near the phase transition point.
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.
Directory of Open Access Journals (Sweden)
B. Funke
2009-04-01
Full Text Available We present global distributions of carbon monoxide (CO from the upper troposphere to the mesosphere observed by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS on Envisat. Vertically resolved volume mixing ratio profiles have been retrieved from 4.7 μm limb emission spectra under consideration of non-local thermodynamic equilibrium. The precision of individual CO profiles is typically 5–30 ppbv (15–40% for altitudes greater than 40 km and lower than 15 km and 30–90% within 15–40 km. Estimated systematic errors are in the order of 8–15%. Below 60 km, the vertical resolution is 4–7 km. The data set which covers 54 days from September 2003 to March 2004 has been derived with an improved retrieval version including (i the retrieval of log(vmr, (ii the consideration of illumination-dependent vibrational population gradients along the instrument's line of sight, and (iii joint-fitted vmr horizontal gradients in latitudinal and longitudinal directions. A detailed analysis of spatially resolved CO distributions during the 2003/2004 Northern Hemisphere major warming event demonstrate the potential of MIPAS CO observations to obtain new information on transport processes during dynamical active episodes, particularly on those acting in the vertical. From the temporal evolution of zonally averaged CO abundances, we derived extraordinary polar winter descent velocities of 1200 m per day inside the recovered polar vortex in January 2004. Middle stratospheric CO abundances show a well established correlation with the chemical source CH_{4}, particularly in the tropics. In the upper troposphere, a moderate CO decrease from September 2003 to March 2004 was observed. Upper tropospheric CO observations provide a detailed picture of long-range transport of polluted air masses and uplift events. MIPAS observations taken on 9–11 September 2003 confirm the trapping of convective outflow of polluted CO-rich air from
Module description of TOKAMAK equilibrium code MEUDAS
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2002-01-01
The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)
Pomeau, Yves; Louët, Sabine
2016-06-01
During the StatPhys Conference on 20th July 2016 in Lyon, France, Yves Pomeau and Daan Frenkel will be awarded the most important prize in the field of Statistical Mechanics: the 2016 Boltzmann Medal, named after the Austrian physicist and philosopher Ludwig Boltzmann. The award recognises Pomeau's key contributions to the Statistical Physics of non-equilibrium phenomena in general. And, in particular, for developing our modern understanding of fluid mechanics, instabilities, pattern formation and chaos. He is recognised as an outstanding theorist bridging disciplines from applied mathematics to statistical physics with a profound impact on the neighbouring fields of turbulence and mechanics. In the article Sabine Louët interviews Pomeau, who is an Editor for the European Physical Journal Special Topics. He shares his views and tells how he experienced the rise of Statistical Mechanics in the past few decades. He also touches upon the need to provide funding to people who have the rare ability to discover new things and ideas, and not just those who are good at filling in grant application forms.
Boltzmann-Langevin one-body dynamics for fermionic systems
Directory of Open Access Journals (Sweden)
Napolitani P.
2012-07-01
Full Text Available A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional approaches, as a projection on suitable subspaces. The advantage of this model is to be specifically adapted to describe processes characterised by instabilities, like the formation of fragments from a hot nuclear system, and by dissipation, like the transparency in nucleus-nucleus collisions.
Classical Boltzmann equation and high-temperature QED
Brandt, F. T.; Ferreira, R. B.; Thuorst, J. F.
2015-01-01
The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the ...
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...
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.
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.
Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation
2011-04-01
important role in modelling granular gases (Bobylev et al., 2000), charged particles in semiconductors (Markowich et al., 1989), neutron transport (Jin...1.6 The splitting approach 1 THE BOLTZMANN EQUATION • Granular gas models : particles undergo inelastic collisions . Energy is dissipated by the model ...A model for collision processes in gases i. small amplitute processes in charged and neutral one component systems. Phys. Rev., 94:511–525. 8
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 r...... the resonant behavior of electronic response to an external electromagnetic field. We demonstrate the approach for planar and circular geometries of the metamolecules....
Extended Mixed Vector Equilibrium Problems
Directory of Open Access Journals (Sweden)
Mijanur Rahaman
2014-01-01
Full Text Available We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005, some existence results for both problems are proved in noncompact domain.
Equilibrium fluctuations for gradient exclusion processes with conductances in random environments
Farfan, Jonathan; Valentim, Fabio J
2009-01-01
We study the equilibrium fluctuations for a gradient exclusion process with conductances in random environments, which can be viewed as a central limit theorem for the empirical distribution of particles when the system starts from an equilibrium measure.
Non-equilibrium thermodynamics
Groot, S R De
2011-01-01
The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena - non-equilibrium thermodynamics.S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dyn
Electromagnetic Radiation From An Equilibrium Quark -Gluon Plasma System
Singh, S S; Jha, Agam K.
2006-01-01
We study the electromagnetic radiation from a hot and slightly strong interacting fireball system of quark-gluon plasma using the Boltzmann distribution function for the incoming particles and Bose-Einstein distribution for gluon in first calculation of electromagnetic radiation and Fermi-Dirac distribution for quark, antiquark and Boltzmann distribution for gluon in our second calculation. The thermal photon emission rate is found that it is infrared divergent for massless quarks which are discussed by many authors and regulate this divergence using different cut-off in the qurak mass. However we remove this divergence using the same technique of Braaten and Pisarski in the thermal mass of the system by using our model calculation in the coupling parameter. Thus the production rate of the thermal photon is found to be smoothly worked by this cut-off technique of our model. The result is found to be matched with the most of the theoretical calculations and it is in the conformity with the experimental results...
Maia, Alex S C; Nascimento, Sheila T; Nascimento, Carolina C N; Gebremedhin, Kifle G
2016-05-01
The effects of air temperature and relative humidity on thermal equilibrium of goats in a tropical region was evaluated. Nine non-pregnant Anglo Nubian nanny goats were used in the study. An indirect calorimeter was designed and developed to measure oxygen consumption, carbon dioxide production, methane production and water vapour pressure of the air exhaled from goats. Physiological parameters: rectal temperature, skin temperature, hair-coat temperature, expired air temperature and respiratory rate and volume as well as environmental parameters: air temperature, relative humidity and mean radiant temperature were measured. The results show that respiratory and volume rates and latent heat loss did not change significantly for air temperature between 22 and 26°C. In this temperature range, metabolic heat was lost mainly by convection and long-wave radiation. For temperature greater than 30°C, the goats maintained thermal equilibrium mainly by evaporative heat loss. At the higher air temperature, the respiratory and ventilation rates as well as body temperatures were significantly elevated. It can be concluded that for Anglo Nubian goats, the upper limit of air temperature for comfort is around 26°C when the goats are protected from direct solar radiation.
[Study on the maximum entropy principle and population genetic equilibrium].
Zhang, Hong-Li; Zhang, Hong-Yan
2006-03-01
A general mathematic model of population genetic equilibrium about one locus was constructed based on the maximum entropy principle by WANG Xiao-Long et al. They proved that the maximum solve of the model was just the frequency distribution that a population reached Hardy-Weinberg genetic equilibrium. It can suggest that a population reached Hardy-Weinberg genetic equilibrium when the genotype entropy of the population reached the maximal possible value, and that the frequency distribution of the maximum entropy was equivalent to the distribution of Hardy-Weinberg equilibrium law about one locus. They further assumed that the frequency distribution of the maximum entropy was equivalent to all genetic equilibrium distributions. This is incorrect, however. The frequency distribution of the maximum entropy was only equivalent to the distribution of Hardy-Weinberg equilibrium with respect to one locus or several limited loci. The case with regard to limited loci was proved in this paper. Finally we also discussed an example where the maximum entropy principle was not the equivalent of other genetic equilibria.
Li, Qing; Yan, H J
2016-01-01
In this paper, the pinning and depinning mechanism of the contact line during droplet evaporation on chemically stripe-patterned surfaces is numerically investigated using a thermal multiphase lattice Boltzmann (LB) model with liquid-vapor phase change. A local force balance in the context of diffuse interfaces is introduced to explain the equilibrium states of droplets on chemically patterned surfaces. It is shown that, when the contact line is pinned on a hydrophobic-hydrophilic boundary, different contact angles can be interpreted as the variation of the length of the contact line occupied by each component. The stick-slip-jump behavior of evaporating droplets on chemically patterned surfaces is well captured by the LB simulations. Particularly, a slow movement of the contact line is clearly observed during the stick (pinning) mode, which shows that the pinning of the contact line during droplet evaporation on chemically stripe-patterned surfaces is actually a dynamic pinning process and the dynamic equili...
Dynamical Non-Equilibrium Molecular Dynamics
Directory of Open Access Journals (Sweden)
Giovanni Ciccotti
2013-12-01
Full Text Available In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD, which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, implemented in the nineteen-seventies by Ciccotti, Jacucci and MacDonald, the approach permits one to separate the problem of dynamical evolution from the problem of sampling the initial condition. D-NEMD provides the theoretical framework to compute time-dependent macroscopic dynamical behaviors by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions generated from a suitable (equilibrium or non-equilibrium distribution at time zero. We also discuss how to generate a large class of initial distributions. The same approach applies also to the calculation of the rate constants of activated processes. The range of problems treatable by this method is illustrated by discussing applications to a few key hydrodynamic processes (the “classical” flow under shear, the formation of convective cells and the relaxation of an interface between two immiscible liquids.
Calculation of momentum distribution function of a non-thermal fermionic dark matter
Biswas, Anirban; Gupta, Aritra
2017-03-01
The most widely studied scenario in dark matter phenomenology is the thermal WIMP scenario. Inspite of numerous efforts to detect WIMP, till now we have no direct evidence for it. A possible explanation for this non-observation of dark matter could be because of its very feeble interaction strength and hence, failing to thermalise with the rest of the cosmic soup. In other words, the dark matter might be of non-thermal origin where the relic density is obtained by the so-called freeze-in mechanism. Furthermore, if this non-thermal dark matter is itself produced substantially from the decay of another non-thermal mother particle, then their distribution functions may differ in both size and shape from the usual equilibrium distribution function. In this work, we have studied such a non-thermal (fermionic) dark matter scenario in the light of a new type of U(1)B‑L model. The U(1)B‑L model is interesting, since, besides being anomaly free, it can give rise to neutrino mass by Type II see-saw mechanism. Moreover, as we will show, it can accommodate a non-thermal fermionic dark matter as well. Starting from the collision terms, we have calculated the momentum distribution function for the dark matter by solving a coupled system of Boltzmann equations. We then used it to calculate the final relic abundance, as well as other relevant physical quantities. We have also compared our result with that obtained from solving the usual Boltzmann (or rate) equations directly in terms of comoving number density, Y. Our findings suggest that the latter approximation is valid only in cases where the system under study is close to equilibrium, and hence should be used with caution.
Wang, Junjian; Kang, Qinjun; Rahman, Sheik S
2016-01-01
Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nanopores ranging in size from a few to hundreds of nanometers. In addition to the noncontinuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation-Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell-Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir ...
Zhang, Jie; Liu, Xiaolin; Wen, Yanwei; Shi, Lu; Chen, Rong; Liu, Huijun; Shan, Bin
2017-01-25
Good electronic transport capacity and low lattice thermal conductivity are beneficial for thermoelectric applications. In this study, the potential use as a thermoelectric material for the recently synthesized two-dimensional TiS3 monolayer is explored by applying first-principles method combined with Boltzmann transport theory. Our work demonstrates that carrier transport in the TiS3 sheet is orientation-dependent, caused by the difference in charge density distribution at band edges. Due to a variety of Ti-S bonds with longer lengths, we find that the TiS3 monolayer shows thermal conductivity much lower compared with that of transition-metal dichalcogenides such as MoS2. Combined with a high power factor along the y-direction, a considerable n-type ZT value (3.1) can be achieved at moderate carrier concentration, suggesting that the TiS3 monolayer is a good candidate for thermoelectric applications.
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.
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Burger, Martin
2016-11-18
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.
Chen, Li; Kang, Qinjun; Yao, Jun; Tao, Wenquan
2014-01-01
Porous structures of shales are reconstructed based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analyzes of the nanoscale reconstructed shales are performed, including porosity, pore size distribution, specific surface area and pore connectivity. The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) fluid flow model and single-relaxation-time (SRT) LBM diffusion model are adopted to simulate the fluid flow and Knudsen diffusion process within the reconstructed shales, respectively. Tortuosity, intrinsic permeability and effective Knudsen diffusivity are numerically predicted. The tortuosity is much higher than that commonly employed in Bruggeman equation. Correction of the intrinsic permeability by taking into consideration the contribution of Knudsen diffusion, which leads to the apparent permeability, is performed. The correction factor under different Knudsen number and pressure are estimated and compared with existing corrections re...
Düring, Bertram
2015-01-01
We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion dynamics under the effect of opinion leadership, where each individual is characterised not only by its opinion, but also by another independent variable which quantifies leadership qualities; (ii) opinion dynamics modelling political segregation in the `The Big Sort', a phenomenon that US citizens increasingly prefer to live in neighbourhoods with politically like-minded individuals. Based on microscopic opinion consensus dynamics such models lead to inhomogeneous Boltzmann-type equations for the opinion distribution. We derive macroscopic Fokker-Planck-type equations in a quasi-invariant opinion limit and present results of numerical experiments.
Fully coupled Lattice Boltzmann simulation of ﬁber reinforced self compacting concrete ﬂow
DEFF Research Database (Denmark)
Svec, Oldrich; Skocek, Jan; Stang, Henrik;
To correctly predict the casting process of a ﬁber reinforced self compacting concrete on a structural level is a challenging task since the distribution and orientation of ﬁbers inﬂuence the global ﬂow pattern and vice versa. In this contribution, a modeling approach capable to represent...... 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...... the ﬁnal dispersion and orientation of ﬁbers during a real casting process....
Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; ZHONG Yi-Jun; HUANG Guo-Xiang
2004-01-01
Based on the lattice Boltzmann method and general theory of fluids flowing in porous media, a numerical model is presented for the diffusion-reaction-transport (DRT) processes in porous media. As a test, we simulate a DRT process in a two-dimensional horizontal heterogeneous porous medium. The influence of gravitation in this case can be neglected, and the DRT process can be described by a strongly heterogeneous diagnostic test strip or a thin confined piece of soil with stochastically distributing property in horizontal directions. The results obtained for the relations between reduced fluid saturation S, concentration c1, and concentration c2 are shown by using the visualization computing technique. The computational efficiency and stability of the model are satisfactory.
Antosiewicz, Jan M; Shugar, David
2011-11-01
All molecules can be viewed as either discrete or continuous assemblies of electric charges, and electrostatics plays a major role in intermolecular and intramolecular interactions. Moreover, charge distribution within molecules may fluctuate due to the presence of ionizable groups capable of exchanging protons with the environment, leading to pH-dependence of phenomena involving such molecules. Electrostatic aspects of complex shapes and environments of biological molecules, in vitro and in vivo, are relatively well amenable to treatment by Poisson-Boltzmann models, which are attractive in that they possess a clear physical meaning, and can be readily solved by several mathematically sound methods. Here we describe applications of these models to obtain valuable insights into some biologically important pH-dependent properties of biomolecules, such as stability, binding of ligands (including potential drugs), enzymatic activity, conformational transitions, membrane transport and viral entry.
A Polynomial Distribution Applied to Income and Wealth Distribution
Elvis Oltean; Kusmartsev, Fedor V.
2013-01-01
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse income and wealth distribution by employing distributions such as Fermi-Dirac, Bose-Einstein, Maxwell-Boltzmann, lognormal (Gibrat), and exponential. Generally, distributions desc...
Equilibrium properties of blackbody radiation in Doubly Special Relativity
Chandra, Nitin; Vaibhav, Vinay
2016-01-01
Doubly Special Relativity (DSR) is an attempt to incorporate an observer independent energy/length scale in the relativistic theory. We study various thermodynamic properties of blackbody radiation in DSR. We find that the energy density, specific heat etc. follows usual acoustic phonon dynamics as has been well studied by Debye. Other thermodynamic quantities like pressure, entropy etc. has also been calculated. The usual Stefan-Boltzmann law gets modified. The phase-space measure is also expected to get modified for an exotic spacetime, which in turn leads to the modification of Planck energy density distribution and the Wien's displacement law.
Momentum representation for equilibrium reduced density matrices
Golovko, V A
2011-01-01
The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not su...
Institute of Scientific and Technical Information of China (English)
SHEN Zai-Yi; HE Ying
2012-01-01
A computational simulation for the separation of red blood cells (RBCs) is presented.The deformability of RBCs is expressed by the spring network model,which is based on the minimum energy principle.In the computation of the fluid flow,the lattice Boltzmann method is used to solve the Navier-Stokes equations.Coupling of the fluid-membrane interaction is carried out by using the immersed boundary method.To verify our method,the motions of RBCs in shear flow are simulated.Typical motions of RBCs observed in the experiments are reproduced,including tank-treading,swinging and tumbling.The motions of 8 RBCs at the bifurcation are simulated when the two daughter vessels have different ratios.The results indicate that when the ratio of the daughter vessel diameter becomes smaller,the distribution of RBCs in the two vessels becomes more non-uniform.%A computational simulation for the separation of red blood cells (RBCs) is presented. The deformability of RBCs is expressed by the spring network model, which is based on the minimum energy principle. In the computation of the fluid Bow, the lattice Boltzmann method is used to solve the Navier-Stokes equations. Coupling of the fluid-membrane interaction is carried out by using the immersed boundary method. To verify our method, the motions of RBCs in shear How are simulated. Typical motions of RBCs observed in the experiments are reproduced, including tank-treading, swinging and tumbling. The motions of 8 RBCs at the bifurcation are simulated when the two daughter vessels have different ratios. The results indicate that when the ratio of te daughter vessel diameter becomes smaller, the distribution of RBCs in the two vessels becomes more non-uniform.
Coupled Boltzmann computation of mixed axion neutralino dark matter in the SUSY DFSZ axion model
Bae, Kyu Jung; Lessa, Andre; Serce, Hasan
2014-01-01
The supersymmetrized DFSZ axion model is highly motivated not only because it offers solutions to both the gauge hierarchy and strong CP problems, but also because it provides a solution to the SUSY mu problem which naturally allows for a Little Hierarchy. We compute the expected mixed axion-neutralino dark matter abundance for the SUSY DFSZ axion model in two benchmark cases-- a natural SUSY model with a standard neutralino underabundance (SUA) and an mSUGRA/CMSSM model with a standard overabundance (SOA). Our computation implements coupled Boltzmann equations which track the radiation density along with neutralino, axion (produced thermally (TH) and via coherent oscillations (CO)), saxion (TH- and CO-produced), axino and gravitino densities. In the SUSY DFSZ model, axions, axinos and saxions go through the process of freeze-in-- in contrast to freeze-out or out-of-equilibrium production as in the SUSY KSVZ model-- resulting in thermal yields which are largely independent of the re-heat temperature. We find ...
Wissocq, Gauthier; Gourdain, Nicolas; Malaspinas, Orestis; Eyssartier, Alexandre
2017-02-01
This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (Re =105), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (Finite Difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.
Zhou, L.; Qu, Z. G.; Ding, T.; Miao, J. Y.
2016-04-01
The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.
Droplet hysteresis investigation on non-wetting striped textured surfaces: A lattice Boltzmann study
Zheng, Rongye; Liu, Haihu; Sun, Jinju; Ba, Yan
2014-10-01
The Cassie-Baxter model is widely used to predict the apparent contact angles on textured super-hydrophobic surfaces. However, it has been challenged by some recent studies, since it does not consider contact angle hysteresis and surface structure characteristics near the contact line. The present study is to investigate the contact angle hysteresis on striped textured surfaces, and its elimination through vibrating the substrate. The two-phase flow is simulated by a recently proposed lattice Boltzmann model for high-density-ratio flows. Droplet evolutions under various initial contact angles are simulated, and it is found that different contact angles exist for the same textured surface. The importance of the contact line structure for droplet pinning is underlined via a study of droplet behavior on a composite substrate, with striped textured structure inside and flat structure outside. A “stick-jump” motion is found for the advancing contact line on the striped textured surface. Due to hysteresis, the contact angles after advancing are not consistent with the Cassie-Baxter model. The stable equilibrium is obtained through properly vibrating the substrate, and the resulted contact angles are consistent with Cassie's predictions.
Khajepor, Sorush; Chen, Baixin
2016-01-01
A method is developed to analytically and consistently implement cubic equations of state into the recently proposed multipseudopotential interaction (MPI) scheme in the class of two-phase lattice Boltzmann (LB) models [S. Khajepor, J. Wen, and B. Chen, Phys. Rev. E 91, 023301 (2015)]10.1103/PhysRevE.91.023301. An MPI forcing term is applied to reduce the constraints on the mathematical shape of the thermodynamically consistent pseudopotentials; this allows the parameters of the MPI forces to be determined analytically without the need of curve fitting or trial and error methods. Attraction and repulsion parts of equations of state (EOSs), representing underlying molecular interactions, are modeled by individual pseudopotentials. Four EOSs, van der Waals, Carnahan-Starling, Peng-Robinson, and Soave-Redlich-Kwong, are investigated and the results show that the developed MPI-LB system can satisfactorily recover the thermodynamic states of interest. The phase interface is predicted analytically and controlled via EOS parameters independently and its effect on the vapor-liquid equilibrium system is studied. The scheme is highly stable to very high density ratios and the accuracy of the results can be enhanced by increasing the interface resolution. The MPI drop is evaluated with regard to surface tension, spurious velocities, isotropy, dynamic behavior, and the stability dependence on the relaxation time.
Statistical physics ""Beyond equilibrium
Energy Technology Data Exchange (ETDEWEB)
Ecke, Robert E [Los Alamos National Laboratory
2009-01-01
The scientific challenges of the 21st century will increasingly involve competing interactions, geometric frustration, spatial and temporal intrinsic inhomogeneity, nanoscale structures, and interactions spanning many scales. We will focus on a broad class of emerging problems that will require new tools in non-equilibrium statistical physics and that will find application in new material functionality, in predicting complex spatial dynamics, and in understanding novel states of matter. Our work will encompass materials under extreme conditions involving elastic/plastic deformation, competing interactions, intrinsic inhomogeneity, frustration in condensed matter systems, scaling phenomena in disordered materials from glasses to granular matter, quantum chemistry applied to nano-scale materials, soft-matter materials, and spatio-temporal properties of both ordinary and complex fluids.
A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models
Luo, Li-Shi
1998-01-01
A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.
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.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A lattice Boltzmann model is developed for investigating the heat conduction process inside the three-dimensional random porous media. Combined with the algorithm for the reconstruction of the three-dimensional porous media, this model is used to investigate the transient heat conduction process inside the porous wick of CPLs/LHPs, which is vital for analyzing the startup stability of a CPL/LHP. The temperature distribution inside the porous wick is obtained and the influence of the porosity and the heat load on the conduction process also is investigated using the present model. The present model is applicable to predicting the effective conductivity of such a complex structure.
Oxygen equilibrium of brachiopod Lingula hemerythrin.
MANWELL, C
1960-08-26
In contrast to hemerythrin from five different species of sipunculid worms, ecardine brachiopod Lingula hemerythrin has an oxygen equilibrium which is reversibly altered by pH changes, both the oxygen affinity (Bohr effect) and the interactions between oxygen-binding centers being a function of pH. The significance of these phenomena is discussed in view of the phylogenetic distribution of hemerythrin and the function of respiratory pigments.
Equilibrium models and variational inequalities
Konnov, Igor
2007-01-01
The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models- Covers the basics of theory and solution methods both for the complementarity and variational inequality probl...
On the Local Equilibrium Principle
Hessling, H
2001-01-01
A physical system should be in a local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This seems to be a natural characterization of local equilibrium, however the problem is to give a precise meaning to the qualitative phrase ``infinitesimally localized measurements''. A solution is suggested in form of a {\\em Local Equilibrium Condition} (LEC) which can be applied to non-interacting quanta. The Unruh temperature of massless quanta is derived by applying LEC to an arbitrary point inside the Rindler Wedge. Massless quanta outside a hot sphere are analyzed. A stationary spherically symmetric local equilibrium does only exist according to LEC if the temperature is globally constant. Using LEC a non-trivial stationary local equilibrium is found for rotating massless quanta between two concentric cylinders of different temperatures. This shows that quanta may behave like a fluid with a B\\'enard instability.
General equilibrium without utility functions
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
2010-01-01
How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to re......How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known...... and the diffeomorphism of the equilibrium manifold with a Euclidean space; (2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; (3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; (4) for small trade vectors, the uniqueness, regularity...
Equilibrium and Sudden Events in Chemical Evolution
Weinberg, David H.; Andrews, Brett H.; Freudenburg, Jenna
2017-03-01
We present new analytic solutions for one-zone (fully mixed) chemical evolution models that incorporate a realistic delay time distribution for Type Ia supernovae (SNe Ia) and can therefore track the separate evolution of α-elements produced by core collapse supernovae (CCSNe) and iron peak elements synthesized in both CCSNe and SNe Ia. Our solutions allow constant, exponential, or linear–exponential ({{te}}-t/{τ {sfh}}) star formation histories, or combinations thereof. In generic cases, α and iron abundances evolve to an equilibrium at which element production is balanced by metal consumption and gas dilution, instead of continuing to increase over time. The equilibrium absolute abundances depend principally on supernova yields and the outflow mass loading parameter η, while the equilibrium abundance ratio [α /{Fe}] depends mainly on yields and secondarily on star formation history. A stellar population can be metal-poor either because it has not yet evolved to equilibrium or because high outflow efficiency makes the equilibrium abundance itself low. Systems with ongoing gas accretion develop metallicity distribution functions (MDFs) that are sharply peaked, while “gas starved” systems with rapidly declining star formation, such as the conventional “closed box” model, have broadly peaked MDFs. A burst of star formation that consumes a significant fraction of a system’s available gas and retains its metals can temporarily boost [α /{Fe}] by 0.1–0.3 dex, a possible origin for rare, α-enhanced stars with intermediate age and/or high metallicity. Other sudden transitions in system properties can produce surprising behavior, including backward evolution of a stellar population from high to low metallicity.
Stability of Spatial Equilibrium
Tabuchi, Takatoshi; Dao-Zhi, Zeng
2000-01-01
This paper focuses on externalities between economic agents. We consider spatial dis- tribution of economic activities in a multiregional dynamical system, where regions may be interpreted as clubs, social subgroups, species, or strategies. Our dynamics includes gravity models and replicator dynamics as special cases. Assuming that other variables, such as prices are solved as a function of the population distribution, we analyze both interior and corner equilibria of spatial distribution in ...
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.
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.
Diffusive-convective transition in the non-equilibrium charging of an electric double layer
Lobaskin, Vladimir; Netz, Roland R.
2016-12-01
We study the non-equilibrium electrolyte kinetics in a planar nanocapacitor that is driven by periodically switching surfaces charges using simulations, theory and scaling analysis. The combined effects of inter-ionic charge correlations and hydrodynamic interactions lead to correlated convective behavior for weakly charged ions. These dynamic correlations, signaling the breakdown of the Poisson-Nernst-Planck theory, are distinct from static correlations that are manifested by the crossover from Poisson-Boltzmann to strong-coupling theory that occurs as the ion valency increases.
Two-Temperature Model of non-equilibrium electron relaxation: A Review
Singh, Navinder
2007-01-01
The present paper is a review of the phenomena related to non-equilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann-Bloch-Peierls (BBP) kinetic equation has been applied to study the ultra-fast(femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro and nano-scale electronic...
Classical Boltzmann equation and high-temperature QED
Brandt, F. T.; Ferreira, R. B.; Thuorst, J. F.
2015-02-01
The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of quantum electrodynamics can be obtained from the Boltzman transport equation. We also present some explicit examples of this interesting equivalence.
Classical Boltzmann equation and high-temperature QED
Brandt, F T; Thuorst, J F
2015-01-01
The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of Quantum Electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of Quantum Electrodynamics can be obtained from the Boltzman transport equation. We also present some explicit examples of this interesting equivalence.
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.
Topological Interactions in a Boltzmann-Type Framework
Blanchet, Adrien; Degond, Pierre
2016-04-01
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 a spatial non-locality instead of the classical non-locality in velocity space. This result relies on the approximation properties of Bernstein polynomials. We illustrate the dynamics with numerical simulations.
Coupling lattice Boltzmann and molecular dynamics models for dense fluids
Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.
2007-04-01
We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
Static contact angle in lattice Boltzmann models of immiscible fluids.
Latva-Kokko, M; Rothman, Daniel H
2005-10-01
We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes.
Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm
Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.
2008-07-01
The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.
Diffusive limit for a quantum linear Boltzmann dynamics
Clark, Jeremy
2010-01-01
We study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model we begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the scattering with the gas particles is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix evolving according to a translation-covariant Lindblad equation. Our main result is a proof that the particle diffuses for large times.
Jet propagation within a Linearized Boltzmann Transport model
Energy Technology Data Exchange (ETDEWEB)
Luo, Tan; He, Yayun [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Wang, Xin-Nian [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Nuclear Science Division, Mailstop 70R0319, Lawrence Berkeley National Laboratory, Berkeley, CA 94740 (United States); Zhu, Yan [Departamento de Física de Partículas and IGFAE, Universidade de Santiago de Compostela, E-15706 Santiago de Compostela, Galicia (Spain)
2014-12-15
A Linearized Boltzmann Transport (LBT) model has been developed for the study of parton propagation inside quark–gluon plasma. Both leading and thermal recoiled partons are tracked in order to include the effect of jet-induced medium excitation. In this talk, we present a study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons and jet-induced medium excitations are found to have significant influences on the jet energy loss and transverse profile.
On space enrichment estimator for nonlinear Poisson-Boltzmann
Randrianarivony, Maharavo
2013-10-01
We consider the mathematical aspect of the nonlinear Poisson-Boltzmann equation which physically governs the ionic interaction between solute and solvent media. The presented a-posteriori estimates can be computed locally in a very efficient manner. The a-posteriori error is based upon hierarchical space enrichment which ensures its efficiency and reliability. A brief survey of the solving of the nonlinear system resulting from the FEM discretization is reported. To corroborate the analysis, we report on a few numerical results for illustrations. We numerically examine some values of the constants encountered in the theoretical study.
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 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.
Phillips, Rob
2015-03-01
It has been said that the cell is the test tube of the twenty-first century. If so, the theoretical tools needed to quantitatively and predictively describe what goes on in such test tubes lag sorely behind the stunning experimental advances in biology seen in the decades since the molecular biology revolution began. Perhaps surprisingly, one of the theoretical tools that has been used with great success on problems ranging from how cells communicate with their environment and each other to the nature of the organization of proteins and lipids within the cell membrane is statistical mechanics. A knee-jerk reaction to the use of statistical mechanics in the description of cellular processes is that living organisms are so far from equilibrium that one has no business even thinking about it. But such reactions are probably too hasty given that there are many regimes in which, because of a separation of timescales, for example, such an approach can be a useful first step. In this article, we explore the power of statistical mechanical thinking in the biological setting, with special emphasis on cell signaling and regulation. We show how such models are used to make predictions and describe some recent experiments designed to test them. We also consider the limits of such models based on the relative timescales of the processes of interest.
Equilibrium avalanches in spin glasses
Le Doussal, Pierre; Müller, Markus; Wiese, Kay Jörg
2012-06-01
We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick (SK) model, we present a detailed derivation of the density ρ(ΔM) of the magnetization jumps ΔM. It is obtained by introducing a multicomponent generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that ρ(ΔM)˜ΔM-τ with an avalanche exponent τ=1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1≪ΔMmodel. For finite-range models, using droplet arguments, we obtain the prediction τ=(df+θ)/dm where df,dm, and θ are the fractal dimension, magnetization exponent, and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.
Field line mapping and equilibrium reconstructions in new CNT Configuration
Traverso, Peter; Pedersen, Thomas; Brenner, Paul; Sarasola, Xabier; Durand de Gevigney, Benoit
2010-11-01
The Columbia Non-neutral Torus (CNT) has the useful feature of having adjustable coil geometry, creating up to three different stellarators each having a completely new shape to its magnetic surfaces and a different Iota profile. Recently the tilt angle between the two interlocking coils has been changed for the first time on CNT, allowing a study of the new magnetic geometry. In the new configuration field line mapping has been accomplished for multiple current ratios and magnetic fields to confirm the existence of good nested magnetic surfaces. At a specific current ratio a large one-three island chain is created. Plasma parameters have been measured with the new coil configuration, both in cases of a large internal island chain, and in cases without. Full 3D equilibrium reconstructions of potential and density are being performed using a modified version of the existing Poisson-Boltzmann solver. Field line mapping in this configuration will be presented, and a progress report on the equilibrium reconstructions will also be given.
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)
An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases
Institute of Scientific and Technical Information of China (English)
布仁满都拉; 赵迎春
2012-01-01
An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.
Rapid-Equilibrium Enzyme Kinetics
Alberty, Robert A.
2008-01-01
Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful because if experimental data can be fit by these simpler rate equations, the Michaelis constants can be interpreted as equilibrium constants. However, for some reactions it is necessary to use the more complicated steady-state rate equations. Thermodynamics is…
Method of measuring charge distribution of nanosized aerosols.
Kim, S H; Woo, K S; Liu, B Y H; Zachariah, M R
2005-02-01
In this paper, we present the development of a method to accurately measure the positive and negative charge distribution of nanosized aerosols using a tandem differential mobility analyzer (TDMA) system. From the series of TDMA measurements, the charge fraction of nanosized aerosol particles was obtained as a function of equivalent mobility particle diameter ranging from 50 to 200 nm. The capability of this new approach was implemented by sampling from a laminar diffusion flame which provides a source of highly charged particles due to naturally occurring flame ionization process. The results from the TDMA measurement provide the charge distribution of nanosized aerosols which we found to be in reasonable agreement with Boltzmann equilibrium charge distribution theory and a theory based upon charge population balance equation (PBE) combined with Fuchs theory (N.A. Fuchs, Geofis. Pura Appl. 56 (1963) 185). The theoretically estimated charge distribution of aerosol particles based on the PBE provides insight into the charging processes of nanosized aerosols surrounded by bipolar ions and electrons, and agree well with the TDMA results.
Detection of Hypertension Retinopathy Using Deep Learning and Boltzmann Machines
Triwijoyo, B. K.; Pradipto, Y. D.
2017-01-01
hypertensive retinopathy (HR) in the retina of the eye is disturbance caused by high blood pressure disease, where there is a systemic change of arterial in the blood vessels of the retina. Most heart attacks occur in patients caused by high blood pressure symptoms of undiagnosed. Hypertensive retinopathy Symptoms such as arteriolar narrowing, retinal haemorrhage and cotton wool spots. Based on this reasons, the early diagnosis of the symptoms of hypertensive retinopathy is very urgent to aim the prevention and treatment more accurate. This research aims to develop a system for early detection of hypertension retinopathy stage. The proposed method is to determine the combined features artery and vein diameter ratio (AVR) as well as changes position with Optic Disk (OD) in retinal images to review the classification of hypertensive retinopathy using Deep Neural Networks (DNN) and Boltzmann Machines approach. We choose this approach of because based on previous research DNN models were more accurate in the image pattern recognition, whereas Boltzmann machines selected because It requires speedy iteration in the process of learning neural network. The expected results from this research are designed a prototype system early detection of hypertensive retinopathy stage and analysed the effectiveness and accuracy of the proposed methods.
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.
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.
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
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.
Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
Directory of Open Access Journals (Sweden)
Bertrand Lods
2015-06-01
Full Text Available Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives.
Contact angles in the pseudopotential lattice Boltzmann modeling of wetting
Li, Qing; Luo, K. H.; Kang, Q. J.; Chen, Q.
2014-11-01
In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρL/ρV=500 . The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994), 10.1103/PhysRevE.49.2941] 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 θ static contact angles close to 180∘. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ >90∘ as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.
A Multiperiod Equilibrium Pricing Model
Directory of Open Access Journals (Sweden)
Minsuk Kwak
2014-01-01
Full Text Available We propose an equilibrium pricing model in a dynamic multiperiod stochastic framework with uncertain income. There are one tradable risky asset (stock/commodity, one nontradable underlying (temperature, and also a contingent claim (weather derivative written on the tradable risky asset and the nontradable underlying in the market. The price of the contingent claim is priced in equilibrium by optimal strategies of representative agent and market clearing condition. The risk preferences are of exponential type with a stochastic coefficient of risk aversion. Both subgame perfect strategy and naive strategy are considered and the corresponding equilibrium prices are derived. From the numerical result we examine how the equilibrium prices vary in response to changes in model parameters and highlight the importance of our equilibrium pricing principle.
Non-equilibrium phase transitions
Henkel, Malte; Lübeck, Sven
2009-01-01
This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed. The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.
Equilibrium with arbitrary market structure
DEFF Research Database (Denmark)
Grodal, Birgit; Vind, Karl
2005-01-01
Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The compl......Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model....... The complete market predicted by this theory is clearly unrealistic, and Radner [10] formulated and proved existence of equilibrium in a multiperiod model with incomplete markets. In this paper the Radner result is extended. Radner assumed a specific structure of markets, independence of preferences...
Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method
Januszewski, M.; Kostur, M.
2014-09-01
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. Catalogue identifier: AETA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License, version 3 No. of lines in distributed program, including test data, etc.: 225864 No. of bytes in distributed program, including test data, etc.: 46861049 Distribution format: tar.gz Programming language: Python, CUDA C, OpenCL. Computer: Any with an OpenCL or CUDA-compliant GPU. Operating system: No limits (tested on Linux and Mac OS X). RAM: Hundreds of megabytes to tens of gigabytes for typical cases. Classification: 12, 6.5. External routines: PyCUDA/PyOpenCL, Numpy, Mako, ZeroMQ (for multi-GPU simulations), scipy, sympy Nature of problem: GPU-accelerated simulation of single- and multi-component fluid flows. Solution method: A wide range of relaxation models (LBGK, MRT, regularized LB, ELBM, Shan-Chen, free energy, free surface) and boundary conditions within the lattice
The Dynamical Equilibrium of Galaxy Clusters
Carlberg, R. G.; Yee, H. K. C.; Ellingson, E.; Morris, S. L.; Abraham, R.; Gravel, P.; Pritchet, C. J.; Smecker-Hane, T.; Hartwick, F. D. A.; Hesser, J. E.; Hutchings, J. B.; Oke, J. B.
1997-02-01
If a galaxy cluster is effectively in dynamical equilibrium, then all galaxy populations within the cluster must have distributions in velocity and position that individually reflect the same underlying mass distribution, although the derived virial masses can be quite different. Specifically, within the Canadian Network for Observational Cosmology cluster sample, the virial radius of the red galaxy population is, on the average, a factor of 2.05 +/- 0.34 smaller than that of the blue population. The red galaxies also have a smaller rms velocity dispersion, a factor of 1.31 +/- 0.13 within our sample. Consequently, the virial mass calculated from the blue galaxies is 3.5 +/- 1.3 times larger than from the red galaxies. However, applying the Jeans equation of stellar hydrodynamic equilibrium to the red and blue subsamples separately gives statistically identical cluster mass profiles. This is strong evidence that these clusters are effectively equilibrium systems and therefore demonstrates empirically that the masses in the virialized region are reliably estimated using dynamical techniques.
Park, J.; Li, X.
The gas diffusion layer of a polymer electrolyte membrane (PEM) fuel cell is a porous medium generally made of carbon cloth or paper. The gas diffusion layer has been modeled conventionally as a homogeneous porous medium with a constant permeability in the literature of PEM fuel cell. However, in fact, the permeability of such fibrous porous medium is strongly affected by the fiber orientation having non-isotropic permeability. In this work, the lattice Boltzmann (LB) method is applied to the multi-phase flow phenomenon in the inhomogeneous gas diffusion layer of a PEM fuel cell. The inhomogeneous porous structure of the carbon cloth and carbon paper has been modeled as void space and porous area using Stokes/Brinkman formulation and void space and impermeable fiber distributions obtained from various microscopic images. The permeability of the porous medium is calculated and compared to the experimental measurements in literature showing a good agreement. Simulation results for various fiber distributions indicate that the permeability of the medium is strongly influenced by the effect of fiber orientation. Present lattice Boltzmann flow models are applied to the multi-phase flow simulations by incorporating multi-component LB model with inter-particle interaction forces. The model successfully simulates the complicated unsteady behaviors of liquid droplet motion in the porous medium providing a useful tool to investigate the mechanism of liquid water accumulation/removal in a gas diffusion layer of a PEM fuel cell.
Fluctuation theorem for constrained equilibrium systems
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Tsallis Distributions and the q-Triplet of the Magnetic Field in the Heliosheath
Burlaga, L. F.
2014-12-01
The Tsallis distribution (which is proportional to the q-exponential function and is related to the κ-distribution) was derived from an entropy function, inspired by multifractals, which gives a generalization of Boltzmann-Gibbs statistical mechanics. A Tsallis distribution describes the distribution of increments of daily averages of the magnetic field strength B observed by Voyager 2 (V2) in the heliosheath during 2010 in association with exceptionally low solar activity. A parameter q derived from this distribution is qstat = 1.75. The correlation function of B(t) is a power law on scales from 1 to 16 days, and from the exponent one obtains the parameter qrel = 3.9. The fluctuations of B are described by a multifractal spectrum f(α) on scales from 1 to 8 days, from which one obtains qsen = 1.75. The "q-triplet" (qsen, qrel, qstat) defines basic observable properties of an open, driven system in a meta-equilibrium state, which strongly constrains physical models of the system. The distribution of B is Gaussian, probably related to the unipolar region in which V2 was located. A 1/f spectrum of B was observed on scales from 1 to 100 days. The Tsallis distribution also describes the "turbulence" observed on very small scales, from 48 sec to several hours, observed by V2 behind the termination shock from day 245 - 301, 2007.
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Self-graviting Gas Spheres in Equilibrium State
Smirnov, Andrei
2015-01-01
In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation, which relates the pressure distribution and mass density in the body. The density distributions of constant, potential, gaussian, and exponential forms are discussed. Exact expressions for the distribution of mass and pressure along the radial direction, and the central pressure were obtained.
Radial equilibrium of relativistic particle bunches in plasma wakefield accelerators
Lotov, K V
2016-01-01
Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principle simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum distribution of beam particles depends on the observation radius and is neither separable, nor Gaussian.
Shafei, B.; Huber, C.; Parmigiani, A.; Taillefert, M.
2012-12-01
Physical and chemical heterogeneities associated with biogeochemical processes influence the fate and transport of contaminants in subsurface environments. We develop a new multi-species pore-scale reactive transport model based on the lattice Boltzmann method (LBM) to examine the temporal and spatial evolution of chemical species during the sorption of Arsenic. This model couples a fluid flow solver to an optimal advection-diffusion transport model where transport and reactions between chemical species are solved iteratively yielding a better stability and accuracy over a wide range of peclet numbers. It has already been applied to study 1) the permeability change of a porous medium during dissolution and precipitation and 2) the effect of spatial and chemical heterogeneities on the uptake of arsenic from the aqueous solution. By combining these two scenarios, we extend the model to incorporate arsenic speciation (i.e. As(III) and As(V)) and solid iron phase transformation, explore the distribution of iron, arsenic and partitioning of arsenic on various iron bearing solid phases. We investigate how the multitude of pore-domains affects the formation of redox gradients. As(III) and magnetite concentrations increase toward the anoxic zones while ferrihydrite and As(V) remains the dominant species in oxic conditions. The proposed reaction network includes: biotic reduction of ferrihydrite and magnetite to Fe2+(aq), of ferrihydrite to magnetite, biologically-mediated organic matter oxidation coupled with reduction of O2(aq) and As(V) , abiotic oxidation of Fe(II) by O2(aq) and sorption of As(V) and As(III) on Fe (hydr)oxide(s). All of these reactions are treated as kinetically controlled except As(V) and As(III) adsorption/desorption reactions which are expressed by equilibrium mass action laws. Similar set of reactions has been applied to simulate the distribution of As within constructed soil aggregates using continuum-scale model MIN3P (Masue-Slowey et al., 2010
Matsunaga, Ryusuke; Matsuda, Kazunari; Kanemitsu, Yoshihiko
2009-03-01
We have performed micro-photoluminescence (PL) spectroscopy for single carbon nanotubes under magnetic fields at various temperatures. Sharp PL spectra of single carbon nanotubes allow us to directly observe the dark exciton PL peak a few meV below the bright exciton PL peak due to the Aharonov-Bohm effect [1]. From the PL intensity ratio of the dark to the bright excitons under magnetic fields, we found that the non-equilibrium (non-Boltzmann) distribution occurs between the bright and dark states, because phonons cannot scatter excitons between the two states with different parities [2]. Furthermore, we discuss the diameter dependence of the exciton population of the bright and dark states in single carbon nanotubes. [1] R. Matsunaga, K. Matsuda, and Y. Kanemitsu, Phys. Rev. Lett. 101, 147404 (2008). [2] V. Perebeinos, J. Tersoff, and Ph. Avouris, Nano Lett. 5, 2495 (2005).