Ab initio molecular dynamics on the electronic Boltzmann equilibrium distribution
Energy Technology Data Exchange (ETDEWEB)
Alonso, J L; Echenique, P [Departamento de Fisica Teorica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Castro, A; Polo, V [Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza (Spain); Rubio, A [Nano-Bio Spectroscopy group and ETSF Scientific Development Centre, Departamento de Fisica de Materiales, Universidad del PaIs Vasco, Centro de Fisica de Materiales, CSIC-UPV/EHU-MPC and DIPC, E-20018 San Sebastian (Spain); Zueco, D, E-mail: dzueco@unizar.e [Instituto de Ciencia de Materiales de Aragon and Departamento de Fisica de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza (Spain)
2010-08-15
We prove that for a combined system of classical and quantum particles, it is possible to describe a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics (MD) do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach) and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings). A practical application of this MD to the study of the effect of temperature on molecular systems presenting (nearly) degenerate states-such as the avoided crossing in the ring-closure process of ozone-is presented.
Baldovin, Fulvio; Moyano, Luis G.; Tsallis, Constantino
2004-01-01
We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\\Gamma$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $\\beta$-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (${\\mathbf F}=m{\\mathbf a}$). At higher energies we discuss partia...
International Nuclear Information System (INIS)
Many calculations of the electrical conductivity of non-equilibrium MHD plasmas have been based on a simple two-temperature theory. This theory assumes that (a) the electron number density has the equilibrium (Saha) value corresponding to the electron temperature Te , and (b) the free electron energy distribution function f(u) is Maxwellian. The validity of assumption (a) has been studied by several authors who, however, used assumption (b) in their analyses. Assumption (b) has been less thoroughly studied. Because both excitation and ionization rates are sensitive to f(u) and bound states may be out of equilibrium due to radiative transitions, it is unrealistic to treat these two assumptions separately. This paper reports preliminary results of an investigation undertaken to establish the range of validity of the two-temperature theory for MHD plasmas by solving the Boltzmann equation for f(u) and the steady-state rate equations for the bound electronic states. The problem was attacked in three stages. First, f(u) was calculated from a Boltzmann equation including only the electric field and the elastic collision terms. The results showed that for typical MHD systems (e.g., Ar + K at 1 atm) .electron-electron collisions drive f(u) to Maxwellian. Second, the solution of the rate equations for a Maxwellian f(u), using a five-level caesium atomic model, demonstrated the importance of radiative transitions in determining the bound-state populations and magnitudes of the inelastic collision terms. The model atom consisted of four discrete states (6S; 6P,P'; 5D, D'; 7S) and a lumped state, to which were assigned various binding energies and degeneracies. Criteria for selecting the latter were based on the maximum stable orbit radius that would be likely for the plasmas of interest. Both the classical Bohr-Thomson and Gryzinski cross-sections were used to calculate the rate coefficients and collision terms for excitation, de-excitation, ionization, and three-body capture
Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
Birrell, Jeremiah
2014-01-01
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature $T(t)$ and phase space occupation factor $\\Upsilon(t)$. In this first paper we address (effectively) massless fermions and derive dynamical equations for $T(t)$ and $\\Upsilon(t)$ such that the zeroth order term of the basis alone captures the number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component ($e^\\pm$-annihilation).
Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure
Shi, Wei; Lu, Wei-Zhen; Xue, Yu; He, Hong-Di
2016-02-01
A revised lattice Boltzmann model concerning the equilibrium traffic pressure is proposed in this study to tackle the phase transition phenomena of traffic flow system. The traditional lattice Boltzmann model has limitation to investigate the complex traffic phase transitions due to its difficulty for modeling the equilibrium velocity distribution. Concerning this drawback, the equilibrium traffic pressure is taken into account to derive the equilibrium velocity distribution in the revised lattice Boltzmann model. In the proposed model, a three-dimensional velocity-space is assumed to determine the equilibrium velocity distribution functions and an alternative, new derivative approach is introduced to deduct the macroscopic equations with the first-order accuracy level from the lattice Boltzmann model. Based on the linear stability theory, the stability conditions of the corresponding macroscopic equations can be obtained. The outputs indicate that the stability curve is divided into three regions, i.e., the stable region, the neutral stability region, and the unstable region. In the stable region, small disturbance appears in the initial uniform flow and will vanish after long term evolution, while in the unstable region, the disturbance will be enlarged and finally leads to the traffic system entering the congested state. In the neutral stability region, small disturbance does not vanish with time and maintains its amplitude in the traffic system. Conclusively, the stability of traffic system is found to be enhanced as the equilibrium traffic pressure increases. Finally, the numerical outputs of the proposed model are found to be consistent with the recognized, theoretical results.
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).
An alternative approach to the Boltzmann distribution through the chemical potential
D'Anna, Michele; Job, Georg
2016-05-01
The Boltzmann distribution is one of the most significant results of classical physics. Despite its importance and its wide range of application, at high school level it is mostly presented without any derivation or link to some basic ideas. In this contribution we present an approach based on the chemical potential that allows to derive it directly from the basic idea of thermodynamical equilibrium.
Equilibrium Distribution of Labor Productivity
Aoyama, Hideaki; Iyetomi, Hiroshi; Yoshikawa, Hiroshi
2012-01-01
We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors ...
Frausto-Solis, Juan; Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J Javier; González-Flores, Carlos; Castilla-Valdez, Guadalupe
2016-01-01
A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA. PMID:27413369
Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J. Javier; González-Flores, Carlos
2016-01-01
A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA. PMID:27413369
International Nuclear Information System (INIS)
This paper reports the development of an object-oriented programming methodology for particle simulations. It is established on the [m reductionist] view that many physical phenomena cana be reduced to many-body problems. By doing the reduction, many seemly unrelated physical phenomena can be simulated in a systematic way and a high-level programming system can be constructed to facilitate the programming and the solution of the simulations. In the object-oriented particle simulation methodology, a hierarchy of abstract particles is defined to represent a variety of characteristics in physical system simulations. A simulation program is constructed from particles derived from the abstract particles. The object- oriented particle simulation methodology provides a unifying modeling and simulation framework for a variety of simulation applications with the use of particle methods. It allows easy composition of simulation programs from predefined software modules and facilitates software reusability. It greatly increase the productivity of simulation program constructions. Boltzmann (after Ludwig Boltzmann, 1844-1906) is a prototype programming system in the object-oriented particle simulation methodology. Boltzmann is implemented in C++ and the X Window System. It contains a library of data types and functions that support simulations in particle methods. Moreover, it provides a visualization window to support friendly user-computer interaction. Examples of the application of the Boltzmann programming system are presented. The effectiveness of the object-oriented particle simulation methodology is demonstrated. A user's manual is included in the appendix
Ausloos, M.
2000-09-01
Recent observations have indicated that the traditional equilibrium market hypothesis (EMH; also known as Efficient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-field approximations like a Gaussian distribution of price fluctuations. A kinetic theory for prices can be simply derived, considering in a first approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium (isothermal) equation for the price (taken as the order parameter) of a stock as a function of the volume of money available are obtained.
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.
Energy Technology Data Exchange (ETDEWEB)
Riotto, A. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.
1998-05-04
The closed time path (CTP) formalism is a powerful Green function formulation to describe non-equilibrium phenomena in field theory and it leads to a complete non-equilibrium quantum kinetic theory. In this paper we make use of the CTP formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ````memory```` effects which are typical of the quantum transport theory and are not present in the classical approach. The slowdown of the relaxation processes may keep the system out of equilibrium for longer times and therefore enhance the final baryon asymmetry. We also stress that the classical approximation is not adequate to describe the quantum interference nature of CP violation and that a quantum approach should be adopted to compute the sources since they are most easily built up by the transmission of low momentum particles. (orig.). 26 refs.
Distribution Learning in Evolutionary Strategies and Restricted Boltzmann Machines
DEFF Research Database (Denmark)
Krause, Oswin
The thesis is concerned with learning distributions in the two settings of Evolutionary Strategies (ESs) and Restricted Boltzmann Machines (RBMs). In both cases, the distributions are learned from samples, albeit with different goals. Evolutionary Strategies are concerned with finding an optimum of...... an objective function for which the gradient is not available. The algorithm samples function values from a search distribution and adapts the parameters of the distribution during the optimization process. In the thesis, new update schemes for the covariance matrix used by the CMA-ES are...... second part of the thesis is concerned with RBMs that are fitted to a dataset using maximum log-likelihood. As the computation of the distribution's normalization constant is intractable, Markov Chain Monte Carlo methods are required to estimate and follow the log-likelihood gradient. The thesis...
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.
Derivation of the Second Law of Thermodynamics from Boltzmann's Distribution Law.
Nelson, P. G.
1988-01-01
Shows how the thermodynamic condition for equilibrium in an isolated system can be derived by the application of Boltzmann's law to a simple physical system. States that this derivation could be included in an introductory course on chemical equilibrium to help prepare students for a statistical mechanical treatment presented in the curriculum.…
Equilibrium size distribution of rouleaux
Energy Technology Data Exchange (ETDEWEB)
Perelson, A.S. (Los Alamos National Lab., NM); Wiegel, F.W.
1982-02-01
Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) the average number of branch points per rouleau; and (d) the number of rouleaux with n cells, n = 1, 2,..., in a system containing a total of N cells. We also present the results of numerical evaluations to establish the validity of asymptotic expressions that simplify our formal analytic results.
On convergence to equilibrium for solutions to the linear, space-inhomogeneous Boltzmann equation
International Nuclear Information System (INIS)
In this paper, the linear space-inhomogeneous transport equation for a distribution function (describing, for instance, a neutron distribution) in a bounded body with general boundary conditions is considered. Results on weak convergence to equilibrium, when t→ infinity, are given for general initial data, first in the cutoff case and then for infinite-range collision forces. To handle these problems, general H theorems (concerning monotonicity in time of convex entropy functionals) are presented. Furthermore, general results on collision invariants, i.e., on functions satisfying detailed balance relations in a binary collision, are given
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.
Liang, Jun; Liu, Yan-Chun; Zhu, Qiao
2014-02-01
In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole.
International Nuclear Information System (INIS)
In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole. (authors)
Lucia, Umberto
2016-02-01
The balance of forces and processes between the system and the environment and the processes inside the system are the result of the flows of the quanta. Moreover, the transition between two thermodynamic states is the consequence of absorption or emission of quanta, but, during the transition, the entropy variation due to the irreversibility occurs and it breaks any symmetry of time. Consequently, the irreversibility is the result of a transition, a process, an interaction between the system and its environment. This interaction results completely time-irreversible for any real process because of irreversibility. As a consequence, a proof of the third law is obtained proving that the zero temperature state can be achieved only for an infinite work lost for dissipation or in an infinite time. The fundamental role of time both in equilibrium and in non equilibrium analysis is pointed out. Moreover, the non equilibrium temperature is related to the entropy generation and its fluctuation rate; indeed, non-stationary temperature means that the system has not yet attained free energy minimum state, i.e., the maximum entropy state; the consequence is that the zero temperature state can be achieved only for an infinite work lost for dissipation or in an infinite time. In engineering thermodynamics the efficiency is always obtained without any consideration on time, while, here, just the time is introduced as a fundamental quantity of the analysis of non equilibrium states.
Far-from-equilibrium distribution from near-steady-state work fluctuations.
Marsland, Robert; England, Jeremy
2015-11-01
A long-standing goal of nonequilibrium statistical mechanics has been to extend the conceptual power of the Boltzmann distribution to driven systems. We report some new progress towards this goal. Instead of writing the nonequilibrium steady-state distribution in terms of perturbations around thermal equilibrium, we start from the linearized driven dynamics of observables about their stable fixed point, and expand in the strength of the nonlinearities encountered during typical fluctuations away from the fixed point. The first terms in this expansion retain the simplicity of known expansions about equilibrium, but can correctly describe the statistics of a certain class of systems even under strong driving. We illustrate this approach by comparison with a numerical simulation of a sheared Brownian colloid, where we find that the first two terms in our expansion are sufficient to account for the shear thinning behavior at high shear rates. PMID:26651660
Dyatko, Nikolay; Donko, Zoltan
2015-01-01
At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This "bistability effect" - in which electron-electron (Coulomb) collisions play an essential role - is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms ("two-term app...
Dechant, Andreas; Shafier, Shalom Tzvi; Kessler, David A.; Barkai, Eli
2016-01-01
The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for non-thermal systems such as cold atoms in optical lattices, where the heat bath is replaced by the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy o...
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...
Philippi, P C; Surmas, R; Philippi, Paulo Cesar; Santos, Luis Orlando Emerich dos; Surmas, Rodrigo
2005-01-01
The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its conceptual support: the continuous Boltzmann equation (BE). Most collision models are based on the BGK, single parameter, relaxation-term leading to constant Prandtl numbers. The polynomial expansion used for the equilibrium distribution introduces an upper-bound in the local macroscopic speed. Most widely used time discretization procedures give an explicit numerical scheme with second-order time step errors. In thermal problems, quadrature did not succeed in giving discrete velocity sets able to generate multi-speed regular lattices. All these problems, greatly, difficult the numerical simulation of LBM based algorithms. In present work, the systematic derivation of lattice-Boltzmann models from the continuous Boltzmann equation is discussed. The collision term in the li...
Bisi, Marzia; Lods, Bertrand
2011-01-01
We consider the spatially homogeneous Boltzmann equation for inelastic hard-spheres (with constant restitution coefficient $\\alpha \\in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove uniqueness of the stationary solution (with given mass) in the weakly inelastic regime; i.e., for any inelasticity parameter $\\alpha \\in (\\alpha_0,1)$, with some constructive $\\alpha_0 \\in [0, 1)$. Our analysis is based on a perturbative argument which uses the knowledge of the stationary solution in the elastic limit and quantitative estimates of the convergence of stationary solutions as the inelasticity parameter goes to 1. In order to achieve this we give an accurate spectral analysis of the associated linearized collision operator in the elastic limit. Several qualitative properties of this unique steady state $F_\\alpha$ are also derived; in particular, we prove that $F_\\alpha$ is bounded from above and from below by two explicit universal (i.e. independent of $\\alpha$...
The equilibrium size distribution of rouleaux.
Perelson, A. S.; Wiegel, F.W.
1982-01-01
Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) th...
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 Distribution of Labor Productivity: A Theoretical Model
Hideaki Aoyama; Hiroshi Iyetomi; Hiroshi Yoshikawa
2012-01-01
We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors ...
Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; Maznev, Alexei A.; Nelson, Keith A.; Chen, Gang
2016-04-01
The phonon Boltzmann transport equation (BTE) is a powerful tool for studying nondiffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime.
Equilibrium of global amphibian species distributions with climate
DEFF Research Database (Denmark)
Munguía, Mariana; Rahbek, Carsten; Rangel, Thiago F.; Diniz-Filho, Jose Alexandre F.; Bastos Araujo, Miguel
2012-01-01
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...... 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...
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
INVARIANT KAPPA DISTRIBUTION IN SPACE PLASMAS OUT OF EQUILIBRIUM
International Nuclear Information System (INIS)
Recent advances in Space Physics theory have shown 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. The non-equilibrium temperature and the kappa index that govern these distributions are the two independent controlling parameters of non-equilibrium systems. 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, while its physical meaning is connected to the correlation between the system's particles. The classical, single stationary state at equilibrium is generalized into a whole set of different non-equilibrium stationary states labeled by the kappa index. This paper addresses certain crucial issues about the physical meaning and role of the kappa index in identifying stationary states. The origin of the emerged inconsistencies is that the kappa index is not an invariant physical quantity, but instead depends on the degrees of freedom of the system's particles. This leads in several misleading conclusions, such as (1) only large kappa index, practically infinite, can characterize the many-particle kappa distribution, and (2) the correlation between particles depends on the total number of the system's particles. Here we show that a modified kappa index, invariant for any number of degrees of freedom, can be naturally defined. Then, we develop and examine the relevant corrected formulation of many-particle multidimensional kappa distribution, and discuss the physical meaning of the invariant kappa index.
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…
Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution.
Chang, Chien C; Kuo, Chih-Yu; Wang, Chang-Yi
2011-11-01
The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λlinearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ. PMID:22072500
Dechant, Andreas; Shafier, Shalom Tzvi; Kessler, David A; Barkai, Eli
2016-08-01
The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density. PMID:27627290
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.
Lanyi, Gabor E.
2003-01-01
This viewgraph presentation reviews the 1901 work in Planck's constant and blackbody radiation law and the 1916 Einstein rederivation of the blackbody radiation law. It also reviews Wien's law. It also presents equations that demonstrate the thermal balance between radiation and matter.
Investigation of the Boltzmann relation in plasmas with non-Maxwellian electron distribution
International Nuclear Information System (INIS)
An experimental investigation of the Boltzmann relation at various radio frequency (RF) powers was performed in a low pressure RF inductively coupled plasma (ICP). The measured electron energy probability functions (EEPFs) show a high population of low energy electrons at low RF powers, while the population of high energy electrons is high at high RF powers. In these bi-Maxwellian EEPFs, radial variations of the electron density and the plasma potential from the center to the edge of the discharge chamber were plotted according to the Boltzmann relation with the effective temperature Teff and the screening temperature Ts, and it was found that the Boltzmann relation with the screening temperature, rather than with the effective temperature, describes the relation between the electron density and the plasma potential
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzman
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.
Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion
Coelho, Rodrigo C V; Doria, M M; Pereira, R M; Aibe, Valter Yoshihiko
2013-01-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded until fourth order in the Hermite polynomials.
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
Molnar, E.; Niemi, H.; Rischke, D. H.
2016-01-01
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break dow...
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 electron equilibrium distribution function in the kinetic theory of electron cyclotron maser
Shenggang, Liu
1981-11-01
The problems concerning the specification of electron equilibrium distribution function for the kinetic theory of ECRM are investigated in this paper. After detailed analysis of the published equilibium distribution functions, several conclusion have been achieved.
Equilibrium charge state distributions of high energy heavy ions
International Nuclear Information System (INIS)
Equilibrium charge state fractions have been measured for N, O, Ne, S, Ar and Kr ions at 1.04 MeV/nucleon after passing through various stripping materials. Further data were obtained at higher energy for S ions (4.12 MeV/nucleon) and Ar ions (4.12 and 9.6 MeV/nucleon). The mean charge fractions can be fitted to universal curves for both solid and gaseous strippers. Measurements of the equilibrium fraction of krypton ions at 1.04 MeV/nucleon passing through heavy vapours have shown that a higher average charge state is obtained than for lighter gaseous strippers. (Auth.)
Basu, Prasad
2011-01-01
Following the original approach of Maxwell-Boltzmann(MB), we derive a 4-velocity distribution function for the relativistic ideal gas. This distribution function perfectly reduces to original MB distribution in the non-relativistic limit. We express the relativistic equation of state(EOS), $\\rho-\\rho_0=(\\gamma-1)^{-1}p$,\\ in the two equations: $\\rho=\\rho_0 f(\\lambda)$,\\ and $p=\\rho_0 g(\\lambda)$, where $\\lambda$\\ is a parameter related to the kinetic energy, hence the temperature, of the gas. In the both extreme limits, they give correct EOS:\\ $\\rho=3p$\\ in the ultra-relativistic, and\\ $\\rho-\\rho_0=3/2p$ in the non-relativistic regime. Using these equations the adiabatic index $\\gamma$ (=$\\frac{c_p}{c_v}$) and the sound speed $a_s$ are calculated as a function of $\\lambda$. They also satisfy the inequalities: $4/3 \\le \\gamma \\le 5/3$ and $a_s \\le \\frac{1}{\\sqrt{3}}$ perfectly.
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
Modified Lattice Boltzmann method for compressible fluid simulations
International Nuclear Information System (INIS)
A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory
Modified lattice Boltzmann method for compressible fluid simulations.
Hinton, F L; Rosenbluth, M N; Wong, S K; Lin-Liu, Y R; Miller, R L
2001-06-01
A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory. PMID:11415085
Equilibrium charge state distributions of 14N and 20Ne ions emerging from solids
International Nuclear Information System (INIS)
A new technique of backscattering has been developed for the measurement of equilibrium charge state distributions of ions emerging from a solid medium. By this method, equilibrium charge fractions for nitrogen in the energy range from 0.8 to 1.7 MeV and for neon from 1.5 to 4.4 MeV have been measured. The influence of inner shell vacancies produced by violent collisions on the charge state equilibrium is discussed. (Auth.)
Quantum distribution functions in non-equilibrium statistical mechanics
International Nuclear Information System (INIS)
As we have emphasized in previous investigations of this question, the optimum approach to the problem is via the use of characteristic functions, which are nothing more than Fourier transforms of distribution distributions. The next step is to write P/sub w/(q,p) in terms of the complex variable α. Then we obtain relationships between the various distribution functions, which are readily converted into relationships between the distribution functions, either in q-p or α language. For simplicity, we treat a one-dimensional system in a pure state since the case of a mixture in multi-dimensions presents no essential complications. Since the touchstone of our considerations is the Wigner distribution, we write down its properties. We then summarize the properties of the generalized distribution functions of the Cahill-Glauber class and their relation to the Wigner distribution. In addition, we discuss the Husimi (smoothed) distribution function and point out its exact equivalence with the anti-normal distribution. We discuss the Glauber-Sudarshan P (α) function as well as the Q(α) function and also the relation between them and P/sub w/. Then we show that the Q(α), Husimi and anti-normal distributions are identical to each other and, similarly, the Glauber-Sudarshan and normal distributions are identical. Finally, we introduce a new class of generalized distribution functions, with emphasis on two particular cases of same viz., the standard of anti-standard distributions, and we also demonstrate the equivalence of the latter to the Kirkwood distribution. 19 refs
International Nuclear Information System (INIS)
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/cm2 and this remained unchanged until a maximum target thickness of 98 μg/cm2. 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 C2+, C3+, and C4+ incident ions merged into quasi-equilibrium values at a target thickness of 5.7 μg/cm2 in the pre-equilibrium region and evolved simultaneously to the ‘real equilibrium’ values for all of the initial charge states, including C5+ and C6+ 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
International Nuclear Information System (INIS)
The kinetic theory of charged particles in gases has come a long way in the last 60 years or so, but many of the advances have yet to find their way into contemporary studies of low-temperature plasmas. This review explores the way in which this gap might be bridged, and focuses in particular on the analytic framework and numerical techniques for the solution of Boltzmann's equation for both electrons and ions, as well as on the development of fluid models and semi-empirical formulae. Both hydrodynamic and non-hydrodynamic regimes are considered and transport properties are calculated in various configurations of dc and ac electric and magnetic fields. We discuss in particular the duality in transport coefficients arising from non-conservative collisions (attachment, ionization). (review article)
International Nuclear Information System (INIS)
Both equilibrium and non-equilibrium charge-state distributions for 2.0 MeV/u sulfur ions after passing through carbon foils were studied experimentally. For the equilibrium charge-state distribution, incident ions of S7+, S12+, S14+ and S16+ were injected into carbon foils 54, 98, 150 and 200 μg/cm2 in thickness, whereas for the non-equilibrium distributions, new measurements for S15+ and S16+ incidences were made through carbon foils of 0.9-10 μg/cm2 to supplement our previous experiments regarding S6+-S14+ incidences [M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 230 (2005) 63; M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 256 (2007) 11]. Mean charge states for S6+-S14+ incidences as functions of the penetration thickness merged at 6.9 μg/cm2 and changed together until reaching equilibrium at around 100 μg/cm2, while those for S15+ and S16+ incidences took different paths to equilibrium, which was also the case for distribution widths for S6+-S14+, S15+ and S16+ incidences. An equilibrium mean charge state of 12.68 and distribution width of 1.11 were attained with equilibrium charge distributions between 6+ and 16+.
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
Ramachandran, S.; Kumar, P. B. Sunil; Pagonabarraga, I.
2006-06-01
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.
Non-linear effects in the Boltzmann equation
International Nuclear Information System (INIS)
The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.)
Modelling Thomson scattering for systems with non-equilibrium electron distributions
Chapman D.A.; Vorberger J.; Wünsch K.; Gericke D.O.
2013-01-01
We investigate the effect of non-equilibrium electron distributions in the analysis of Thomson scattering for a range of conditions of interest to inertial confinement fusion experiments. Firstly, a generalised one-component model based on quantum statistical theory is given in the random phase approximation (RPA). The Chihara expression for electron-ion plasmas is then adapted to include the new non-equilibrium electron physics. The theoretical scattering spectra for both diffuse and dense p...
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...
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...
Uncertainty Principle Consequences at Thermal Equilibrium
Pachon, Leonardo A; Zueco, David; Brumer, Paul
2014-01-01
Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that these deviations are intimately linked to the power spectrum of the thermal bath. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum and therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. This is in sharp contrast to the classical case, for which the thermal equilibrium distribution of a system interacting via central forces with pairwise-self-interacting environment, irrespective of the interaction strength, is shown to be \\emph{exactly} characterized by the canonical Boltzmann distribution. As a consequence of this analysis, we define an \\emph{effective coupling} to the environment that depends on all energy scales in the system and reservoir interactio...
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.
Radiative equilibrium in Monte Carlo radiative transfer using frequency distribution adjustment
Baes, M; Davies, J I; Whitworth, A P; Sabatini, S; Roberts, S; Linder, S M; Evans, R; Baes, Maarten; Stamatellos, Dimitris; Davies, Jonathan I.; Whitworth, Anthony P.; Sabatini, Sabina; Roberts, Sarah; Linder, Suzanne M.; Evans, Rhodri
2005-01-01
The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes them numerically very demanding. Bjorkman & Wood recently proposed a frequency distribution adjustment scheme, which allows radiative equilibrium Monte Carlo calculations to be performed without iteration, by choosing the frequency of each re-emitted photon such that it corrects for the incorrect spectrum of the previously re-emitted photons. Although the method appears to yield correct results, we argue that its theoretical basis is not completely transparent, and that it is not completely clear whether this technique is an exact rigorous method, or whether it is just a good and convenient approximation. We critically study the general problem of how an already sampled distribution can be adjusted to a new distribution by adding data points sampled from an adjustment ...
Modelling Thomson scattering for systems with non-equilibrium electron distributions
Directory of Open Access Journals (Sweden)
Chapman D.A.
2013-11-01
Full Text Available We investigate the effect of non-equilibrium electron distributions in the analysis of Thomson scattering for a range of conditions of interest to inertial confinement fusion experiments. Firstly, a generalised one-component model based on quantum statistical theory is given in the random phase approximation (RPA. The Chihara expression for electron-ion plasmas is then adapted to include the new non-equilibrium electron physics. The theoretical scattering spectra for both diffuse and dense plasmas in which non-equilibrium electron distributions are expected to arise are considered. We find that such distributions strongly influence the spectra and are hence an important consideration for accurately determining the plasma conditions.
Modelling spectral properties of non-equilibrium atomic hydrogen plasma
D'Ammando, G.; Pietanza, L. D.; Colonna, G.; Longo, S.; Capitelli, M.
2010-02-01
A model to predict the emissivity and absorption coefficient of atomic hydrogen plasma is presented in detail. Non-equilibrium plasma is studied through coupling of the model with a collisional-radiative code for the excited states population as well as with the Boltzmann equation for the electron energy distribution function.
Modelling spectral properties of non-equilibrium atomic hydrogen plasma
International Nuclear Information System (INIS)
A model to predict the emissivity and absorption coefficient of atomic hydrogen plasma is presented in detail. Non-equilibrium plasma is studied through coupling of the model with a collisional-radiative code for the excited states population as well as with the Boltzmann equation for the electron energy distribution function.
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…
Sell, Friedrich L.; Öllinger, Michael
2015-01-01
The paper first aims at showing that personal income distribution - at least after government intervention - tends to be a stationary variable for many European countries. This finding backs earlier results achieved by Ramser (1987). Furthermore, personal incomes follow a log-normal distribution, regardless of time and location. The authors set up a theoretical equilibrium concept for personal income distribution which is located in status theory and which can explain why a certain or likewis...
Gao, Haixia; Li, Ting; Xiao, Changming
2016-05-01
When a simple system is in its nonequilibrium state, it will shift to its equilibrium state. Obviously, in this process, there are a series of nonequilibrium states. With the assistance of Bayesian statistics and hyperensemble, a probable probability distribution of these nonequilibrium states can be determined by maximizing the hyperensemble entropy. It is known that the largest probability is the equilibrium state, and the far a nonequilibrium state is away from the equilibrium one, the smaller the probability will be, and the same conclusion can also be obtained in the multi-state space. Furthermore, if the probability stands for the relative time the corresponding nonequilibrium state can stay, then the velocity of a nonequilibrium state returning back to its equilibrium can also be determined through the reciprocal of the derivative of this probability. It tells us that the far away the state from the equilibrium is, the faster the returning velocity will be; if the system is near to its equilibrium state, the velocity will tend to be smaller and smaller, and finally tends to 0 when it gets the equilibrium state.
C7+ characterization of related equilibrium fluids using the gamma distribution
International Nuclear Information System (INIS)
A method is developed for dividing the C7+ (heptanes-plus) fraction of crude oil and condensate fluids into an arbitrary number of discrete pseudocomponents using Gauss--Laguerre quadrature and the gamma distribution model. Our method can be applied simultaneously to several related or equilibrium mixtures. This ensures that the properties of C7+ cuts are the same for each mixture, but that the molar quantity of each cut correctly reflects the overall molar distribution of each C7+ mixture. Example applications include multiple samples taken from a reservoir with a strong compositional gradient and reservoir fluids in equilibrium at a gas-oil contact
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
Lu, Jianfeng; Mendl, Christian B.
2015-06-01
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 × 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as a special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
Lu, Jianfeng
2014-01-01
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 x 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.
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.
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.
International Nuclear Information System (INIS)
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 3d54s4p 6P excited levels. The 3d54s4p 6P 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.104. The Boltzmann plots give important information on the reason why a variety of iron ionic lines can be emitted from glow discharge plasmas.
Energy Technology Data Exchange (ETDEWEB)
Imai, M. [Department of Nuclear Engineering, Kyoto University, Sakyo, Kyoto 606-8501 (Japan)], E-mail: imai@nucleng.kyoto-u.ac.jp; Sataka, M. [Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195 (Japan); Kawatsura, K.; Takahiro, K. [Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Sakyo, Kyoto 606-8585 (Japan); Komaki, K. [National Center for University Entrance Examinations, Meguro, Tokyo 153-8501 (Japan); Shibata, H. [Department of Nuclear Engineering, Kyoto University, Sakyo, Kyoto 606-8501 (Japan); Sugai, H.; Nishio, K. [Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195 (Japan)
2009-08-15
Both equilibrium and non-equilibrium charge-state distributions for 2.0 MeV/u sulfur ions after passing through carbon foils were studied experimentally. For the equilibrium charge-state distribution, incident ions of S{sup 7+}, S{sup 12+}, S{sup 14+} and S{sup 16+} were injected into carbon foils 54, 98, 150 and 200 {mu}g/cm{sup 2} in thickness, whereas for the non-equilibrium distributions, new measurements for S{sup 15+} and S{sup 16+} incidences were made through carbon foils of 0.9-10 {mu}g/cm{sup 2} to supplement our previous experiments regarding S{sup 6+}-S{sup 14+} incidences [M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 230 (2005) 63; M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 256 (2007) 11]. Mean charge states for S{sup 6+}-S{sup 14+} incidences as functions of the penetration thickness merged at 6.9 {mu}g/cm{sup 2} and changed together until reaching equilibrium at around 100 {mu}g/cm{sup 2}, while those for S{sup 15+} and S{sup 16+} incidences took different paths to equilibrium, which was also the case for distribution widths for S{sup 6+}-S{sup 14+}, S{sup 15+} and S{sup 16+} incidences. An equilibrium mean charge state of 12.68 and distribution width of 1.11 were attained with equilibrium charge distributions between 6+ and 16+.
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.
International Nuclear Information System (INIS)
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)
The nuclear fusion reaction rate based on relativistic equilibrium velocity distribution
Liu, Jian-Miin
2002-01-01
The Coulomb barrier is in general much higher than thermal energy. Nuclear fusion reactions occur only among few protons and nuclei with higher relative energies than Coulomb barrier. It is the equilibrium velocity distribution of these high-energy protons and nuclei that participates in determining the rate of nuclear fusion reactions. In the circumstance it is inappropriate to use the Maxwellian velocity distribution for calculating the nuclear fusion reaction rate. We use the relativistic ...
Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks
DEFF Research Database (Denmark)
Anderson, David F.; Craciun, Gheorghe; Gopalkrishnan, Manoj; Wiuf, Carsten Henrik
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...
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...
Radtke, Gregg A; Hadjiconstantinou, Nicolas G
2009-05-01
We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated. PMID:19518597
Temperature based Restricted Boltzmann Machines
Li, Guoqi; Deng, Lei; Xu, Yi; Wen, Changyun; Wang, Wei; Pei, Jing; Shi, Luping
2016-01-01
Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics
Tirnakli, Ugur; Borges, Ernesto P.
2016-03-01
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results.
The lattice Boltzmann model for the second-order Benjamin–Ono equations
International Nuclear Information System (INIS)
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations
The non-linear Boltzmann equation and its application to time and space dependent problems
International Nuclear Information System (INIS)
This thesis is divided into two parts which both involve finding solutions of the Boltzmann Equation. The motivation behind Part 1 is laser fusion where energy transport is by electrons but the temperature gradients are so large in relation to their mean free paths that classical conduction theory breaks down. In this treatment the electron distribution function is found from an appropriate space-dependent Boltzmann Equation and thus physical quantities (in particular heat flux) are calculated for typical parameters from laser fusion. In part 2, an analytic solution of a certain non-linear one-dimensional Boltzmann Equation is obtained which describes the temporal relaxation to equilibrium of a system of particles. Solutions to the corresponding linearised equation and two E.G.K models (with energy-dependent and ''averaged'' collision times) are also derived and compared with that of the non-linear equation. (author)
Joaquim B de Souza Ferreira Filho; Carliton V dos Santos; Sandra M do Prado Lima
2010-01-01
This case study considers two frequently advocated approaches to reducing indirect taxation in Brazil: reduction in taxes on food; reduction in taxes on intermediate inputs to agriculture. To asses the effects of both on income distribution poverty levels, a bottom-up general equilibrium model of Brazil (TERM-BR) is linked to a microsimulation model. It is shown that one of the favoured policies is more poverty reducing, the other more income inequality reducing. Perhaps even more importantly...
Equilibrium distribution of samarium and europium between fluoride salt melts and liquid bismuth
Zagnit'ko, A. V.; Ignat'ev, V. V.
2016-01-01
The extraction of samarium and europium from a melt of a molar composition 73LiF-27BeF2 into liquid bismuth with additions of lithium as a reducing agent at a temperature of 600-610°C was studied. The equilibrium distribution coefficients of samarium and europium were measured. In the metal fluoride salt melt under study, the valence of samarium and europium was shown to be equal to two.
Relaxation to equilibrium and the spacing distribution of zeros of the Riemann ζ function
Pimpinelli, Alberto
2007-06-01
A novel approach is proposed to the distribution of spacings between zeros of the Riemann zeta function. Starting from the observation that the spacing distribution for zeros near the real axis is sharper than the asymptotic distribution, and that all computed moments grow monotonically as zeros are computed farther and farther away from image(z) = 0, an analogy with relaxation to equilibrium in a statistical system is drawn. Namely, it is conjectured that the spacing distribution evolves in a fictitious time t=\\sqrt{\\log_{10} T} , where T is the zeros' imaginary part, in the same way as the eigenvalues of a random matrix with mixed GUE and GSE symmetries. The time evolution restores asymptotically (at T → ∞) the GUE symmetry. Dyson's Brownian motion model for the eigenvalues of a random matrix is used for describing the time evolution, and an approximate, analytic description of the spacing distribution is conjectured, valid to first order in exp(-t).
Relaxation to equilibrium and the spacing distribution of zeros of the Riemann ζ function
International Nuclear Information System (INIS)
A novel approach is proposed to the distribution of spacings between zeros of the Riemann zeta function. Starting from the observation that the spacing distribution for zeros near the real axis is sharper than the asymptotic distribution, and that all computed moments grow monotonically as zeros are computed farther and farther away from J(z) = 0, an analogy with relaxation to equilibrium in a statistical system is drawn. Namely, it is conjectured that the spacing distribution evolves in a fictitious time √(log10T), where T is the zeros' imaginary part, in the same way as the eigenvalues of a random matrix with mixed GUE and GSE symmetries. The time evolution restores asymptotically (at T → ∞) the GUE symmetry. Dyson's Brownian motion model for the eigenvalues of a random matrix is used for describing the time evolution, and an approximate, analytic description of the spacing distribution is conjectured, valid to first order in exp(-t)
Boltzmann's Concept of Reality
Ribeiro, Marcelo B.; Videira, Antonio A. P.
2007-01-01
In this article we describe and analyze the concept of reality developed by the Austrian theoretical physicist Ludwig Boltzmann. It is our thesis that Boltzmann was fully aware that reality could, and actually was, described by different points of view. In spite of this, Boltzmann did not renounce the idea that reality is real. We also discuss his main motivations to be strongly involved with philosophy of science, as well as further developments made by Boltzmann himself of his main philosop...
Zagnit'ko, A. V.; Ignat'ev, V. V.
2013-04-01
The distribution of lanthanum, neodymium, and thorium between a lithium chloride melt and liquid bismuth with additions of lithium as a reducing agent are investigated at 650°C. Equilibrium values of their distribution constants are measured. It is shown that in contrast to neodymium and lanthanum, thorium cannot be extracted from bismuth into lithium chloride. This allows us to propose an efficient scheme for separating lanthanides and thorium in a system for the extraction of fuel salts in molten-salt nuclear reactors.
Equilibrium charge-state distributions of highly stripped ions in carbon foils
International Nuclear Information System (INIS)
Asymmetric equilibrium charge-state distributions observed for heavy ions (Z approx. >= 7) in carbon foils at high velocities (v > 3.6 x 108 Z0sup(.)45 cm s-1) are closely approximated by a simple statistical distribution: the reduced chi-squared model. The dependences of the mean charge and of the standard deviation of the charge on the projectile velocity are obtained by a previously-known and a newly-proposed relation, respectively. Finally charge-state fractions may be easily predicted using a simple formula depending only on the atomic number and on the velocity of the projectile. (orig.)
Park, S H; Ahn, J K; Kim, E S
2004-01-01
We investigate the effects of a localized constant wake and a localized linear wake on the longitudinal beam distribution in equilibrium. We also examine the effects of the composite wake on the particle distribution when the constant wake and linear wake simultaneously exist in the ring. While moving around the parameter space, the system can show bifurcation phenomena and transition features between periodic states. We study the dynamical states in a beam, using the multi-particle tracking method in a Gaussian approximation. They show good qualitative agreement.
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...
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.
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.
Di Troia, C.
2015-11-01
A class of parametric distribution functions was proposed in (Di Troia 2012 Plasma Phys. Control. Fusion 54 105017) as equilibrium distribution functions (EDFs) for charged particles in fusion plasmas, representing supra-thermal particles in anisotropic equilibria for Neutral Beam Injection and Ion Cyclotron Heating scenarios. Moreover, those EDFs can be used to represent also nearly isotropic equilibria for Slowing-Down alpha particles and core thermal plasma populations. Such EDFs depend on constants of motion (COMs). In axisymmetric system with no equilibrium electric field, they depend on toroidal canonical momentum {{P}φ} , kinetic energy w and magnetic moment μ. In the present work, the same EDFs are obtained from first principles and general hypothesis. The derivation is probabilistic and makes use of the Bayes’ Theorem. The bayesian argument is used to describe how the plasma is far from the prior probability distribution function (pdf), e.g. Maxwellian, based on the information obtained from magnetic moment and guiding center velocity pdf. Once the general functional form of the EDF has been settled, it is shown how to associate a modified Landau collision operator in the Fokker-Planck equation, to describe the system relaxation towards the proposed EDF.
Diffusion and near-equilibrium distribution of MRI and CT contrast agents in articular cartilage
International Nuclear Information System (INIS)
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 (Oe = 4.0 mm, n = 64) were prepared from fresh bovine patellae. Contrast agent (gadopentetate: Magnevist (registered) , gadodiamide: Omniscan(TM), ioxaglate: Hexabrix(TM) 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.
Diffusion and near-equilibrium distribution of MRI and CT contrast agents in articular cartilage
Energy Technology Data Exchange (ETDEWEB)
Silvast, Tuomo S; Toeyraes, Juha [Department of Clinical Neurophysiology, Kuopio University Hospital, PO Box 1777, 70211 Kuopio (Finland); Kokkonen, Harri T; Jurvelin, Jukka S [Department of Physics, University of Kuopio, PO Box 1627, 70211 Kuopio (Finland); Quinn, Thomas M [Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec H3A 2B2 (Canada); Nieminen, Miika T [Department of Diagnostic Radiology, Oulu University Hospital, PO Box 50, 90029, Oulu (Finland)], E-mail: Tuomo.Silvast@uku.fi
2009-11-21
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 (Oe = 4.0 mm, n = 64) were prepared from fresh bovine patellae. Contrast agent (gadopentetate: Magnevist (registered) , gadodiamide: Omniscan(TM), ioxaglate: Hexabrix(TM) 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.
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
2009-11-21
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((R)), 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. PMID:19864699
Fission fragment mass and angular distributions: probes to study non-equilibrium fission
International Nuclear Information System (INIS)
It is found that the experimental observables in non-equilibrium fission are found to crucially depend on the interaction time (sticking time) of the di-nuclear complex with respect to the characteristic relaxation time of various degrees of freedom, before it decays into binary fission like fragments. This interaction time in turn depends on the entrance channel parameters of the colliding nuclei. Recent results on mass-angle correlations and mass distributions in fissile and less fissile systems will be presented. The importance of the sticking time of the dinuclear complex with respect to the equilibration times of various degrees of freedom is emphasized
Equilibrium distribution of the elements in the gas in the Coma cluster
International Nuclear Information System (INIS)
The equations governing the equilibrium distribution of the elements for an isothermal plasma in a gravitational potential well are presented, together with a rapidly converging iterative procedure for determining their solution. These results are applied to the case of the intracluster gas in clusters of galaxies and are shown to have important implications (i) for the recent controversy as to whether or not the iron nuclei ''settle out'' in the cluster core, and (ii) for the interpretation of the size and shape of the distribution of the continuum X-ray emission from clusters. We consider a model for the Coma cluster in which the intracluster gas is in equilibrium and is ''partially processed''; that is, the elements with Z>2 have abundances proportional to their cosmic values, but reduced by a factor of approx.20. We find that this model can account for the angular dependence of the continuum X-ray emission from Coma, as determined by recent Einstein observations, as well as or better than the traditional uniform composition model, although the latter is not ruled out. This suggests that the heavy elements in Coma may have settled in the cluster core and that the iron abundance for this cluster may have been overestimated by nearly an order of magnitude
From the orbit theory to a guiding center parametric equilibrium distribution function
International Nuclear Information System (INIS)
This work proposes a parametric equilibrium distribution function Feq to be applied to the gyrokinetic studies of the finite orbit width behavior of guiding centers representing several species encountered in axisymmetric tokamak plasmas, such as fusion products, thermal bulk and energetic particles from ion cyclotron radiation heating and negative neutral beam injections. Feq can be used to fit experimental profiles and it could provide a useful tool for experimental and numerical data analysis. Moreover, it could help one to develop analytical computations for facilitating data interpretation in the light of theoretical models. This distribution function can be easily implemented in gyrokinetic codes, where it could be used to simulate plasma also in the presence of external heating sources. (paper)
International Nuclear Information System (INIS)
A novel method to obtain a shaped neutron energy spectrum for accelerator-based neutron source is presented in this paper. The proposed method modify the monoenergetic proton beam coming from an accelerator to a proton energy distribution, so the produced neutron spectra has the desired energy distribution. The application to a 5 MeV, 50 mA proton beam of the superconductive RFQ of the SPES project at Laboratori Nazionali di Legnaro is investigated for the production of a Maxwell-Boltzmann neutron spectrum at kT=30keV via the 7Li(p, n)7Be reaction. Concept, solutions, and calculations for a setup consisting of a proton energy shaper and a lithium target are presented. Calculations show that a power density of 3 kW/cm2 can be sustained by the lithium target and a forward-directed neutron flux higher than 1010 n/s at the sample position could be obtained
Relativistic Entropy and Related Boltzmann Kinetics
Kaniadakis, G
2009-01-01
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitely remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle, suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativ...
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.
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
Molnár, Etele; Niemi, Harri; Rischke, Dirk H.
2016-06-01
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function, f^0 k, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from f^0 k. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.
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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.
International Nuclear Information System (INIS)
Many policies to limit greenhouse gas emissions have at their core efforts to put a price on carbon emissions. Carbon pricing impacts households both by raising the cost of carbon intensive products and by changing factor prices. A complete analysis requires taking both effects into account. The impact of carbon pricing is determined by heterogeneity in household spending patterns across income groups as well as heterogeneity in factor income patterns across income groups. It is also affected by precise formulation of the policy (how is the revenue from carbon pricing distributed) as well as the treatment of other government policies (e.g. the treatment of transfer payments). What is often neglected in analyses of policy is the heterogeneity of impacts across households even within income or regional groups. In this paper, we incorporate 15,588 households from the U.S. Consumer and Expenditure Survey data as individual agents in a comparative-static general equilibrium framework. These households are represented within the MIT USREP model, a detailed general equilibrium model of the U.S. economy. In particular, we categorize households by full household income (factor income as well as transfer income) and apply various measures of lifetime income to distinguish households that are temporarily low-income (e.g., retired households drawing down their financial assets) from permanently low-income households. We also provide detailed within-group distributional measures of burden impacts from various policy scenarios. - Highlights: → We develop a simulation model with 15,588 households to study the distributional impacts of carbon pricing in the US. → Sources side impacts have typically been ignored in the literature biasing studies towards finding carbon pricing to be regressive. → Our general equilibrium framework allows us to capture uses and sources side impacts from carbon pricing. → We find that variation in impacts within broad socioeconomic groups may
Modeling of Eddy current distribution and equilibrium reconstruction in the SST-1 Tokamak
International Nuclear Information System (INIS)
Toroidal continuity of the vacuum vessel and the cryostat leads to the generation of large eddy currents in these passive structures during the Ohmic phase of the steady state superconducting tokamak SST-1. This reduces the magnitude of the loop voltage seen by the plasma as also delays its buildup. During the ramping down of the Ohmic transformer current (OT), the resultant eddy currents flowing in the passive conductors play a crucial role in governing the plasma equilibrium. Amount of this eddy current and its distribution has to be accurately determined such that this can be fed to the equilibrium reconstruction code as an input. For the accurate inclusion of the effect of eddy currents in the reconstruction, the toroidally continuous conducting structures like the vacuum vessel and the cryostat with large poloidal cross-section and any other poloidal field (PF) coil sitting idle on the machine are broken up into a large number of co-axial toroidal current carrying filaments. The inductance matrix for this large set of toroidal current carrying conductors is calculated using the standard Green's function and the induced currents are evaluated for the OT waveform of each plasma discharge. Consistency of this filament model is cross-checked with the 11 in-vessel and 12 out-vessel toroidal flux loop signals in SST-1. Resistances of the filaments are adjusted to reproduce the experimental measurements of these flux loops in pure OT shots and shots with OT and vertical field (BV). Such shots are taken routinely in SST-1 without the fill gas to cross-check the consistency of the filament model. A Grad-Shafranov (GS) equation solver, named as IPREQ, has been developed in IPR to reconstruct the plasma equilibrium through searching for the best-fit current density profile. Ohmic transformer current (OT), vertical field coil current (BV), currents in the passive filaments along with the plasma pressure (p) and current (Ip) profiles are used as inputs to the IPREQ
Equilibrium ion distribution modeling in RF ion traps and guides with regard to Coulomb effects
Energy Technology Data Exchange (ETDEWEB)
Grinfeld, D.E., E-mail: dm.greenfield@yahoo.com [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation); Kopaev, I.A. [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation); Makarov, A.A. [Thermo Fisher Scientific, Bremen (Germany); Monastyrskiy, M.A. [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-07-21
Considered is the problem of numerical simulation of the equilibrium ion distributions for ions with different m/z ratios in RF ion traps and guides, in which the ion confinement is due to the averaged RF pseudopotential field and collision cooling. The proposed algorithm takes into account the buffer gas temperature and Coulomb interaction between the particles. The original self-consistent problem for the Poisson equation is reduced to a variational problem for a thermodynamic potential, which is solved numerically basing on the smooth spline approximations and the conjugate gradients method. The algorithm is implemented as a separate program module of the MASIM 3D package and comprehensively tested. Some numerical results are discussed.
Barthes, Laurent; Mallet, Cécile
2010-05-01
Keywords: Rain Drop Size Distribution, Breakup, coalescence, disdrometer The study of the vertical evolution of raindrop size distributions (DSDs) during rainfall, from the freezing level isotherm to ground level, is a key to improving our understanding of the microphysics of rain. In numerous domains such as remote sensing, telecommunications, soil erosion, and the study of the rain's efficiency in 'washing' the atmosphere, the DSD plays an important role. Among the different processes affecting the evolution of DSD, breakup and coalescence are two of the most significant. Models of coalescence and breakup lead to equilibrium of the raindrop size distribution (DSD) after a fall through sufficient vertical height. At equilibrium, the DSD no longer evolves, and its shape is unique whatever the rain rate or LWC. This implies that the DSD is known, to within a multiplication constant. These models based on experimental measurements have been developed over the past 40 years. The Low and List (1982a,b) parameterization (hereinafter LL82) and the Greg M. McFarquhar (2004) model are both based on the same laboratory experiments, which lead to an equilibrium drop size distribution (EDSD) with two or three peaks, and an exponential tail with a slope of approximately Λ=65 cm-1. Numerous measurements using disdrometer collected in different climatic areas: Paris, France (Mars to October 2000), Iowa-City (April to October 2002), and Djougou (Benin June to September 2006) corresponding to 537 hours of rain period have shown that for high rain rates, close to a state of equilibrium, this slope lies between Λ=20 - 22 cm-1. This latter value is corroborated by others measurements found in the literature (Hu & Srivastava, 1995). Hu & Srivastava suggested that the Low and List parameterization may overestimate the effects of the breakup process. This hypothesis is in adequation with recent laboratory experiments (A.P. Barros 2008) in which the authors conclude that the number of
Directory of Open Access Journals (Sweden)
Samir Cury
2005-12-01
Full Text Available This paper presents a Computable General Equilibrium model specified to simulate the policy impacts on income distribution in Brazil, with complex and systemic propagation methods. To capture the distributive impacts, the model adopts a design focused on the separation of production and institutional factors, as labor and households. The model has three blocks: product and factor markets, and a block that handles with income transfers among institutions. The labor market specification incorporates a recent theoretical advance that allows the determination of involuntary unemployment in the equilibrium. The third block specifies the distribution of the value added among production factors and the redistribution of income among agents/institutions. The simulations of a partial economic "closure" show modest welfare reduction for most workers and families. Also, we checked that the homogeneity property of the model holds only with full indexation of all income transfers, which has important implications for the income distribution process modeling.Neste artigo é apresentado um modelo de Equilíbrio Geral Computável especificado para simular os impactos de políticas na distribuição de renda no Brasil. Para capturar os impactos distributivos, fatores de produção e instituições, como trabalho e famílias, são especificados separadamente. O modelo apresenta três blocos: mercados de produtos e fatores, e outro bloco com especificação das transferências de renda entre instituições. A especificação do mercado de trabalho incorpora recente avanço teórico que permite a determinação do desemprego involuntário no equilíbrio. No terceiro bloco, especifica-se a distribuição do valor adicionado entre fatores de produção e a redistribuição de renda entre agentes/instituições. As simulações do fechamento "parcial" da economia mostram pequena redução de bem-estar para a maioria dos trabalhadores e famílias. Verificou-se ainda
Energy distribution and heat transfer mechanisms in atmospheric pressure non-equilibrium plasmas
International Nuclear Information System (INIS)
Energy distribution and heat transfer mechanisms in atmospheric pressure non-equilibrium plasmas were investigated extensively through energy balance analysis, emission spectroscopy of the rotational band of CH (A2Δ→XΠ2), and gas chromatographic analysis. Two plasma sources were examined: methane-fed dielectric barrier discharge (DBD) and atmospheric pressure glow-discharge (APG). The DBD features filamentary microdischarges accompanied by surface discharge along a dielectric barrier. As a result, 60% of the input power was measured as heat transfer to the dielectric electrode, whereas 20% was to the metallic electrode. Consequently, feed gas average temperature was increased only by 20-40 K. On the other hand, rotational temperature of the corresponding emission region exceeded average gas temperature by 100 K. In APG, heat transfer to electrodes was dominated by formation of negative glow regardless of whether the electrode was covered by a dielectric. However, negative glow tended to be thinner and more intense when it formed on a metallic electrode, leading to slightly higher metallic heating. Rotational temperature in APG was close to average gas temperature since APG does not show radial localization of plasma. Energy efficiency for methane decomposition process to produce ethane, ethylene, and hydrogen was about 1% regardless of the plasma source. Energy distribution and heat transfer mechanisms depend strongly on the plasma spatial structure rather than flow fields or feed gas physical properties. (author)
Dyatko, Nikolay; Donkó, Zoltán
2015-08-01
At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This ‘bistability effect’—in which electron-electron (Coulomb) collisions play an essential role—is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms (‘two-term approximation’), (ii) neglecting the Coulomb part of the collision integral for the anisotropic part of the distribution function, (iii) treating Coulomb collisions as binary events, and (iv) truncating the range of the electron-electron interaction beyond a characteristic distance. The particle-based simulation method avoids these approximations: the many-body interactions within the electron gas with a true (un-truncated) Coulomb potential are described by a molecular dynamics algorithm, while the collisions between electrons and the background gas atoms are treated with Monte Carlo simulation. We find a good general agreement between the results of the two techniques, which confirms, to a certain extent, the approximations used in the solution of the Boltzmann equation. The differences observed between the results are believed to originate from these approximations and from the presence of statistical noise in the particle simulations.
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Hahn, M.; Savin, D. W. [Columbia Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY 10027 (United States)
2015-02-10
We describe the influence of electron-impact multiple ionization (EIMI) on the ionization balance of collisionally ionized plasmas. Previous ionization balance calculations have largely neglected EIMI. Here, EIMI cross-section data are incorporated into calculations of both equilibrium and non-equilibrium charge-state distributions (CSDs). For equilibrium CSDs, we find that EIMI has only a small effect and can usually be ignored. However, for non-equilibrium plasmas the influence of EIMI can be important. In particular, we find that for plasmas in which the temperature oscillates there are significant differences in the CSD when including versus neglecting EIMI. These results have implications for modeling and spectroscopy of impulsively heated plasmas, such as nanoflare heating of the solar corona.
Hahn, Michael
2014-01-01
We describe the influence of electron-impact multiple ionization (EIMI) on the ionization balance of collisionally ionized plasmas. We are unaware of any previous ionization balance calculations that have included EIMI, which is usually assumed to be unimportant. Here, we incorporate EIMI cross-section data into calculations of both equilibrium and non-equilibrium charge-state distributions (CSDs). For equilibrium CSDs, we find that EIMI has only a small effect and can usually be ignored. However, for non-equilibrium plasmas the influence of EIMI can be important. In particular, we find that for plasmas in which the temperature oscillates there are significant differences in the CSD when including versus neglecting EIMI. These results have implications for modeling and spectroscopy of impulsively heated plasmas, such as nanoflare heating of the solar corona.
The statistical distribution of money and the rate of money transference
Ferrero, Juan C.
2003-01-01
The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma function, confirming the validity of the statistical distribution at equilibrium. The equilibrium state is reached through pair wise money transference processes, independently of the shape of the initial distribution and also of the detailed nature of the...
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.
Theory for non-equilibrium statistical mechanics.
Attard, Phil
2006-08-21
This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life. PMID:16883388
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.
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.
International Nuclear Information System (INIS)
In this study, the equilibrium crystal shape (ECS) of a model system, strontium titanate, is compared with the grain boundary plane distribution (GBPD) as a function of temperature. Strontium titanate has a pronounced surface energy anisotropy and a grain growth anomaly, with the grain growth rate decreasing by orders of magnitude with increasing temperature. The ECS was determined from the shape of small intragranular pores and the GBPD was determined from orientation measurements on surfaces, with the relative areas of grain boundary planes in a polycrystal correlated to the surface energy of both adjacent crystal planes. The grain boundary energy has been previously proposed to be the sum of the surface energy of the adjacent grains less a binding energy that is assumed to be constant. While much experimental evidence exists for this assumption at a fixed temperature, the influence of temperature is not known. While the anisotropy of the ECS was found to decrease with temperature, the anisotropy of the GBPD increased with temperature. These findings indicate that changes in the binding energy with temperature must be considered, as the binding energy links the surface energy to the grain boundary energy. The results are discussed with respect to the grain growth anomaly of strontium titanate, in which the grain growth decreases with increasing temperature
Energy Technology Data Exchange (ETDEWEB)
Delmau, L.H.
2002-06-13
An extension of the model developed in FY01 for predicting equilibrium distribution ratios in the Caustic-Side Solvent Extraction (CSSX) process is presented here. Motivation for extending the model arose from the need to predict extraction performance of the recently optimized solvent composition and the desire to include additional waste components. This model involves the extraction of cesium and potassium from different cesium, potassium, and sodium media over a large range of concentrations. Those different media include a large variety of anions such as nitrate, hydroxide, nitrite, chloride, fluoride, sulfate, and carbonate. The model was defined based on several hundreds of experimental data points and predicted satisfactorily the cesium extraction from five different SRS waste simulants. This process model encompassed almost exclusively 1:1:1 metal:anion:ligand species. Fluoride, sulfate, and carbonate species were found to be very little extractable, and their main impact is reflected through their activity effects. This model gave a very good cesium and potassium extraction prediction from sodium salts, which is what is needed when trying to predict the behavior from actual waste. However, the extraction from potassium or cesium salts, and the extraction of sodium could be improved, and some additional effort was devoted to improve the thermodynamic rigor of the model. Toward this end, more detailed anion-specific models were developed based on the cesium, potassium, and sodium distribution ratios obtained with simple systems containing single anions, but it has not yet proven possible to combine those models to obtain better predictions than provided by the process model.
Boltzmann-Gaussian transition under specific noise effect
International Nuclear Information System (INIS)
It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.
Gauss Quadratures - the Keystone of Lattice Boltzmann Models
Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor
2014-01-01
In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics
Ahmad, Mushfiq; Talukder, Muhammad O. G.
2007-01-01
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The solutions of this equation come in Boson-Fermion pairs. Reciprocal symmetric Boltzmann's function, thus, unifies both Bosonic and Fermionic distributions.
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
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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.
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.
Fabien Postel-Vinay; Jean-Marc Robin
2002-01-01
We construct an equilibrium job search model with on-the-job search in which firms implement optimal-wage strategies under full information in the sense that they leave no rent to their employees and counter the offers received by their employees from competing firms. Productivity dispersion across firms results in wage mobility both within and across firms. Workers may accept wage cuts to move to firms offering higher future wage prospects. Equilibrium productivity dispersion across ex ante ...
Ludwig Boltzmann: Atomic genius
International Nuclear Information System (INIS)
On the centenary of the death of Ludwig Boltzmann, Carlo Cercignani examines the immense contributions of the man who pioneered our understanding of the atomic nature of matter. The man who first gave a convincing explanation of the irreversibility of the macroscopic world and the symmetry of the laws of physics was the Austrian physicist Ludwig Boltzmann, who tragically committed suicide 100 years ago this month. One of the key figures in the development of the atomic theory of matter, Boltzmann's fame will be forever linked to two fundamental contributions to science. The first was his interpretation of 'entropy' as a mathematically well-defined measure of the disorder of atoms. The second was his derivation of what is now known as the Boltzmann equation, which describes the statistical properties of a gas as made up of molecules. The equation, which described for the first time how a probability can evolve with time, allowed Boltzmann to explain why macroscopic phenomena are irreversible. The key point is that while microscopic objects like atoms can behave reversibly, we never see broken coffee cups reforming because it would involve a long series of highly improbable interactions - and not because it is forbidden by the laws of physics. (U.K.)
Equilibrium fluctuation theorems compatible with anomalous response
Velazquez, L.; Curilef, S.
2010-12-01
Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations C = β2langδU2rang, which is able to describe the existence of macrostates with negative heat capacities C < 0. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the fundamental and the complementary fluctuation theorems, which represent the generalization of two fluctuation identities already obtained in previous works, and the associated fluctuation theorem, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of the 2D Ising model.
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.
Boltzmann-Electron Model in Aleph.
Energy Technology Data Exchange (ETDEWEB)
Hughes, Thomas Patrick; Hooper, Russell
2014-11-01
We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical %22grid instability%22 that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model
William B Monahan; Tingley, Morgan W.
2012-01-01
The ability of species to respond to novel future climates is determined in part by their physiological capacity to tolerate climate change and the degree to which they have reached and continue to maintain distributional equilibrium with the environment. While broad-scale correlative climatic measurements of a species' niche are often described as estimating the fundamental niche, it is unclear how well these occupied portions actually approximate the fundamental niche per se, versus the fun...
International Nuclear Information System (INIS)
Communications between the equilibrium distribution coefficients of impurities KA0limB in some elements of the IV-VI group in periodic table and the Rb parameters, containing energies of ionization, charge numbers of atoms and other data are considered. It is shown, that the use of the Rb parameters allows to define the values KA0limB for many impurities in the metals solvents W, V, Zr by known expressions, but without introduction of melting of elements
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...
Transition state theory: a generalization to nonequilibrium systems with power-law distributions
Du, Jiulin
2011-01-01
Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the Langevin equations and corresponding Fokker-Planck equations. It is assumed that the system far away from equilibrium has not to relax to a thermal equilibrium state with Boltzmann-Gibbs distribution, but asymptotically approaches to a nonequilibrium stationary-...
Institute of Scientific and Technical Information of China (English)
张红; 张继彦; 杨向东; 杨国洪; 郑志坚
2003-01-01
A collisional radiative model based on the spin-orbit-split-arrays is used to determine the charge state distribution of gold plasmas. The ab initio atomic structure code of Cowan and the spin-orbit-split-array model were used to calculate all the emission spectra of the different gold species, and a non-local thermodynamic-equilibrium model was coupled to calculate the ion populations at a given plasma density and electron temperature. The charge state distribution and other plasma parameters were determined by comparing the experimental spectra with the theoretical simulated spectra of gold plasmas.
Louis-Martinez, Domingo J.
2010-01-01
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions fo...
Wiegel, Frederik W.; Perelson, Alan S.
1982-01-01
When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting ofn cells and havingm branch points; (2) the average number of cells per rouleau; (3) the average number ...
Variably saturated flow described with the anisotropic Lattice Boltzmann methods
Ginzburg, I.
2006-01-01
This paper addresses the numerical solution of highly nonlinear parabolic equations with Lattice Boltzmann techniques. They are first developed for generic advection and anisotropic dispersion equations (AADE). Collision configurations handle the anisotropic diffusion forms by using either anisotropic eigenvalue sets or anisotropic equilibrium functions. The coordinate transformation from the orthorhombic (rectangular) discretization grid to the cuboid computational grid is equivalen...
Second-order Boltzmann equation: gauge dependence and gauge invariance
International Nuclear Information System (INIS)
In the context of cosmological perturbation theory, we derive the second-order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: (i) the polarization of light is incorporated in this formalism by using a tensor-valued distribution function; (ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; (iii) we perform a separation between temperature and spectral distortion, both for the intensity and polarization for the first time; (iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gauge dependence for the observed temperature. (paper)
Second order Boltzmann equation : gauge dependence and gauge invariance
Naruko, Atsushi; Koyama, Kazuya; Sasaki, Misao
2013-01-01
In the context of cosmological perturbation theory, we derive the second order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: i) the polarisation of light is incorporated in this formalism by using a tensor-valued distribution function; ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; iii) we perform a separation between temperature and spectral distortion, both for the intensity and for polarisation for the first time; iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gaug...
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.
Collisional equilibrium, particle production and the inflationary universe
Zimdahl, W; Pavón, D; Zimdahl, Winfried; Triginer, Josep; Pavon, Diego
1996-01-01
Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the backreaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.
Classical non-Markovian Boltzmann equation
Energy Technology Data Exchange (ETDEWEB)
Alexanian, Moorad, E-mail: alexanian@uncw.edu [Department of Physics and Physical Oceanography, University of North Carolina Wilmington, Wilmington, North Carolina 28403-5606 (United States)
2014-08-01
The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
International Nuclear Information System (INIS)
We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses
Boltzmann map for quantum oscillators
International Nuclear Information System (INIS)
The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega1, omega2, and omega3 mutually irrational, but obeying a relation n1omega1 + n2omega2 = n3omega3, n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) β1, β2, β3 obeying the equation n1omega1β1 + n2omega3β1number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case
Fermion particle production in semiclassical Boltzmann-Vlasov transport theory
International Nuclear Information System (INIS)
We present numerical solutions of the semiclassical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and antiquarks on a second Casimir invariant of color SU(3).
Monthus, Cecile
2010-01-01
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy associated to the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to generalized Gibbs distribution for the pro...
Equilibrium distributions and relaxation times in gaslike economic models: an analytical derivation.
Calbet, Xavier; López, José-Luis; López-Ruiz, Ricardo
2011-03-01
A step-by-step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDFs) of well-known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into the evolution of the PDF, for example, allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others. This should provide some guidance into the type of PDFs that can be derived from particular economic agent exchange rules or, for that matter, any other kinetic model of gases with particular collision physics. PMID:21517559
Wiegel, Frederik W.; Perelson, Alan S.
1982-12-01
When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting of n cells and having m branch points; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux with n cells in a system containing a total of N cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.
Energy Technology Data Exchange (ETDEWEB)
Wiegel, F.W.; Perelson, A.S.
1982-12-01
When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting of n cells and having m branch points: (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux with n cells in a system containing a total of N cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.
International Nuclear Information System (INIS)
In this Letter, a three-dimensional (3D) lattice-Boltzmann model is presented following the non-free-parameter lattice-Boltzmann method of Qu et al. [K. Qu, C. Shu, Y.T. Chew, Phys. Rev. E 75 (2007) 036706]. A simple function, which satisfies the zeroth- through third-order moments of the Maxwellian distribution function, is introduced to replace the Maxwellian distribution function as the continuous equilibrium distribution function in 3D space. The function is then discretized to discrete-velocity directions via a 25-point Lagrangian interpolation polynomial. To simulate compressible flows with shock waves, an implicit-explicit finite-difference scheme based on the total variation diminishing flux limitation is adopted to solve the discrete Boltzmann-BGK equation in order to capture the shock waves in compressible flows with a finite number of grid points. The model is validated by its application to some typical inviscid compressible flows ranging from 1D to 3D, and the numerical results are found to be in excellent agreement with the analytical solutions and/or other numerical results.
"Equilibrium" states of non equilibrium system
Lev, Bohdan
2008-01-01
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution which can be interpreted as the equilibrium distribution function for new energetic state. The proposed approach takes into account the possible motion between different states of system, induced by dissipation of energy and influence of environment which d...
Spherical Harmonic Expansion Method for Coupled Electron-Phonon Boltzmann Transport
Santia, Marco; Albrecht, John
2014-03-01
Thermoelectric transport modeling often relies on independent Boltzmann transport equations (BTEs) for electrons and phonons which work best near equilibrium (linearized) and steady-state. Device design relies heavily on this baseline approximation. Monte Carlo methods can allow for complex physical interactions (e.g., anharmonicity) but their stochastic nature has practical limits. Distribution functions with wide disparities in population (e.g., ratios >108 between majority and minority carriers.[1]) are a computational challenge. We present a coupled BTE solver based on a k-space spherical harmonic expansion (SHE) of the distribution functions and eigenstates of electrons and phonons. The method is deterministic and allows for detailed treatments of scattering processes, yet ameliorates the issues with population disparity within phase space. We set the formalism and examine the accuracy of the SHE for phonon band structures, calculate scattering rates determined within that representation, and compare our preliminary results for distribution statistics in control examples such as thermal conductivity and drift velocity.
The length distribution of vortex strings in U(1) equilibrium scalar field theory
Antunes, Nuno D.; Bettencourt, Luís M. A.
1998-01-01
We characterize the statistical length distribution of vortex strings by studying the non-perturbative thermodynamics of scalar U(1) field theory in 3D. All parameters characterizing the length distributions exhibit critical behavior at $T_c$ and we measure their associated critical exponents. Moreover we show that vortex strings are generally self-seeking at finite temperature and that there exists a natural separation between long strings and small loops based on their spatial correlation b...
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
Molnar, E; Rischke, D H
2016-01-01
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. To zeroth order this expansion yields ideal fluid dynamics, to first order Navier-Stokes theory, and to second order transient theories of dissipative fluid dynamics. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, so-called anisotropic fluid dynamics, in terms of an expansion around a single-particle distribution function which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. In this paper we derive, up to terms of second order in this expansion, the equations of mo...
Lattice Boltzmann approaches to magnetohydrodynamics and electromagnetism
Dellar, Paul
2010-03-01
J u B E g We present a lattice Boltzmann approach for magnetohydrodynamics and electromagnetism that expresses the magnetic field using a discrete set of vector distribution functions i. The i were first postulated to evolve according to a vector Boltzmann equation of the form ti+ ξi.∇i= - 1τ ( i- i^(0) ), where the ξi are a discrete set of velocities. The right hand side relaxes the i towards some specified functions i^(0) of the fluid velocity , and of the macroscopic magnetic field given by = ∑ii. Slowly varying solutions obey the equations of resistive magnetohydrodynamics. This lattice Boltzmann formulation has been used in large-scale (up to 1800^3 resolution) simulations of magnetohydrodynamic turbulence. However, this is only the simplest form of Ohm's law. We may simulate more realistic extended forms of Ohm's law using more complex collision operators. A current-dependent relaxation time yields a current-dependent resistivity η(|∇x|), as used to model ``anomalous'' resistivity created by small-scale plasma processes. Using a hydrodynamic matrix collision operator that depends upon the magnetic field , we may simulate Braginskii's magnetohydrodynamics, in which the viscosity for strains parallel to the magnetic field lines is much larger than the viscosity for strains in perpendicular directions. Changing the collision operator again, from the above vector Boltzmann equation we may derive the full set of Maxwell's equations, including the displacement current, and Ohm's law, - 1c^2 tE+ ∇x= μo,= σ( E + x). The original lattice Boltzmann scheme was designed to reproduce resistive magnetohydrodynamics in the non-relativistic limit. However, the kinetic formulation requires a system of first order partial differential equations with collision terms. This system coincides with the full set of Maxwell's equations and Ohm's law, so we capture a much wider range of electromagnetic phenomena, including electromagnetic waves.
International Nuclear Information System (INIS)
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 deg. C. 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.
International Nuclear Information System (INIS)
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 C. 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.
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.
Privacy-Preserving Restricted Boltzmann Machine
Yu Li; Yuan Zhang; Yue Ji
2014-01-01
With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provi...
The Milne problem for the Boltzmann equation
International Nuclear Information System (INIS)
Existence, uniqueness and asymptotic properties are proved for the solution of the Milne problem for the Boltzmann equation, in which the incoming velocity distribution and the total mass flux are specified arbitrarily. The collision law corresponds to a hard sphere gas. The solution uses energy estimates and is similar to that of Bardos, Santos and Sentis for neutron transport. From the Milne problem one can then easily deduce the solution of the Kramers problem
Relativistic Rotating Boltzmann Gas Using the Tetrad Formalism
Directory of Open Access Journals (Sweden)
Ambrus Victor E.
2015-12-01
Full Text Available We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to rel- ativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle ow four-vector and of the equilibrium stress-energy tensor.
Thermal equilibrium of non-neutral plasma in dipole magnetic field
Energy Technology Data Exchange (ETDEWEB)
Sato, N.; Kasaoka, N.; Yoshida, Z. [Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8561 (Japan)
2015-04-15
Self-organization of a long-lived structure is one of the remarkable characteristics of macroscopic systems governed by long-range interactions. In a homogeneous magnetic field, a non-neutral plasma creates a “thermal equilibrium,” which is a Boltzmann distribution on a rigidly rotating frame. Here, we study how a non-neutral plasma self-organizes in inhomogeneous magnetic field; as a typical system, we consider a dipole magnetic field. In this generalized setting, the plasma exhibits its fundamental mechanism that determines the relaxed state. The scale hierarchy of adiabatic invariants is the determinant; the Boltzmann distribution under the topological constraint by the robust adiabatic invariants (hence, the homogeneous distribution with respect to the fragile invariant) is the relevant relaxed state, which turns out to be a rigidly rotating clump of particles (just same as in a homogeneous magnetic field), while the density is no longer homogeneous.
The temperature and size distribution of large water clusters from a non-equilibrium model
International Nuclear Information System (INIS)
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 (H2O)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
Haubold, H J; Saxena, R K
2004-01-01
Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intense investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technology 2003'to Professor Constantino Tsallis from the Brazilian Center for Research in Physics.
Generalizing the Boltzmann equation in complex phase space.
Zadehgol, Abed
2016-08-01
In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)JCTPAH0021-999110.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015)PLEEE81539-375510.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others. PMID:27627421
Garrett, T. J.; Alva, S.; Glenn, I. B.; Krueger, S. K.
2015-12-01
There are two possible approaches for parameterizing sub-grid cloud dynamics in a coarser grid model. The most common is to use a fine scale model to explicitly resolve the mechanistic details of clouds to the best extent possible, and then to parameterize these behaviors cloud state for the coarser grid. A second is to invoke physical intuition and some very general theoretical principles from equilibrium statistical mechanics. This approach avoids any requirement to resolve time-dependent processes in order to arrive at a suitable solution. The second approach is widely used elsewhere in the atmospheric sciences: for example the Planck function for blackbody radiation is derived this way, where no mention is made of the complexities of modeling a large ensemble of time-dependent radiation-dipole interactions in order to obtain the "grid-scale" spectrum of thermal emission by the blackbody as a whole. We find that this statistical approach may be equally suitable for modeling convective clouds. Specifically, we make the physical argument that the dissipation of buoyant energy in convective clouds is done through mixing across a cloud perimeter. From thermodynamic reasoning, one might then anticipate that vertically stacked isentropic surfaces are characterized by a power law dlnN/dlnP = -1, where N(P) is the number clouds of perimeter P. In a Giga-LES simulation of convective clouds within a 100 km square domain we find that such a power law does appear to characterize simulated cloud perimeters along isentropes, provided a sufficient cloudy sample. The suggestion is that it may be possible to parameterize certain important aspects of cloud state without appealing to computationally expensive dynamic simulations.
Boyer, Timothy H.
2010-01-01
The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski space...
The Boltzmann equation theory of charged particle transport
International Nuclear Information System (INIS)
It is shown how a formally exact Kubo-like response theory equivalent to the Boltzmann equation theory of charged particle transport can be constructed. The response theory gives the general wavevector and time-dependent velocity distribution at any time in terms of an initial distribution function, to which is added the response induced by a generalized perturbation over the intervening time. The usual Kubo linear response result for the distribution function is recovered by choosing the initial velocity distribution to be Maxwellian. For completeness the response theory introduces an exponential convergence function into the response time integral. This is equivalent to using a modified Boltzmann equation but the general form of the transport theory is not changed. The modified transport theory can be used to advantage where possible convergence difficulties occur in numerical solutions of the Boltzmann equation. This paper gives a systematic development of the modified transport theory and shows how the response theory fits into the broader scheme of solving the Boltzmann equation. The discussion extends both the work of Kumar et al. (1980), where the distribution function is expanded out in terms of tensor functions, and the propagator description where the non-hydrodynamic time development of the distribution function is related to the wavevector dependent Green function of the Boltzmann equation
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.
Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces
Lee, Deok-Sun
2005-01-01
We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $ \\sim \\sqrt{2/(\\pi K)} \\ln N$ and the asymptotic behavior of the whole distribution $P(m) \\sim N^2 e^{-{\\rm (const)} N^2 e^{-\\sqrt{2\\pi K} m} - \\sqrt{2\\pi K} m}$ for $m$ finite with $N^2$ and $K$ the interface size and tension, respectively. The standardized form o...
International Nuclear Information System (INIS)
On the basis of the proposed numerical procedure the solution of the nonlinear Boltzmann-Poisson equation for bounded plasma in the presence of strong external electric field is obtained. The numerical analysis of the electric field, potential, and equilibrium profiles of charged particles distributions in the plasma half-space is performed in detail. 6 refs.; 8 figs. (author)
Inhomogeneous similarity solutions of the Boltzmann equation with confining external forces
International Nuclear Information System (INIS)
The Nikolskii transform makes it possible to construct inhomogeneous solutions of the Boltzmann equation from homogeneous ones. These solutions correspond to a gas in expansion, but if the authors introduce external forces, they can relax toward absolute Maxwellians. This property holds independently of the assumed intermolecular inverse power force. Consequently, for Maxwell molecules and from energy-dependent homogeneous distributions, they construct effectively a class of inhomogeneous similarity distributions with Maxwellian equilibrium relaxation. They review and investigate again the homogeneous distributions which can be written in closed form, for instance, they show that an elliptic exact solution proposed some years ago violates positivity. For Maxwell interaction with singular cross sections, they numerically construct inhomogeneous distributions having Maxwellian equilibrium states and study the Tjon overshoot effect. They show that both the sign and the time decrease of the external force as well as the microscopic model of the cross section contribute to the asymptotic behavior of the distribution. These inhomogeneous similarity solutions include a class of distributions that asymptotically oscillate between different Maxwellians. Two classes of external forces are considered: linear spatial-dependent forces or linear velocity-dependent forces plus source term
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.)
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.
International Nuclear Information System (INIS)
This study focuses on the relative distribution among urban and rural household income classes on the economic impacts of two water-related policies in the Columbia River Basin in the northwestern US. The two policies involve: (1) strategies to improve downstream anadromous fish migrations currently hindered by hydropower operations; and (2) proposals to transfer water from irrigation to hydropower generation. A regional input-output model traces the economic effects of the initial demand and price changes through the entire region. The model incorporates price changes in both a short-run (all endogenous prices are fixed) and a longer-run framework based on a Cobb-Douglas representation (all prices can vary). The analysis suggests that the construction of facilities to enhance fish migration and the physical transport of fish have opposite relative effects. The former benefits rural households, while the latter benefits urban households. Electricity price increases resulting from altered hydropower operations harm middle-income rural households, in the short-run. In the longer-run, electricity price increases seem to favor relatively all rural households. Changes associated with the water transfer policy also include electricity price alterations, as well as price and demand changes for agricultural products. Rural households benefit relative to urban households from agricultural product final demand increases, and tend to lose relatively with agricultural price and demand decreases. The inclusion of secondary impacts allows decision makers to asses the income effects of a project across a wider segment of the population, while the incorporation of short-and longer-run economic frameworks allows policy makers to assess both immediate and future income changes
Jacxsens, L; Devlieghere, F; Debevere, J
2002-03-01
The impact of temperature fluctuations in a simulated cold distribution chain, typical of commercial practice, was investigated on both the microbial and sensorial quality of equilibrium modified atmosphere (EMA) packaged minimally processed vegetables. The internal O2 concentration of the designed packages could be predicted for the different steps of the simulated distribution chain by applying an integrated mathematical system. The internal atmosphere in the packages remained in its aerobic range during storage in the chain due to the application of high permeable packaging films for O2 and CO2. Spoilage microorganisms were proliferating fast on minimally processed bell peppers and lettuce. Yeasts showed to be the shelf-life limiting group. Visual properties limited the sensorial shelf-life. Listeria monocytogenes was able to multiply on cucumber slices, survived on minimally processed lettuce and decreased in number on bell peppers due to the combination of low pH and refrigeration. Aeromonas caviae was multiplying on both cucumber slices and mixed lettuce, but was as well inhibited by the low pH of bell peppers. Storage temperature control was found to be of paramount importance for the microbial (spoilage and safety) and sensorial quality evaluation of EMA-packaged minimally processed vegetables. PMID:11934040
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
The Boltzmann-Langevin approach and its application to nuclear multifragmentation
International Nuclear Information System (INIS)
We present the Boltzmann-Langevin approach which provides a description of the strongly out of equilibrium dynamics encountered in the course of violent heavy-ion collisions. After having introduced the Boltzmann-Langevin model we present some applications to a situation where fluctuations are expected to play an important role: the production of Intermediate Mass Fragments in heavy-ion collisions at beam energies of a few tens of MeV/u. (authors)
Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics
de Soria, M. I. Garcia; Maynar, P.; Schehr, G.; Barrat, A.; Trizac, E.
2008-01-01
We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\\em ballistic annihilation} therefore constantly looses particles. The dynamics of perturbations around the free decay regime is investigated from the spectral properties of the linearized Boltzmann operator, that characterize linear excitations on all time scales. The linearized Boltzma...
Ling, G N; Niu, Z; Ochsenfeld, M
1993-01-01
We determined the equilibrium distribution of twenty-one nonmetabolized nonelectrolytes in frog muscle cells. In all cases, plots of the equilibrium intracellular concentrations of a solute in the cell water against the external concentrations of the solute yielded straight lines in agreement with the prediction of such a rectilinear plot by the polarized multilayer (PM) theory. The slopes of these straight lines yield the equilibrium distribution coefficients or q-value of that solute. It was shown that, again in agreement with the PM theory, the q-values of fourteen nonelectrolytes vary with the molecular volumes of the nonelectrolytes, obeying the "size rule", i.e., the larger the solute, the lower its q-value. The q-values of the remaining seven nonelectrolytes also decrease with their molecular volumes but on a separate curve. These q-value vs. molecular volume plots (q-v plots) show strong resemblance to similar q-v plots of solutes in dialysis sacs containing proteins and polymers assuming the fully-extended conformation (extrovert models) but no, or only weak, resemblance to q-v plots of solutions containing native globular proteins (introvert models). These findings also support the PM theory, according to which some protein(s) pervasively present in cells are in the fully-extended conformation; and that these fully extended cell protein(s) polarize(s) in multilayers all or virtually all cell water. The relationship between the q-values of the nonelectrolytes and the solutes' respective molecular volume are described by two sets of theoretical curves, calculated from an equation introduced in the preceding paper. Both curves were computed on the basis of the same exclusion intensity (Uvp = 126 cal/mole). This factor measures the extra water-to-water interaction of the polarized water which acts to keep solute out of the cell water in degree according to the size of the solute. The two curves are computed on the basis of two different values of U(s), which
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-06-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.
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...
Observation of a Persistent Non-Equilibrium State in an Extremely Isotropic Harmonic Potential
Lobser, D. S.
Ludwig Boltzmann made tremendously important contributions to the problem of con- necting macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end of the nineteenth century, Boltzmann was confronted with various strong objections to his work. For example, Boltzmann's atomistic explanations presuppose the reality of atoms, a notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique by Loschmidt that Boltzmann's H-theorem, put forth as a microscopic explanation for the Second Law of Thermodynamics, could hardly account for irreversible physics when the individual two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence of special cases of the Boltzmann equation in which time-varying distributions of atoms re- sist the imperative of equilibration, even in the presence of collisions. Boltzmann discussed such situations in a paper dedicated to responding to Loschmidt's critique [7, 4]. Perhaps Boltzmann's motivation was to enumerate special cases where his famous H value does not relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality. Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is an all-but universal result predicted by the Boltzmann equation. Such improbable systems of atoms have only very recently been realized experimentally. Kinoshita et al. [36] experimentally confirmed that atoms constrained to move in a quasi one-dimensional potential, an atomistic Newtons cradle, exhibit vastly suppressed relaxation. Chevy et al. [15] observed long-lived breathe-mode oscillations in highly elongated but still 3D geometries. Perhaps one of the more interesting cases is the vanishing damping of the monopole breathe-mode oscillation in a spherically symmetric harmonic oscillator [29], where a cloud of atoms experiences undamped temperature oscillations, causing the cloud to expand and contract as if it
Application of the concept of local equilibrium to solve the Fokker-Planck equation
International Nuclear Information System (INIS)
A method for speeding up the classical Monte Carlo method is presented. The proposed method is based on the observation that the Boltzmann transition probability and the concept of local thermodynamic equilibrium give rise to an initial state of maximum entropy. This state can be modified by using internal structural information of the system. In classical thermodynamic models, internal structures of systems are not taken into account. It is proposed to use the Dempster-Shafer theory. Starting from local thermodynamic equilibrium (local symmetry), the proposed algorithm computes the new distribution over subsystems, resulting in a non-uniform distribution and in symmetry breaking. For the more general case, an initial local distribution that is induced by different symmetries can be assumed. From this, the global distribution which breaks the local symmetry can be calculated
Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation
Jaiswal, Amaresh; Redlich, Krzysztof
2016-01-01
We consider a momentum dependent relaxation time for the Boltzmann equation in the relaxation time approximation. We employ a power law parametrization for the momentum dependence of the relaxation time, and calculate the shear and bulk viscosity, as well as, the charge and heat conductivity. We show, that for the two popular parametrizations, referred to as the linear and quadratic ansatz, one can obtain transport coefficients which corresponds to the weak and strong coupling regimes, respectively. We also show that, for a system of massless particles with vanishing chemical potential, the off-equilibrium corrections to the phase-space distribution function calculated with the quadratic ansatz are identical with those of the Grad's 14-moment method.
International Nuclear Information System (INIS)
As a part of the advanced subchannel code development project sponsored by Ministry of Economy, Trade and Industry, Japan, this paper describes improvement of the equilibrium void distribution model that is a main part of the vapor-liquid cross flow model. The three-component cross flow (TCCF) model is defined as the present framework that separates contributions of diversion, turbulent mixing and void drift. The Lahey's void settling model is introduced to express the latter two components. Based on the high-resolution air-water database and other published data of steam-water tests, general trends of vapor-liquid cross flow processes are examined. It can be assumed that subchannel void distributions are dominated by the three major effects, i.e. the fluid dynamic effect, the geometrical effect and the narrow gap effect. The equilibrium void distribution model is modified to include the above-mentioned three effects. Three characteristic parameters are assigned for each of the three effects and they are identified experimentally as functions of the void fraction. Multi-dimensional lattice geometries are incorporated based on the two-dimensional flow network model. The network equation is constructed by mapping the equilibrium void balance problem into the force-deflection problem. The resultant models are verified based on equilibrium void distribution data obtained by Sadatomi and Kawahara
Gastis, P; Robertson, D; Almus, R; Anderson, T; Bauder, W; Collon, P; Lu, W; Ostdiek, K; Skulski, M
2015-01-01
Equilibrium charge state distributions of stable 60Ni, 59Co, and 63Cu beams passing through a 1um thick Mo foil were measured at beam energies of 1.84 MeV/u, 2.09 MeV/u, and 2.11 MeV/u respectively. A 1-D position sensitive Parallel Grid Avalanche Counter detector (PGAC) was used at the exit of a spectrograph magnet, enabling us to measure the intensity of several charge states simultaneously. The number of charge states measured for each beam constituted more than 99% of the total equilibrium charge state distribution for that elements. Currently, little experimental data exists for equilibrium charge state distributions for heavy ions with 19
Privacy-Preserving Restricted Boltzmann Machine
Directory of Open Access Journals (Sweden)
Yu Li
2014-01-01
Full Text Available With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM. The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model.
Privacy-preserving restricted boltzmann machine.
Li, Yu; Zhang, Yuan; Ji, Yue
2014-01-01
With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model. PMID:25101139
Application of lattice Boltzmann scheme to nanofluids
Institute of Scientific and Technical Information of China (English)
XUAN; Yimin; LI; Qiang; YAO; Zhengping
2004-01-01
A nanofluid is a particle suspension that consists of base liquids and nanoparticles. Nanofluid has greater potential for heat transfer enhancement than traditional solid-liquid mixture. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles,a lattice Boltzmann model for simulating flow and energy transport processes inside the nanofluids is proposed. The irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids are discussed. The distributions of suspended nanoparticles inside nanofluids are calculated.
Determining Equilibrium Position For Acoustical Levitation
Barmatz, M. B.; Aveni, G.; Putterman, S.; Rudnick, J.
1989-01-01
Equilibrium position and orientation of acoustically-levitated weightless object determined by calibration technique on Earth. From calibration data, possible to calculate equilibrium position and orientation in presence of Earth gravitation. Sample not levitated acoustically during calibration. Technique relies on Boltzmann-Ehrenfest adiabatic-invariance principle. One converts resonant-frequency-shift data into data on normalized acoustical potential energy. Minimum of energy occurs at equilibrium point. From gradients of acoustical potential energy, one calculates acoustical restoring force or torque on objects as function of deviation from equilibrium position or orientation.
International Nuclear Information System (INIS)
This paper describes several interesting excitation phenomena occurring in a microwave-induced plasma (MIP) excited with Okamoto-cavity, especially when a small amount of oxygen was mixed with nitrogen matrix in the composition of the plasma gas. An ion-to-atom ratio of iron, which was estimated from the intensity ratio of ion to atomic lines having almost the same excitation energy, was reduced by adding oxygen gas to the nitrogen MIP, eventually contributing to an enhancement in the emission intensities of the atomic lines. Furthermore, Boltzmann plots for iron atomic lines were observed in a wide range of the excitation energy from 3.4 to 6.9 eV, indicating that plots of the atomic lines having lower excitation energies (3.4 to 4.8 eV) were well fitted on a straight line while those having more than 5.5 eV deviated upwards from the linear relationship. This overpopulation would result from any other excitation process in addition to the thermal excitation that principally determines the Boltzmann distribution. A Penning-type collision with excited species of nitrogen molecules probably explains this additional excitation mechanism, in which the resulting iron ions recombine with captured electrons, followed by cascade de-excitations between closely-spaced excited levels just below the ionization limit. As a result, these high-lying levels might be more populated than the low-lying levels of iron atom. The ionization of iron would be caused less actively in the nitrogen–oxygen plasma than in a pure nitrogen plasma, because excited species of nitrogen molecule, which can provide the ionization energy in a collision with iron atom, are consumed through collisions with oxygen molecules to cause their dissociation. It was also observed that the overpopulation occurred to a lesser extent when oxygen gas was added to the nitrogen plasma. The reason for this was also attributed to decreased number density of the excited nitrogen species due to collisions with oxygen
Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi
2016-01-01
The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. PMID:26561778
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.
International Nuclear Information System (INIS)
The one-dimensional linear homogeneous Boltzmann equation is solved for a binary mixture of quasi-Maxwellian particles in the presence of a time-dependent external field. It is assumed that the charged particles move in a bath of neutral scatterers. The neutral scatterers are in thermal equilibrium and the concentration of the charged particles is low enough to neglect collisions between them. Two cases are considered in detail, the constant and the periodic external field. The quantities calculated are the equilibrium and the stationary distribution function, respectively, from which any desired property can be derived. The solution of the Boltzmann equation for Maxwellian particles can be reduced to the solution of the so-called cold gas equation by employing the one-dimensional variant of a convolution theorem due to Wannier. The two limiting cases, the Lorentz gas (m/sub A/ → 0) and the Rayleigh gas (m/sub a/ → ∞) are treated explicitly. Furthermore, by computing the central moments, the deviations from the Gaussian approximation are discussed, and in particular the large-velocity tails are evaluated
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.
Nomura, Yasunori
2015-10-01
Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except for the one imposed by the Poincaré recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.
Phase dynamics of non-equilibrium distributions of free electron-hole pairs in GaAs quantum wells
Energy Technology Data Exchange (ETDEWEB)
Bigot, J.Y.; Mycek, M.A.; Weiss, S.; Chemla, D.S.
1994-05-01
The authors resolve the phase and amplitude of the coherent emission of a non-equilibrium Fermi-Sea in four wave mixing experiments. It exhibits an ultrafast dynamical blue shift, due to Fermi-edge many-body effects.
Joint Training of Deep Boltzmann Machines
Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua
2012-01-01
We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.
Hong, Y.; Kirschbaum, D. B.; Fukuoka, H.
2011-12-01
The key to advancing the predictability of rainfall-triggered landslides is to use physically based slope-stability models that simulate the dynamical response of the subsurface moisture to spatiotemporal variability of rainfall in complex terrains. An early warning system applying such physical models has been developed to predict rainfall-induced shallow landslides over Java Island in Indonesia and Honduras. The prototyped early warning system integrates three major components: (1) a susceptibility mapping or hotspot identification component based on a land surface geospatial database (topographical information, maps of soil properties, and local landslide inventory etc.); (2) a satellite-based precipitation monitoring system (http://trmm.gsfc.nasa.gov) and a precipitation forecasting model (i.e. Weather Research Forecast); and (3) a physically-based, rainfall-induced landslide prediction model SLIDE (SLope-Infiltration-Distributed Equilibrium). The system utilizes the modified physical model to calculate a Factor of Safety (FS) that accounts for the contribution of rainfall infiltration and partial saturation to the shear strength of the soil in topographically complex terrains. The system's prediction performance has been evaluated using a local landslide inventory. In Java Island, Indonesia, evaluation of SLIDE modeling results by local news reports shows that the system successfully predicted landslides in correspondence to the time of occurrence of the real landslide events. Further study of SLIDE is implemented in Honduras where Hurricane Mitch triggered widespread landslides in 1998. Results shows within the approximately 1,200 square kilometers study areas, the values of hit rates reached as high as 78% and 75%, while the error indices were 35% and 49%. Despite positive model performance, the SLIDE model is limited in the early warning system by several assumptions including, using general parameter calibration rather than in situ tests and neglecting
A path-integral approach to the collisional Boltzmann gas
Chen, C Y
2000-01-01
Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due to collisions, both the colliding molecules and the scattered molecules are allowed to have distributions; thus the calculation is done smoothly and no singularities arise.
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...
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.
Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium
Institute of Scientific and Technical Information of China (English)
Geraldine FAURE
2012-01-01
Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.
Robin, Jean-Marc; Berg, van den, T.J.T.P.; BONTEMPS, Christian
1998-01-01
In this paper we present and estimate a synthesis of previous equilibrium search models: allowing for continuous distributions of workers opportunity costs of employment, as well as firms’ productivities. The model allows for on-the-job search, and we assume that job offer arrival rates for workers are independent of their labor market state. We derive the theoretical implications of these assumptions, we provide simulations, and we develop a semi-parametric estimation procedure that we apply...
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
International Nuclear Information System (INIS)
The development of a thermodynamic equilibrium model to predict the cobalt distribution coefficient in the CoCl2-HCl-H2O-TBP system is described. The model makes use of the various aqueous phase cobaltous chloride complexes stoichiometric stability constants expressed as their degree of formation, their mechanism of extraction into the organic phase, and the equilibrium constant for the extraction reaction. The model was verified by the good agreement between the calculated cobalt distribution coefficients and those obtained experimentally both in the present study and published by other investigators. The optimum extraction of cobalt by the TBP occurred at an HCl equilibrium aqueous place concentration between 8.5 and 9.5M. The development of efficient procedures for the separation and concentration of important industrial metals from their aqueous solutions by liquid-liquid extraction has recently been given impetus by the realization of an impending shortage of energy and mineral resources. Liquid-liquid extraction is one of the few methods by which it is possible to quantitatively separate elements which are similar in properties. The use of liquid-liquid extraction to separate cobalt and nickel, which very frequently occur in nature together, is an important separation problem in nonferrous metallurgy. There is some fundamental information available in the chemical literature regarding the mechanism and equilibrium thermodynamic properties of selected liquid-liquid extraction systems. This research effort shows how this available information can be utilized to improve existing separation and concentration theory and technique. The development and application of a thermodynamic equilibrium model for describing the liquid-liquid extraction of cobaltous chloride from aqueous HCl solutions by tributyl phosphate (TBP) using experimental data obtained in this investigation and from the literature are presented
International Nuclear Information System (INIS)
Filyokov and Karpov (1967 Inzh.-Fiz. Zh. 13 624) have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states: the principle is to maximize the Shannon entropy associated with the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to the generalized Gibbs distribution for the probability distribution of dynamical trajectories, and to some fluctuation relation of the integrated current. The simplest stochastic dynamics where these ideas can be applied are discrete-time Markov chains, defined by transition probabilities Wi→j between configurations i and j: instead of choosing the dynamical rules Wi→j a priori, one determines the transition probabilities and the associate stationary state that maximize the entropy of dynamical trajectories with the other physical constraints that one wishes to impose. We give a self-contained and unified presentation of this type of approach, both for discrete-time Markov chains and for continuous-time master equations. The obtained results are in full agreement with the Bayesian approach introduced by Evans (2004 Phys. Rev. Lett. 92 150601) under the name 'Non-equilibrium Counterpart to detailed balance', and with the 'invariant quantities' derived by Baule and Evans (2008 Phys. Rev. Lett. 101 240601), but provide a slightly different perspective via the formulation in terms of an eigenvalue problem
Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan
2016-01-01
A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice ...
Ludwig Boltzmann A Pioneer of Modern Physics
Flamm, D
1997-01-01
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus broke with the classical prejudice, that fundamental laws have to be strictly deterministic. Even Max Planck had not been ready to accept Boltzmann's statistical methods until 1900. With Boltzmann's pioneering work the probabilistic interpretation of quantum mechanics had already a precedent. In fact in a paper in 1897 Boltzmann had already suggested to Planck to use his statistical methods for the treatment of black body radiation. The second pioneering step towards quantum mechanics was Boltzmann's introduction of discrete energy levels. Boltzmann used this method already in his 1872 paper on the H-theorem. One may ask whether Boltzmann considered this procedure only as a mathematical device or whether he attributed physical significance to it. In this connection Ostwald repo...
A Non-Equilibrium Ionization Model of the Local and Loop I Bubbles - Tracing the Ovi Distribution
de Avillez, Miguel A; Spitoni, Emanuele; Carvalho, Nuno
2011-01-01
We present the first to date three-dimensional high-resolution hydrodynamical simulation tracing the non-equilibrium ionization evolution (using the Eborae Atomic and Molecular Plasma Emission Code - E(A+M)PEC) of the Local Bubble and Loop I superbubbles embedded in a turbulent supernova-driven interstellar medium.
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
Stationary velocity distribution in an external field: a one-dimensional model
International Nuclear Information System (INIS)
The velocity distribution of a charged hard rod coupled to an external field and moving in a neutral equilibrium hard rod gas is studied on the basis of Boltzmann's equation. The exact stationary solution is found. Above a threshold value the field becomes effective in the high-velocity region slowing down the decay of the velocity distribution. The drift velocity and the mean kinetic energy are discussed as functions of the field
Influence of radiation resorption on criteria of the existence of local thermodynamic equilibrium
Energy Technology Data Exchange (ETDEWEB)
Denisova, N.V.; Preobrazhenskii, N.G.; Sevast' yanenko, V.G.
1986-12-01
The emission of radiation from a plasma volume upsets the Boltzmann equilibrium. A number of authors have proposed criteria for approximate testing of the existence of local thermodynamic equilibrium on the basis of collision and radiation processes. However, those criteria give excessive values, because they do not take into account radiation resorption, which can moderate the test conditions. The present article is concerned with the influence of radiation resorption on the criterion of the existence of local thermodynamic equilibrium in a low-temperature plasma. The domain of existence of local thermodynamic equilibrium (in the sense of Saha-Boltzmann equilibrium) is calculated for electric arcs.
Podolsky Electromagnetism at Finite Temperature: Implications on Stefan-Boltzmann Law
Bonin, C. A.; Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2009-01-01
In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.
Podolsky electromagnetism at finite temperature: Implications on the Stefan-Boltzmann law
International Nuclear Information System (INIS)
In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.
Steady detonation waves via the Boltzmann equation for a reacting mixture
International Nuclear Information System (INIS)
Based on the Boltzmann equation, the detonation problem is dealt with on a mesoscopic level. The model is based on the assumption that ahead of a shock an explosive gas mixture is in meta stable equilibrium. Starting from the Von Neumann point the chemical reaction, initiated by the pressure jump, proceeds until the chemical equilibrium is reached. Numerical solutions of the derived macroscopic equations as well as the corresponding Hugoniot diagrams which reveal the physical relevance of the mathematical model are provided
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.
Djerroud, Khelifa; Gauguet, Alexandre; Daussy, Christophe; Briaudeau, Stephan; Darquié, Benoît; Lopez, Olivier; Amy-Klein, Anne; Chardonnet, Christian; Bordé, Christian J
2009-01-01
In this paper, we describe an experiment performed at the Laboratoire de Physique des Lasers and dedicated to an optical measurement of the Boltzmann constant. With the proposed innovative technique, determining comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell-Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to sqrt(kT) and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO2 laser with a wavelength . The absorption cell is placed in a thermostat keeping the temperature at 273.15 K within 1.4 mK. We were able to measure with a relative uncertainty as small as 3.8x10-5, which represents an improvement of an order of magnitude for an integration time comparable to our previous measu...
Ismail M.S
2014-01-01
We introduce a new concept which extends von Neumann and Morgensterns maximin strategy solution by incorporating individual rationality of the players. Maximin equilibrium, extending Nashs value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that maximin equilibrium is invariant under strictly increasing transformations of the payoffs. Notably, every finite game possesses a maximin equilibrium in pure strategies. Considering the games in von Neuma...
On Training Deep Boltzmann Machines
Desjardins, Guillaume; Courville, Aaron; Bengio, Yoshua
2012-01-01
The deep Boltzmann machine (DBM) has been an important development in the quest for powerful "deep" probabilistic models. To date, simultaneous or joint training of all layers of the DBM has been largely unsuccessful with existing training methods. We introduce a simple regularization scheme that encourages the weight vectors associated with each hidden unit to have similar norms. We demonstrate that this regularization can be easily combined with standard stochastic maximum likelihood to yie...
Boltzmann equation and hydrodynamic fluctuations.
Colangeli, Matteo; Kröger, Martin; Ottinger, Hans Christian
2009-11-01
We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics. PMID:20364972
Boltzmann equation and hydrodynamic fluctuations
Colangeli, M.; Kroger, M.; Ottinger, H. C.
2009-01-01
We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.
Wiggins, Philippa M.; van Ryn, René T.; Ormrod, Dale G. C.
1991-01-01
Equilibration of ions and water with a charged gel does not follow the simple equations of the classical Gibbs-Donnan membrane equilibrium. Partition of ions between the gel and the external solution show specific effects, which require that activity coefficients are different in the two compartments. Highly hydrated ions, such as Na+ and H+ are accumulated into the gel water, whereas less highly hydrated ions, such as K+ and NH4+ accumulate in the external water. This selectivity is the obve...
International Nuclear Information System (INIS)
In the magnetic field range Hc1, where the london approach is usually used to describe the properties of type II superconductors, the spatial distribution of the order parameter is taken into account in the calculation of the vibrational contribution to the dynamic magnetic permeability. The behavior of μν(H) is analyzed for the case where the vortices oscillate near their equilibrium positions related to the thermodynamically equilibrium vortex lattice. It is shown that the effect of depression of the order parameter in the vortex cores leads to essential differences in the behaviour of μν in comparison with the analogous dependence obtained in the framework of the London model. The main reason of these differences is a change of the form of the effective potential well, in which the oscillations of near surface vortices take place
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.
Zhang, Jianying; Yan, Guangwu
2016-04-01
A lattice Boltzmann model for solving the (2+1) dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a two-dimensional space, and the evolution of the model is about a spatial axis rather than time. The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Numerical results reproduce the phenomena of the fusion of necklace-ring pattern and the effect of non-linearity on the soliton in the CQCGLE.
Energy Technology Data Exchange (ETDEWEB)
Sawada, Y.; Sugiyama, Y.; Iga, T.; Hanano, M.
1987-08-01
Tracer distribution kinetics in the determination of local cerebral blood flow (LCBF) were examined by using three models, i.e., venous equilibrium, tube, and distributed models. The technique most commonly used for measuring LCBF is the tissue uptake method, which was first developed and applied by Kety. The measurement of LCBF with the /sup 14/C-iodoantipyrine (IAP) method is calculated by using an equation derived by Kety based on the Fick's principle and a two-compartment model of blood-tissue exchange and tissue concentration at a single data point. The procedure, in which the tissue is to be in equilibrium with venous blood, will be referred to as the tissue equilibration model. In this article, effects of the concentration gradient of tracer along the length of the capillary (tube model) and the transverse heterogeneity in the capillary transit time (distributed model) on the determination of LCBF were theoretically analyzed for the tissue sampling method. Similarities and differences among these models are explored. The rank order of the LCBF calculated by using arterial blood concentration time courses and the tissue concentration of tracer based on each model were tube model (model II) less than distributed model (model III) less than venous equilibrium model (model I). Data on /sup 14/C-IAP kinetics reported by Ohno et al. were employed. The LCBFs calculated based on model I were 45-260% larger than those in models II or III. To discriminate among three models, we propose to examine the effect of altering the venous infusion time of tracer on the apparent tissue-to-blood concentration ratio (lambda app). A range of the ratio of the predicted lambda app in models II or III to that in model I was from 0.6 to 1.3.
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.
Feldman, Michal; Tennenholtz, Moshe
We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent selects a resource from a set of resources, and its payoff is an increasing (or non-decreasing) function of the number of agents selecting its resource. While it has been shown that strong equilibrium exists in resource selection games, these games do not possess super-strong equilibrium, in which a fruitful deviation benefits at least one deviator without hurting any other deviator, even in the case of two identical resources with increasing cost functions. Similarly, strong equilibrium does not exist for that restricted two identical resources setting when the game is played repeatedly. We prove that for any given partition there exists a super-strong equilibrium for resource selection games of identical resources with increasing cost functions; we also show similar existence results for a variety of other classes of resource selection games. For the case of repeated games we identify partitions that guarantee the existence of strong equilibrium. Together, our work introduces a natural concept, which turns out to lead to positive and applicable results in one of the basic domains studied 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...
Lattice-Boltzmann Simulation of Tablet Disintegration
Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip
Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.
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.
Directory of Open Access Journals (Sweden)
R.S.A.P. Oliveira
2014-08-01
Full Text Available INTRODUCTION. Chemical equilibrium is recognized as a topic of several misconceptions. Its origins must be tracked from previous scholarship. Its impact on biochemistry learning is not fully described. A possible bulk of data is the FUVEST exam. OBJECTIVES: Identify students’ errors profile on chemical equilibrium tasks using public data from FUVEST exam. MATERIAL AND METHODS: Data analysis from FUVEST were: i Private and Public school distribution in Elementary and Middle School, and High School candidates of Pharmacy-Biochemistry course and total USP careers until the last call for enrollment (2004-2013; ii Average performance in 1st and 2nd parts of FUVEST exam of Pharmacy-Biochemistry, Chemistry, Engineering, Biological Sciences, Languages and Medicine courses and total enrolled candidates until 1st call for enrollment (2008- 2013; iii Performance of candidates of Pharmacy-Biochemistry, Chemistry, Engineering, Biological Sciences, Languages and Medicine courses and total USP careers in chemical equilibrium issues from 1st part of FUVEST (2011-2013. RESULTS AND DISCUSSION: i 66.2% of candidates came from private Elementary-Middle School courses and 71.8%, came from High School courses; ii Average grade over the period for 1st and 2nd FUVEST parts are respectively (in 100 points: Pharmacy-Biochemistry 66.7 and 61.2, Chemistry 65.9 and 58.9, Engineering 75.9 and 71.9, Biological Sciences 65.6 and 54.6, Languages 49.9 and 43.3, Medicine 83.5 and 79.5, total enrolled candidates 51,5 and 48.9; iii Four chemical equilibrium issues were found during 2011-2013 and the analysis of multiplechoice percentage distribution over the courses showed that there was a similar performance of students among them, except for Engineering and Medicine with higher grades, but the same proportional distribution among choices. CONCLUSION: Approved students came majorly from private schools. There was a different average performance among courses and similar on
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...
A Characteristic Non-Reflecting Boundary Treatment in Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
KIM Dehee; KIM Hyung Min; JHON Myung S.; VINAY Ⅲ Stephen J.; BUCHANAN John
2008-01-01
In lattice Boltzmann methods, disturbances develop at the initial stages of the simulation, the decay characteristics depend mainly on boundary treatment methods; open boundary conditions such as equilibrium and bounce-back schemes potentially generate uncontrollable disturbances. Excessive disturbances originate from non-physical reflecting waves at boundaries. Characteristic boundary conditions utilizing the signs of waves at boundaries which suppress these reflecting waves, as well as their implementation in the lattice Boltzmann method, are introduced herein. The performance of our novel boundary treatment method to effectively suppress excessive disturbances is verified by three different numerical experiments.
A Fokker-Planck model of the Boltzmann equation with correct Prandtl number
Mathiaud, J
2015-01-01
We propose an extension of the Fokker-Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier-Stokes asymptotics. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model (ES) is obtained from the Bathnagar-Gross-Krook model (BGK) of the Boltzmann equation. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman-Enskog analysis and two numerical tests show that a correct Prandtl number of 2/3 can be obtained.
International Nuclear Information System (INIS)
A straight, helical plasma equilibrium equation is solved numerically for a plasma with a helical magnetic axis. As is expected, by a suitable choice of the plasma boundary, the vacuum configuration is made line ∫ dl/B stable. As the plasma pressure increases, the line ∫ dl/B criterion will improve (again as expected). There is apparently no limit on the plasma β from the equilibrium consideration. Thus helical-axis stellarator β will presumably be limited by MHD stability β, and not by equilibrium β
A generalized linear Boltzmann equation for non-classical particle transport
International Nuclear Information System (INIS)
This paper presents a derivation and initial study of a new generalized linear Boltzmann equation (GLBE), which describes particle transport for random statistically homogeneous systems in which the distribution function for chord lengths between scattering centers is non-exponential. Such problems have recently been proposed for the description of photon transport in atmospheric clouds; this paper is a first attempt to develop a Boltzmann-like equation for these and other related applications.
International Nuclear Information System (INIS)
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well-known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions for the total entropy, total energy and rest mass of the gas are obtained. The position of the center of mass of the gas in equilibrium is found. The non-relativistic and ultrarelativistic approximations are also considered. The phase space volume of the system is calculated explicitly in the ultrarelativistic approximation.
Protonation Equilibrium of Linear Homopolyacids
Directory of Open Access Journals (Sweden)
Požar J.
2015-07-01
Full Text Available The paper presents a short summary of investigations dealing with protonation equilibrium of linear homopolyacids, in particularly those of high charge density. Apart from the review of experimental results which can be found in the literature, a brief description of theoretical models used in processing the dependence of protonation constants on monomer dissociation degree and ionic strength is given (cylindrical model based on Poisson-Boltzmann equation, cylindrical Stern model, the models according to Ising, Högfeldt, Mandel and Katchalsky. The applicability of these models regarding the polyion charge density, electrolyte concentration and counterion type is discussed. The results of Monte Carlo simulations of protonation equilibrium are also briefly mentioned. In addition, frequently encountered errors connected with calibration of of glass electrode and the related unreliability of determined protonation constants are pointed out.
Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel
Hohenegger, A.
2008-01-01
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. Th...
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.
Pruning Boltzmann networks and hidden Markov models
DEFF Research Database (Denmark)
Pedersen, Morten With; Stork, D.
1996-01-01
Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...
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).
Geometric aspects in extended approach of equilibrium classical fluctuation theory
Velazquez, L.
2011-11-01
Previously, an extended approach of equilibrium classical fluctuation theory was developed compatible with the existence of anomalous response functions, e.g. states with negative heat capacities. Now, the geometric aspects associated with this new framework are analyzed. The analysis starts from the so-called reparametrization invariance: a special symmetry of distribution functions dp (I|θ) employed in classical equilibrium statistical mechanics that allows us to express the thermo-statistical relations in the same mathematical appearance in different coordinate representations. The existence of reparametrization invariance can be related to three different geometric frameworks: (1) a non-Riemannian formulation for classical fluctuation theory based on the concept of reparametrization dualities; (2) a Riemannian formulation defined on the manifold {P} of control parameters θ, where the main theorems of inference theory appear as dual counterparts of general fluctuation theorems, and Boltzmann-Gibbs distributions ωBG(I|θ) = exp(-θiIi)/Z(θ) admit a geometric generalization; and finally, (3) a Riemannian formulation defined on the manifold {M}_{\\theta } of macroscopic observables I, which appears as a counterpart approach of inference geometry.
Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel
Hohenegger, A
2008-01-01
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.
Solving the homogeneous Boltzmann equation with arbitrary scattering kernel
International Nuclear Information System (INIS)
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space-homogeneous Boltzmann equation with an isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the scattering kernel in terms of two cosines of the 'scattering angles'. The scattering functions used by previous authors in particle physics for matrix elements in the Fermi approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.
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.
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.
Directory of Open Access Journals (Sweden)
F. Wania
2014-10-01
Full Text Available 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 equilibrium partitioning coefficients between the gas phase, an aqueous phase and a water insoluble organic matter (WIOM phase. Placing compounds formed from the oxidation of n-alkanes, terpenes and mono-aromatic hydrocarbons on the maps based on their predicted partitioning properties allows for a simple graphical assessment of their equilibrium phase distribution behaviour. Specifically, it allows for the simultaneous visualization and quantitative comparison of the impact on phase distribution of changes in atmospheric parameters (such as temperature, salinity, WIOM phase polarity, organic aerosol load, and liquid water content, and chemical properties (such as oxidation state, molecular size, functionalization, and dimerisation. The graphical analysis reveals that the addition of hydroxyl, carbonyl and carboxyl groups increases the affinity of aliphatic, alicyclic and aromatic hydrocarbons for the aqueous phase more rapidly than their affinity for WIOM, suggesting that the aqueous phase may often be relevant even for substances that are considerably larger than the C2 and C3 compounds that are typically believed to be associated with aqueous SOA. In particular, the maps identify some compounds that contribute to SOA formation if partitioning to both WIOM and aqueous phase is considered, but would remain in the gas phase if either condensed phase were neglected. For example, many semi-volatile α-pinene oxidation products will contribute to aqueous SOA under the high liquid water
Variational formulation of the steady Boltzmann equation for semiconductors and applications
International Nuclear Information System (INIS)
We present a variational formulation of the steady Boltzmann equation for semiconductors. In this formulation, the distribution function is replaced by a weighted distribution function, and the symmetry of the drift operator is obtained by using the parity operator. We show that the solutions of the Boltzmann equation for the weighted distribution function are stationary functions of a suitable functional, which takes into account realistic boundary conditions. After introducing a general numerical framework, the approach proposed is tested in the bulk case, by computing an approximate expression for carrier mobility in silicon.
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
Equilibrium charge state distributions of Ni, Co, and Cu beams in molybdenum foil at 2 MeV/u
Gastis, Panagiotis; Perdikakis, George; Robertson, Daniel; Bauder, Will; Skulski, Michael; Collon, Phillipe; Anderson, Tyler; Ostdiek, Karen; Aprahamian, Ani; Lu, Wenting; Almus, Robert
2015-10-01
The charge states of heavy-ions are important for the study of nuclear reactions in inverse kinematics when electromagnetic recoil mass spectrometers are used. The passage of recoil products through a material, like the windows of gas cells or charge state boosters, results a charge state distribution (CSD) in the exit. This distribution must be known for the extraction of any cross section since only few charge-state can be transmitted through a magnetic separator separator for a given setting. The calculation of CSDs for heavy ions is challenging. Currently we rely on semi-empirical models with unknown accuracy for ion/target combinations in the Z > 20 region. In the present study were measured the CSDs of the stable 60Ni, 59Co, and 63Cu beams while passing through a 1 μm molybdenum foil. The beam energies were 1.84 MeV/u, 2.09 MeV/u, and 2.11 MeV/u for the 60Ni, 59Co, and 63Cu respectively. The results of this study mainly check the accuracy of the semi-empirical models used by the program LISE++, on calculating CSDs for ion/target combinations of Z > 20. In addition, other empirical models on calculating mean charge states were compared and checked.
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...
Simulation of a Natural Convection by the Hybrid Thermal Lattice Boltzmann Equation
Energy Technology Data Exchange (ETDEWEB)
Ryu, Seungyeob; Kang, Hanok; Seo, Jaekwang; Yun, Juhyeon; Zee, Sung-Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2006-07-01
Recently, the lattice Boltzmann method(LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. In spite of its success in solving various challenging problems involving athermal fluids, the LBM has not been able to handle realistic thermal fluids with a satisfaction. The difficulty encountered in the thermal LBM seems to be the numerical instabilities. The existing thermal lattice Boltzmann models may be classified into three categories based on their approach in solving the Boltzmann equation, namely, the multispeed, the passive scalar and the thermal energy distribution approach. For more details see Ref. In the present work, the hybrid thermal lattice Boltzmann scheme proposed by Lallemand and Luo is used for simulating a natural convection in a square cavity. They proposed a hybrid thermal lattice Boltzmann equation(HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time(MRT) model, whereas the diffusion-advection equations for the temperature are solved separately by using finite-difference technique. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of temperature fields at high Rayleigh numbers.
Relativistic Boltzmann theory for a plasma
International Nuclear Information System (INIS)
This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)
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
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
Degond, Pierre; Dimarco, Giacomo
2010-01-01
In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations. Recently we presented in [14],[16],[17] different methodologies which permit to solve fluid dynamics problems with localized regions of departure from thermodynamical equilibrium. The methods rely on the introduction of buffer zones which realize a smooth transi...
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
Lods, Bertrand; Mouhot, Clément; Toscani, Giuseppe
2008-01-01
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional fo...
A Spectral Study of the Linearized Boltzmann Equation for Diffusively Excited Granular Media
Rey, Thomas
2013-01-01
In this work, we are interested in the spectrum of the diffusively excited granular gases equation, in a space inhomogeneous setting, linearized around an homogeneous equilibrium. We perform a study which generalizes to a non-hilbertian setting and to the inelastic case the seminal work of Ellis and Pinsky about the spectrum of the linearized Boltzmann operator. We first give a precise localization of the spectrum, which consists in an essential part lying on the left of the imaginary axis an...
Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances
Lahanas, A B; Nanopoulos, Dimitri V
2006-01-01
In this work we derive the modifications to the Boltzmann equation governing the cosmic evolution of relic abundances induced by dilaton dissipative-source and non-critical-string terms in dilaton-driven non-equilibrium string Cosmologies. We also discuss briefly the most important phenomenological consequences, including modifications of the constraints on the available parameter space of cosmologically appealing particle physics models, imposed by recent precision data of astrophysical measurements.
Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances
Lahanas, Ab; Mavromatos, Ne; Nanopoulos, Dv
In this work we derive the modifications to the Boltzmann equation governing the cosmic evolution of relic abundances induced by dilaton dissipative-source and non-critical-string terms in dilaton-driven non-equilibrium string Cosmologies. We also discuss briefly the most important phenomenological consequences, including modifications of the constraints on the available parameter space of cosmologically appealing particle physics models, imposed by recent precision data of astrophysical measurements.
Thermal Lattice Boltzmann Model for Compressible Fluid
Institute of Scientific and Technical Information of China (English)
SUN Cheng-Hai
2000-01-01
We formulate a new thermal lattice Boltzmann model to simulate compressible flows with a high Mach number.The main difference from the standard lattice Boltzmann models is that the particle velocities are no longer a constant, varying with the mean velocity and internal energy. The proper heat conduction term in the energy equation is recovered by modification of the fluctuating kinetic energy transported by particles. The simulation of Couette flow is in good agreement with the analytical solutions.
A Viscosity Adaptive Lattice Boltzmann Method
Conrad, Daniel
2015-01-01
The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice. By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics methods. The LBM has been shown to be an accurate and efficient tool for the numerical...
Lattice Boltzmann approach for complex nonequilibrium flows.
Montessori, A; Prestininzi, P; La Rocca, M; Succi, S
2015-10-01
We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion. PMID:26565365
Poisson-Boltzmann-Nernst-Planck model
International Nuclear Information System (INIS)
The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external
Lattice Boltzmann algorithm for continuum multicomponent flow.
Halliday, I; Hollis, A P; Care, C M
2007-08-01
We present a multicomponent lattice Boltzmann simulation for continuum fluid mechanics, paying particular attention to the component segregation part of the underlying algorithm. In the principal result of this paper, the dynamics of a component index, or phase field, is obtained for a segregation method after U. D'Ortona [Phys. Rev. E 51, 3718 (1995)], due to Latva-Kokko and Rothman [Phys. Rev. E 71 056702 (2005)]. The said dynamics accord with a simulation designed to address multicomponent flow in the continuum approximation and underwrite improved simulation performance in two main ways: (i) by reducing the interfacial microcurrent activity considerably and (ii) by facilitating simulational access to regimes of flow with a low capillary number and drop Reynolds number [I. Halliday, R. Law, C. M. Care, and A. Hollis, Phys. Rev. E 73, 056708 (2006)]. The component segregation method studied, used in conjunction with Lishchuk's method [S. V. Lishchuk, C. M. Care, and I. Halliday, Phys. Rev. E 67, 036701 (2003)], produces an interface, which is distributed in terms of its component index; however, the hydrodynamic boundary conditions which emerge are shown to support the notion of a sharp, unstructured, continuum interface. PMID:17930175
The relativistic linear Boltzmann transport equation
International Nuclear Information System (INIS)
In this thesis the relativistic linear Boltzmann transport equation is applied to an experiment in pion production by 740 MeV protons incident on a variety of nuclei. This equation is solved by the Monte Carlo method of generating a single particle intranuclear cascade. The transport equation is derived starting with the N-body equation of motion for quantum mechanics in phase in order to determine under what conditions it is a valid approximation. It is shown that it should be a valid semi-classical approximation provided that: (1) The kinetic energy of the transport particle is much greater than its energy of interaction with the mean nuclear potential field. (2) The two-body collision interactions which make up the single particle intranuclear cascade take place over space and time intervals which are small relative to the internucleon space and time intervals for interactions within the nucleus and also compared to the space and time scales over which the probability distribution undergoes variation. In the pion production calculation condition (2) is only approximately met but reasonable agreement with the experimental data is obtained similar to that obtained in other theoretical calculations compared to this experiment
Kinetic equilibrium and relativistic thermodynamics
Ván P.
2011-01-01
Relativistic thermodynamics is treated from the point of view of kinetic theory. It is shown that the generalized J\\"uttner distribution suggested in [1] is compatible with kinetic equilibrium. The requirement of compatibility of kinetic and thermodynamic equilibrium reveals several generalizations of the Gibbs relation where the velocity field is an independent thermodynamic variable.
Non-equilibrium hot carrier dynamics in plasmonic nanostructures
Narang, Prineha; Sundararaman, Ravishankar; Jermyn, Adam; Cortes, Emiliano; Maier, Stefan A.; Goddard, William A., III
Decay of surface plasmons to hot carriers is a new direction that has attracted considerable fundamental and application interest, yet a fundamental understanding of ultrafast plasmon decay processes and the underlying microscopic mechanisms remain incomplete. Ultrafast experiments provide insights into the relaxation of non-equilibrium carriers at the tens and hundreds of femtoseconds time scales, but do not yet directly probe shorter times with nanometer spatial resolution. Here we report the first ab initio calculations of non equilibrium transport of plasmonic hot carriers in metals and experimental observation of the injection of these carriers into molecules tethered to the metal surface. Specifically, metallic nanoantennas functionalized with a molecular monolayer allow for the direct probing of electron injection via surface enhanced Raman spectroscopy of the original and reduced molecular species. We combine first principles calculations of electron-electron and electron-phonon scattering rates with Boltzmann transport simulations to predict the ultrafast dynamics and transport of carriers in real materials. We also predict and compare the evolution of electron distributions in ultrafast experiments on noble metal nanoparticles.
Equilibrium cluster fluids: pair interactions via inverse design.
Jadrich, R B; Bollinger, J A; Lindquist, B A; Truskett, T M
2015-12-28
Inverse methods of statistical mechanics are becoming productive tools in the design of materials with specific microstructures or properties. While initial studies have focused on solid-state design targets (e.g., assembly of colloidal superlattices), one can alternatively design fluid states with desired morphologies. This work addresses the latter and demonstrates how a simple iterative Boltzmann inversion strategy can be used to determine the isotropic pair potential that reproduces the radial distribution function of a fluid of amorphous clusters with prescribed size. The inverse designed pair potential of this "ideal" cluster fluid, with its broad attractive well and narrow repulsive barrier at larger separations, is qualitatively different from the so-called SALR form most commonly associated with equilibrium cluster formation in colloids, which features short-range attractive (SA) and long-range repulsive (LR) contributions. These differences reflect alternative mechanisms for promoting cluster formation with an isotropic pair potential, and they in turn produce structured fluids with qualitatively different static and dynamic properties. Specifically, equilibrium simulations show that the amorphous clusters resulting from the inverse designed potentials display more uniformity in size and shape, and they also show greater spatial and temporal resolution than those resulting from SALR interactions. PMID:26434352
The scattering kernel of the nonlinear Boltzmann equation and its expansion into spherical harmonics
International Nuclear Information System (INIS)
The method of polynomial approximation i.e. the expansion of the particle density into spherical harmonics, well-known in the linear transport theory, has been generalized by F. Schuerrer 1984 to the nonlinear Boltzmann equation. For practical purposes, a truncation of the series expansion after a few terms requires a good convergence of the scattering kernel expansion into Legendre polynomials. In the present work a few simple examples are used to investigate the convergence. In the most simple case, the elastic collision on a fixed target, the PN-approximations of the scattering kernel in the linear theory serves as a standard of reference for the nonlinear case. A parameter study shows the different approximations as compared to the exact function. Then a more realistic model, a Maxwell gas of target particles, of different temperatures is investigated. The results of this parameter study are represented by three-dimensional computer graphics. In the last chapter the results are applied to the system of moment equations where a considerable simplification is justified for nearly isotropic velocity distributions. It is concluded that nonlinear transport not-too-far from equilibrium can be well described by a Pn approximation. 8 refs., 35 figs. (qui)
Tsumura, Kyosuke; Kikuchi, Yuta; Kunihiro, Teiji
2015-10-01
We derive the second-order hydrodynamic equation and the microscopic formulas of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel development of the renormalization-group method, a powerful reduction theory of dynamical systems, which has been applied successfully to derive the nonrelativistic second-order hydrodynamic equation. Our theory nicely gives a compact expression of the deviation of the distribution function in terms of the linearized collision operator, which is different from those used as an ansatz in the conventional fourteen-moment method. It is confirmed that the resultant microscopic expressions of the transport coefficients coincide with those derived in the Chapman-Enskog expansion method. Furthermore, we show that the microscopic expressions of the relaxation times have natural and physically plausible forms. We prove that the propagating velocities of the fluctuations of the hydrodynamical variables do not exceed the light velocity, and hence our second-order equation ensures the desired causality. It is also confirmed that the equilibrium state is stable for any perturbation described by our equation.
Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth
Jelinek, Bohumir; Eshraghi, Mohsen; Felicelli, Sergio; Peters, John F.
2014-03-01
An extremely scalable lattice Boltzmann (LB)-cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Catalogue identifier: AEQZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29,767 No. of bytes in distributed program, including test data, etc.: 3131,367 Distribution format: tar.gz Programming language: Fortran 90. Computer: Linux PC and clusters. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI
Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime
International Nuclear Information System (INIS)
We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-(1/2) particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 2 spin-density (‘Wigner’) matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the t→∞ thermal (Fermi–Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting. (paper)
Nonequilibrium excited particle population distribution in low-temperature argon discharges
International Nuclear Information System (INIS)
In discharges with either high electron density or high gas pressure, it is often believed that an equilibrium Boltzmann distribution among excited particles will be reached due to the presence of strong collisional processes. In this work, using a new collisional-radiative model for low-temperature argon discharges, it is found that the population distribution of atoms in Paschen 2p excited levels significantly deviates from the Boltzmann distribution over a wide operating parameter range found in many discharges reported in the literature. The finding has also been confirmed by experimental measurement for several different types of discharges with pressure ranging from 1 Pa to atmospheric pressure. This result can have a significant impact on both plasma modelling and the interpretation of the optical emission spectra collected from the discharges, in particular in the microdischarges operated at atmospheric pressure. (fast track communication)
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...
Low-variance Monte Carlo Solutions of the Boltzmann Transport Equation
Hadjiconstantinou, Nicolas G; Baker, Lowell L
2009-01-01
We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is reasonable. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods.
An implicit Lagrangian lattice Boltzmann method for the compressible flows
Yan, Guangwu; Dong, Yinfeng; Liu, Yanhong
2006-08-01
In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results.
Hong, Liu; Yang, Zaibao; Zhu, Yi; Yong, Wen-An
2015-12-01
In this article, we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, properly separating entropy fluxes and production rates, and determining a dissipation matrix. Our approach takes advantage of both extended irreversible thermodynamics and GENERIC formalisms and shows a direct correspondence with Levermore's moment-closure hierarchies for the Boltzmann equation. As a direct application, a new ten-moment model beyond the classical hierarchies is constructed and is shown to recover the Euler equations in the equilibrium state. These interesting results may put various macroscopic modeling approaches, starting from the general principles of non-equilibrium thermodynamics, on a solid microscopic foundation based on the Boltzmann equation.
A tightly coupled non-equilibrium model for inductively coupled radio-frequency plasmas
International Nuclear Information System (INIS)
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
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.
International Nuclear Information System (INIS)
At Atucha I, the present fuel management with natural uranium comprises three burnup areas and one irradiation path, sometimes performing four steps in the reactor core, according to the requirements. The discharge burnup is 6.0 Mw d/kg U for a waste reactivity of 6.5 m k and a heavy water purity of 99.75%. This is a preliminary study to obtain the distribution of equilibrium burnup of an homogeneous core with slightly enriched uranium (0.85% by weight U-235), using the time-averaged method implemented in the code PUMA and a representative model of one third of core and fixed rod position. It was found a strategy of three areas and two paths that agrees with the present limits of channel power and specific power in fuel rod. The discharge burnup obtained is 11.6 Mw d/kg U. This strategy is calculated with the same method and a full core representation model is used to verify the obtained results. (Author)
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
Kinetic Boltzmann, Vlasov and Related Equations
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
Grid refinement for entropic lattice Boltzmann models
Dorschner, B; Chikatamarla, S S; Karlin, I V
2016-01-01
We propose a novel multi-domain grid refinement technique with extensions to entropic incompressible, thermal and compressible lattice Boltzmann models. Its validity and accuracy are accessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the set-ups of turbulent channel flow, flow past a sphere, Rayleigh-Benard convection as well as the supersonic flow around an airfoil. Special attention is payed to analyzing the adaptive features of entropic lattice Boltzmann models for multi-grid simulations.
Rigorous Navier-Stokes Limit of the Lattice Boltzmann Equation
Junk, Michael; Yong, Wen-An
2001-01-01
Here we riqorously investigate the diffusive limit of a velocity-discrete Boltzmann equation which is used in the lattice Boltzmann method to construct approximate solutions of the incompressible Navier-Stokes equation.
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.
Gastis, P.; Perdikakis, G.; Robertson, D.; Almus, R.; Anderson, T.; Bauder, W.; Collon, P.; Lu, W.; Ostdiek, K.; Skulski, M.
2016-04-01
Equilibrium charge state distributions of stable 60Ni, 59Co, and 63Cu beams passing through a 1 μm thick Mo foil were measured at beam energies of 1.84 MeV/u, 2.09 MeV/u, and 2.11 MeV/u respectively. A 1-D position sensitive Parallel Grid Avalanche Counter detector (PGAC) was used at the exit of a spectrograph magnet, enabling us to measure the intensity of several charge states simultaneously. The number of charge states measured for each beam constituted more than 99% of the total equilibrium charge state distribution for that element. Currently, little experimental data exists for equilibrium charge state distributions for heavy ions with 19 ≲Zp,Zt ≲ 54 (Zp and Zt, are the projectile's and target's atomic numbers respectively). Hence the success of the semi-empirical models in predicting typical characteristics of equilibrium CSDs (mean charge states and distribution widths), has not been thoroughly tested at the energy region of interest. A number of semi-empirical models from the literature were evaluated in this study, regarding their ability to reproduce the characteristics of the measured charge state distributions. The evaluated models were selected from the literature based on whether they are suitable for the given range of atomic numbers and on their frequent use by the nuclear physics community. Finally, an attempt was made to combine model predictions for the mean charge state, the distribution width and the distribution shape, to come up with a more reliable model. We discuss this new "combinatorial" prescription and compare its results with our experimental data and with calculations using the other semi-empirical models studied in this work.
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.
Test of Information Theory on the Boltzmann Equation
Hyeon-Deuk, Kim; Hayakawa, Hisao
2002-01-01
We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.
Test of Information Theory on the Boltzmann Equation
Kim, Hyeon-Deuk; Hayakawa, Hisao
2003-01-01
We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.
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
Departures from Local Thermodynamic Equilibrium
International Nuclear Information System (INIS)
This paper starts with a definition of local thermodynamic equilibrium and points out the relationship between local and complete thermodynamic equilibrium. It is shown that electron collisions are essential for the establishment of LTE and a relationship is derived for the minimum electron density at which collision processes are just sufficiently frequent to cause the plasma to be in LTE in face of the competing radiative processes. This relationship is derived for an optically thin plasma. The effect of radiation trapping is considered and some figures given by which the effect of this can be taken into account in assessing the validity of LTE in such cases. Account is now taken of the finite time required for the atomic collision processes to establish the plasma in LTE. A numerical example is worked out which shows that these considerations can be very important for plasmas of rapidly varying temperature. Mention is also made of departures from LTE caused by inhomogeneities in the plasma and by the positive ions having a different kinetic temperature from the electrons. Finally, it is remarked that even if the criteria for LTE to be valid are not met then the Saha and Boltzmann equations may still be applied to describe the population densities of the upper levels of individual species of atoms or ions. (author)
Teiber, Holger; Scharrer, Manuel; Marks, Michael A. W.; Arzamastsev, Andrei A.; Wenzel, Thomas; Markl, Gregor
2015-04-01
The concentration of halogens in apatite, biotite and amphibole is investigated for a large variety of mantle-derived plutonic rocks (gabbros, diorites, monzonites, olivine- and pyroxene-bearing monzonitic to granitic rocks, syenites, carbonatites and a phoscorite). In all rocks studied, apatite occurs as an early magmatic phase, whereas biotite and amphibole may occur either as a late magmatic phase or as late-stage, potentially hydrothermal product replacing precursor olivine, pyroxene and Fe-Ti oxides (ilmenite and magnetite). Based on electron microprobe analyses for F and Cl and detailed textural observations, we test existing models of halogen partitioning between apatite and biotite. Bromine concentration data for apatite, biotite and amphibole are used to further refine our understanding of the geochemical similarities and differences between Cl and Br during magmatic and hydrothermal processes. Our data suggests that F and Cl contents in apatite, biotite and amphibole can indeed be useful monitors of the halogen systematics in magmas, but they may also be subject to post-magmatic changes to variable extents. The relatively small radius and compatible F cation seems to be less prone to post-magmatic alteration and is likely to best reflect the original magmatic halogen abundances - especially in apatite. However, the larger and probably more incompatible Cl anion, is more easily re-mobilized as reflected by strong redistribution of Cl in biotite and amphibole which have been clearly overprinted by hydrothermal fluids. In certain cases, the ability of halogens to re-distribute themselves after magmatic equilibrium partitioning (as emphasized by our data) suggests that observed partitioning (especially between apatite and biotite) may also be used as a very sensitive indicator for post-magmatic hydrothermal processes.
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 of...... equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely non collinear....
Pair Production in the Quantum Boltzmann Equation
Rau, Jochen
1994-01-01
A source term in the quantum Boltzmann equation, which accounts for the spontaneous creation of $e^+e^-$-pairs in external electric fields, is derived from first principles and evaluated numerically. Careful analysis of time scales reveals that this source term is generally non-Markovian. This implies in particular that there may be temporary violations of the $H$-theorem.
The Quantum Boltzmann Equation in Semiconductor Physics
Snoke, D. W.
2010-01-01
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases.
Lattice Boltzmann Models for Complex Fluids
Flekkoy, E. G.; Herrmann, H. J.
1993-01-01
We present various Lattice Boltzmann Models which reproduce the effects of rough walls, shear thinning and granular flow. We examine the boundary layers generated by the roughness of the walls. Shear thinning produces plug flow with a sharp density contrast at the boundaries. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.
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 ...
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...
Generalized Boltzmann equations for on-shell particle production in a hot plasma
Jakovác, A
2002-01-01
A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function. Although it was usually interpreted as a constraint on the solution of the Boltzmann equation, we argue that its dynamics is relevant to the determination and resummation of the particle production cut contributions. The differential equation for this new contribution is illustrated in the example of the cubic scalar model. The analogue of the relaxation time approximation is suggested. It results in the shift of the threshold location and in smearing out of the non-analytic threshold behaviour of the spectral function. Possible consequences for the dilepton production are discussed.
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.
Generalized Market Equilibrium: "Stable" CAPM
Belkacem, Lotfi; Lévy Véhel, Jacques; Walter, Christian
1995-01-01
Our main purpose in this paper is to derive the generalized equilibrium relationship between risk and return under the assumption that the asset returns follow a joint symmetric stable distribution. We show that equilibrium rates of return on all risky assets are functions of their covariation with the market portfolio. The "stable" CAPM highlights a new measure of the quantity of risk which may be interpreted as a "generalized beta coefficient".
Reaction and internal energy relaxation rates in viscous thermochemically non-equilibrium gas flows
International Nuclear Information System (INIS)
In the present paper, reaction and energy relaxation rates as well as the normal stress are studied for viscous gas flows with vibrational and chemical non-equilibrium. Using the modified Chapman-Enskog method, multi-temperature models based on the Treanor and Boltzmann vibrational distributions are developed for the general case taking into account all kinds of vibrational energy transitions, exchange reactions, dissociation, and recombination. Integral equations specifying the first-order corrections to the normal mean stress and reaction rates are derived, as well as approximate systems of linear equations for their numerical computation. Generalized thermodynamic driving forces associated with all non-equilibrium processes are introduced. It is shown that normal stresses and rates of non-equilibrium processes can be expressed in terms of the same driving forces; the symmetry of kinetic coefficients in these expressions is proven. The developed general model is applied to a particular case of a pure N2 viscous flow with slow VT relaxation. Normal stress and rates of vibrational relaxation are studied for various ratios of vibrational and translational temperatures. The cross effects between different vibrational transitions in viscous flows are evaluated, along with the influence of anharmonicity and flow compressibility on the first-order corrections to the relaxation rate. Limits of validity for the widely used Landau–Teller model of vibrational relaxation are indicated
Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow
Institute of Scientific and Technical Information of China (English)
YI Hou-Hui; FAN Li-Juan; YANG Xiao-Feng; LI Hua-Bing
2009-01-01
@@ The moving behaviour of two-and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles' radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.
Exact results for the Boltzmann equation and Smoluchowski's coagulation equation
International Nuclear Information System (INIS)
Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)
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
Ashlagi, Itai; Monderer, Dov; Tennenholtz, Moshe
2012-01-01
We introduce robust learning equilibrium. The idea of learning equilibrium is that learning algorithms in multi-agent systems should themselves be in equilibrium rather than only lead to equilibrium. That is, learning equilibrium is immune to strategic deviations: Every agent is better off using its prescribed learning algorithm, if all other agents follow their algorithms, regardless of the unknown state of the environment. However, a learning equilibrium may not be immune to non strategic m...
Numerical investigations of low-density nozzle flow by solving the Boltzmann equation
Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen
1995-01-01
A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
Ramachandran, Sanoop; Kumar, P. B. Sunil; Pagonabarraga, I.
2006-01-01
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the e...
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
Lattice Boltzmann model for wave propagation.
Zhang, Jianying; Yan, Guangwu; Shi, Xiubo
2009-08-01
A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation. PMID:19792280
Numerical Modelling of Electroosmotic Driven Flow in Nanoporous Media by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
Bo Li; Wenning Zhou; Yuying Yan; Zhiwu Han; Luquan Ren
2013-01-01
The lattice Bohzmann method was employed to simulate electroosmotic driven flow and Debye layer screening in conducting electrolyte around a porous structure with average size of 40 nm.The charge screening around the nanopores was investigated by solving the vector-superpositioned potential equilibrium distribution function and adding electro-kinetic force term to the evolution equation.In this intermediate case of moderate Debye length,the electrophoresis problem becomes complicated.The motion of the particles distorts the screening cloud,which becomes asymmetric,resulting in very complex interactions between the electrolyte,the screening cloud and the particle; but the Electroosmotic Flow (EOF) behaviour was still considered based on the Helmoholtz-Smoluchowski model with adaptation to fit nanoporous flow in the porous structure.In the present approach,the flow in the nanopores is directly modelled; the detailed flow information can be obtained by simplifying the repeated macrostructure.Due to the symmetry of the domain,the size of computational domain can be largely reduced by less repeated spherical nanoparticles.Each pore of the medium contains several lattice nodes on the simplified curved edges and potential gradients are produced by adjusting the zeta potential value.The velocity results for pressure-driven and EOF flows agree well with the analytical solutions and recent experimental results.In particular,the interface between solid particles and fluids,the influences of porosity,solid particle diameter,yield stress and electric parameters in EOF were investigated.The anti-adhesion effect of electroosmotic pumping eflect was evaluated,and the pulsed DC was applied in order to enhance the performance of the electroosmotic pumping.The results demonstrate that the present lattice Boltzmann model is capable of modelling flow through nanoporous media at certain restrictions while some results deviate from the predictions based on the macroscopic theories.
Nuclear Flow in Consistent Boltzmann Algorithm Models
Kortemeyer, G.; Daffin, F.; Bauer, W.
1995-01-01
We investigate the stochastic Direct Simulation Monte Carlo method (DSMC) for numerically solving the collision-term in heavy-ion transport theories of the Boltzmann-Uehling-Uhlenbeck (BUU) type. The first major modification we consider is changes in the collision rates due to excluded volume and shadowing/screening effects (Enskog theory). The second effect studied by us is the inclusion of an additional advection term. These modifications ensure a non-vanishing second virial and change the ...
Lattice Boltzmann Model and Geophysical Hydrodynamic Equation
Institute of Scientific and Technical Information of China (English)
冯士德; 杨京龙; 郜宪林; 季仲贞
2002-01-01
A lattice Boltzmann equation model in a rotating system is developed by introducing the Coriolis force effect.The geophysical hydrodynamic equation can be derived from this model. Numerical computations are performed to simulate the cylindrical annulus experiment and Benard convection. The numerical results have shown the flow behaviour of large-scale geostrophic current and Benard convection cells, which verifies the applicability of this model to both theory and experiment.
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.
The Boltzmann equation in the difference formulation
International Nuclear Information System (INIS)
First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.
Geometry of the restricted Boltzmann machine
Cueto, Maria Angelica; Morton, Jason; Sturmfels, Bernd
2009-01-01
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the first secant variety of the Segre variety of projective lines. We derive a dimension formula for the ...
Nonlocal Boltzmann theory of plasma channels
Energy Technology Data Exchange (ETDEWEB)
Yu, S.S.; Melendez, R.E.
1983-01-03
The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents.
Nonlocal Boltzmann theory of plasma channels
International Nuclear Information System (INIS)
The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents
Improved learning algorithms for restricted Boltzmann machines
Cho, Kyunghyun
2011-01-01
A restricted Boltzmann machine (RBM) is often used as a building block for constructing deep neural networks and deep generative models which have gained popularity recently as one way to learn complex and large probabilistic models. In these deep models, it is generally known that the layer-wise pretraining of RBMs facilitates finding a more accurate model for the data. It is, hence, important to have an efficient learning method for RBM. The conventional learning is mostly performed us...
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.
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
Ba, Yan; Liu, Haihu; Li, Qing; Kang, Qinjun; Sun, Jinju
2016-08-01
In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
Treumann, Rudolf; Baumjohann, Wolfgang
2014-08-01
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative T" claim.
Spherical galaxy models as equilibrium configurations in nonextensive statistics
Cardone, V F; Del Popolo, A
2011-01-01
Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the gravitational force contrasts with the underlying assumptions of Boltzmann statistics where the interactions among particles are assumed to be short ranged. A particular generalization of the classical Boltzmann formalism is available within the nonextensive context of Tsallis q -statistics, subject to non -additivity of the entropies of sub - systems. Assuming stationarity and isotropy in the velocity space, it is possible solving the generalized collsionless Boltzmann equation to derive the galaxy distribution function and density profile. We present a particular set of nonextensive models and investigate their dynamical and observable properties. As a test of the viability of this generalized context, we fit the rotation curve of M33 showing that the proposed approach leads to da...
Xue, Yongqiang; Ratner, Mark A.
2004-01-01
We analyze non-equilibrium current transport in molecular electronic devices, using as an example devices formed by two terphenyl dithiol molecules attached to gold electrodes. Using a first-principles based self-consistent matrix Green's function method, we show that the spatially resolved current density profiles and local electrochemical potential drops provide valuable information regarding the local field effect on molecular transport, which depend on the internal structure of the molecu...
International Nuclear Information System (INIS)
Numerous lattice Boltzmann (LB) methods have been proposed for solution of the convection-diffusion equations (CDE). For the 2D problem, D2Q9, D2Q5 or D2Q4 velocity models are usually used. When LB convection-diffusion models are used to solve a CDE coupled with Navier-Stokes equations, boundary conditions are found to be critically important for accurately solving the coupled simulations. Following the idea of a regularized scheme (Latt et al 2008 Phys. Rev.E 77 056703), a regularized boundary condition for solving a CDE is proposed. A simple extrapolation scheme is also proposed for the Neumann boundary condition. Spatial accuracies of three existing and the proposed boundary conditions are discussed in details. The numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady Taylor-Couette flow. Our studies show that the simplest D2Q4 model with terms of O(u) in the equilibrium distribution function is capable of obtaining results of equal accuracy as D2Q5 or D2Q9 models for the CDE. A slightly revised LB equation for solving a CDE that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows. The regularized boundary condition for solving the CDE has second-order spatial accuracy and it is the best one in terms of the spatial accuracy. The regularized scheme and non-equilibrium extrapolation scheme are applicable to handle both the Dirichlet and Neumann boundary conditions. For the Neumann boundary condition with zero flux, all the five boundary conditions are applicable to give accurate results and the bounce-back scheme is the simplest one.
Shizgal, Bernie D.
2011-05-01
The study of the solution of the linearized Boltzmann equation has a very long history arising from the classic work by Chapman and Cowling. For small departures from a Maxwellian, the nonlinear Boltzmann equation can be linearized and the transport coefficients calculated with the Chapman-Enskog approach. This procedure leads to a set of linear integral equations which are generally solved with the expansion of the departure from Maxwellian in Sonine polynomials. The method has been used successfully for many decades to compare experimental transport data in atomic gases with theory generally carried out for realistic atom-atom differential cross sections. There are alternate pseudospectral methods which involve the discretization of the distribution function on a discrete grid. This paper considers a pseudospectral method of solution of the linearized hard sphere Boltzmann equation for the viscosity in a simple gas. The relaxation of a small departure from a Maxwellian is also considered for the linear test particle problem with unit mass ratio which is compared with the relaxation for the linearized one component Boltzmann equation.
An efficient annealing in Boltzmann machine in Hopfield neural network
Kin, Teoh Yeong; Hasan, Suzanawati Abu; Bulot, Norhisam; Ismail, Mohammad Hafiz
2012-09-01
This paper proposes and implements Boltzmann machine in Hopfield neural network doing logic programming based on the energy minimization system. The temperature scheduling in Boltzmann machine enhancing the performance of doing logic programming in Hopfield neural network. The finest temperature is determined by observing the ratio of global solution and final hamming distance using computer simulations. The study shows that Boltzmann Machine model is more stable and competent in term of representing and solving difficult combinatory problems.
Rapid equilibrium sampling of all-atom peptides using a library-based polymer-growth approach
Mamonov, A B; Zuckerman, D M
2009-01-01
We adapted existing polymer growth strategies for equilibrium sampling of peptides described by modern atomistic forcefields with implicit solvent. The main novel feature of our approach is the use of pre-calculated statistical libraries of molecular fragments. The molecule is sampled by combining fragment configurations stored in the libraries. Ensembles generated from the independent libraries are reweighted to conform with the Boltzmann factor distribution of the forcefield describing the full molecule. The present study uses amino acids as fragments but the choice of molecular fragments is flexible. It is also possible to employ different implementations of the polymer growth formalism, which can greatly affect the ultimate efficiency. We describe several optimization techniques which led to significant efficiency improvements compared to Langevin dynamics for several peptides. We also describe potential future improvements, including a "multi-resolution" implementation of the approach.
Molnár, Etele; Rischke, Dirk H
2016-01-01
In Moln\\'ar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.
``Thermal'' and ``superthermal'' two-class structure of the personal income distribution
Yakovenko, Victor
2005-03-01
In Ref. [1] we proposed an analogy between the thermal Boltzmann-Gibbs probability distribution of energy in physics and the probability distribution of money in economics in statistical equilibrium. In Ref. [2] we find that the probability distribution of personal income in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (``thermal'') distribution, whereas the upper class (1-3% of population) has a Pareto power-law (``superthermal'') distribution. By analyzing the income data for 1983--2001 from IRS, we show that the ``thermal'' part is stationary in time, save for a gradual increase of the effective temperature, whereas the nonequilibrium ``superthermal'' tail swells and shrinks following the stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of the US population. [] [1] A. Dragulescu and V. M. Yakovenko, ``Statistical mechanics of money'', Eur. Phys. J. B 17, 723--729 (2000). [cond-mat/0001432] [] [2] A. C. Silva and V. M. Yakovenko, ``Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983--2001'', accepted to Europhysics Letters. [cond- mat/0406385
Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach
Freguglia, Paolo
2015-01-01
This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.
Lattice Boltzmann Simulation of One Particle Migrating in a Pulsating Flow in Microvessel
Qiu, Bing; Tan, Hui-Li; Li, Hua-Bing
2011-10-01
A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel. The particle is as big as a red blood cell, and the micro vessel is four times as wide as the diameter of the particle. It is found that Segré—Silberberg effect will not respond to the pulsation of the flow when the Reynolds number is relatively high. However, when the Reynolds number is low enough, Segré—Silberberg effect disappears. In the steady flow, different initial position leads to different equilibrium positions. In a pulsating flow, different frequencies of pulsation also cause different equilibrium positions. Particularly, when the frequency of pulsation is closed to the human heart rate, Segré—Silberberg effect presents again. The evolutions of velocity, rotation, and trajectory of the particle are investigated to find the dynamics of such abnormal phenomenon.
Lattice Boltzmann methods for moving boundary flows
Energy Technology Data Exchange (ETDEWEB)
Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 (Japan)
2012-04-01
The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)
Lattice Boltzmann methods for moving boundary flows
International Nuclear Information System (INIS)
The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)
Scattering theory of the linear Boltzmann operator
International Nuclear Information System (INIS)
In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.)
d'Eon, Eugene
2013-01-01
We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing medium with isotropic scattering. We consider both classical transport theory with exponentially-distributed free paths in arbitrary dimensions as well as a number of non-classical transport theories (non-exponential random flights) that describe a broader clas...
Online Semi-Supervised Learning with Deep Hybrid Boltzmann Machines and Denoising Autoencoders
Ororbia II, Alexander G.; Giles, C. Lee; Reitter, David
2015-01-01
Two novel deep hybrid architectures, the Deep Hybrid Boltzmann Machine and the Deep Hybrid Denoising Auto-encoder, are proposed for handling semi-supervised learning problems. The models combine experts that model relevant distributions at different levels of abstraction to improve overall predictive performance on discriminative tasks. Theoretical motivations and algorithms for joint learning for each are presented. We apply the new models to the domain of data-streams in work towards life-l...
Tsumura, Kyosuke; Kunihiro, Teiji
2012-01-01
We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., ...
Application of Boltzmann equation to electron transmission and seconary electron emission
International Nuclear Information System (INIS)
A method is presented for numerical treatment of integro-differential equation, based upon finite difference techniques. This method allows to formulate in a satisfactory manner the Boltzmann's equation applied to backscattering, transmission and secondary emission of metallic targets, avoiding must of the restrictive hypothesis, used until now in these models. For aluminium, the calculated energy spectra, angular distribution, transmission and backscattering coefficients, and secondary emission yield, are found to be in good agreement with experiment
Ma, John Z. G.; St.-Maurice, J.-P.
2015-06-01
By applying a backward mapping technique, we solve the Boltzmann equation to investigate the effects of ion-neutral collisions on the ion velocity distribution and related transport properties in cylindrically symmetric, uniformly charged auroral ionosphere. Such a charge geometry introduces a radial electric field which increases linearly with distance from the axis of symmetry. In order to obtain complete analytical solutions for gaining physical insights into more complicated problems, we have substituted a relaxation collision model for the Boltzmann collision integral in the Boltzmann equation. Our calculations show that collisions drive the velocity distribution to a "horseshoe" shape after a few collision times. This feature extends to all radial positions as long as the electric field keeps increasing linearly versus radius. If the electric field is introduced suddenly, there is a transition from the collision-free pulsating Maxwellian distributions obtained in previous work (Ma and St.-Maurice, J. Geophys. Res., 113:A05312, 2008) to the "horseshoe" shapes on a time scale of within the few collision times. We also show how the transport properties evolve in a similar fashion, from oscillating to a non-oscillating features over the same time interval.
Convolution Inequalities for the Boltzmann Collision Operator
Alonso, Ricardo J.; Carneiro, Emanuel; Gamba, Irene M.
2010-09-01
We study integrability properties of a general version of the Boltzmann collision operator for hard and soft potentials in n-dimensions. A reformulation of the collisional integrals allows us to write the weak form of the collision operator as a weighted convolution, where the weight is given by an operator invariant under rotations. Using a symmetrization technique in L p we prove a Young’s inequality for hard potentials, which is sharp for Maxwell molecules in the L 2 case. Further, we find a new Hardy-Littlewood-Sobolev type of inequality for Boltzmann collision integrals with soft potentials. The same method extends to radially symmetric, non-increasing potentials that lie in some {Ls_{weak}} or L s . The method we use resembles a Brascamp, Lieb and Luttinger approach for multilinear weighted convolution inequalities and follows a weak formulation setting. Consequently, it is closely connected to the classical analysis of Young and Hardy-Littlewood-Sobolev inequalities. In all cases, the inequality constants are explicitly given by formulas depending on integrability conditions of the angular cross section (in the spirit of Grad cut-off). As an additional application of the technique we also obtain estimates with exponential weights for hard potentials in both conservative and dissipative interactions.
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
Thermal equation of state for lattice Boltzmann gases
Institute of Scientific and Technical Information of China (English)
Ran Zheng
2009-01-01
The Galilean invaxiance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model axe proposed together with their rigorous theoretical background. From the viewpoint of group invariance,recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.
Thermal equation of state for lattice Boltzmann gases
Ran, Zheng
2009-06-01
The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.
Droplet collision simulation by multi-speed lattice Boltzmann method
Lycett-Brown, D.; Karlin, I.V.; Luo, K. H.
2011-01-01
Realization of the Shan-Chen multiphase flow lattice Boltzmann model is considered in the framework of the higher-order Galilean invariant lattices. The present multiphase lattice Boltzmann model is used in two dimensional simulation of droplet collisions at high Weber numbers. Results are found to be in a good agreement with experimental findings.
A probabilistic view on the general relativistic Boltzmann equation
Bailleul, Ismael
2011-01-01
A new probalistic approach to general relativistic kinetic theory is proposed. The general relativistic Boltzmann equation is linked to a new Markov process in a completely intrinsic way. This treatment is then used to prove the causal character of the relativistic Boltzmann model.
The possible resolution of Boltzmann brains problem in phantom cosmology
Astashenok, Artyom V.; Yurov, Artyom V.; Yurov, Valerian V.
2013-01-01
We consider the well-known Boltzmann brains problem in frames of simple phantom energy models with little rip and big rip singularity. It is showed that these models (i) satisfy to observational data and (ii) may be free from Boltzmann brains problem. The human observers in phantom models can exist only in during for a certain period $t
Transition flow ion transport via integral Boltzmann equation
International Nuclear Information System (INIS)
A new approach is developed to solve the Integral Boltzmann Equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion/neutral mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion beam extractions from high pressure sources. Theoretical predictions are tested through an experiment in which an atmospheric pressure ion source is coupled to a high vacuum energy analyser. Excellent agreement results for configurations in which the radial velocity remains small. Velocity distributions are applied to predicting the efficiency of coupling an atmospheric pressure ion source to a quadrupole mass spectrometer and results clearly indicate the most desirable extracting configuration. A method is devised to calculate ion-molecule hard sphere collision cross sections for easily fragmented organic ions
Monte Carlo variance reduction approaches for non-Boltzmann tallies
International Nuclear Information System (INIS)
Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed
Zandler, G.; Vass, E.
1988-10-01
The time evolution of the distribution function of hot electrons interacting with ionized impurities, acoustic and polar optical phonons is studied in terms of the Boltzmann integral equation. The calculated distribution functions are used to determine the charge carrier drift velocity, the average energy as well as the average momentum and energy loss rates as a function of time at constant values of the lattice temperature and charge carrier density. The stationary non-equilibrium values of these quantities are found to be established after 3-4 ps.
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.
International Nuclear Information System (INIS)
A Boltzmann plot for many iron atomic lines having excitation energies of 3.3–6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3–4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: ► This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. ► A Boltzmann distribution is studied among iron lines of various excitation levels. ► We find an overpopulation of the high-lying energy levels from the normal distribution. ► It is caused through Penning-type collision of iron atom with argon metastable atom.
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.
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.
International Nuclear Information System (INIS)
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
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.
SIMULATION OF TURBULENT FLOW OVER A BACKWARD FACING STEP USING LATTICE BOLTZMANN METHOD
Directory of Open Access Journals (Sweden)
NOR AZWADI C. SIDIK
2013-12-01
Full Text Available The lattice Boltzmann scheme for solving the equations governing the flow of fluids has become increasingly popular in recent years. In this method, a probability distribution function for the velocity of fluid elements is computed at each grid point, which contrasts with more established computational fluid dynamics methods, which solve for an average velocity. In this paper the effectiveness of the lattice Boltzmann equation (LBE as a computational tool for performing large-eddy simulations (LES of turbulent flows was assessed. Three- dimensional turbulent flow over backward facing step was considered for this investigation. LBE-LES and Navier Stokes Direct Numerical Simulation (NS-DNS results for this case has been compared and it was observed that the LBE-LES simulation is in good agreement with other computational simulations.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, M.F.
2013-06-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
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 ...
Kang, XiuYing; Su, YanPing
2012-10-01
Cross-flows around two, three and four circular cylinders in tandem, side-by-side, isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5 D, where D is the identical circular cylinder diameter. The wake patterns, pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases. The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures, which are interesting, complex and useful for practical applications. This study provides a useful database to validate the simplicity, accuracy and robustness of the Lattice Boltzmann method.
Regularized lattice Boltzmann model for a class of convection-diffusion equations.
Wang, Lei; Shi, Baochang; Chai, Zhenhua
2015-10-01
In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. PMID:26565368
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.
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...
Autotagging music with conditional restricted Boltzmann machines
Mandel, Michael; Larochelle, Hugo; Bengio, Yoshua
2011-01-01
This paper describes two applications of conditional restricted Boltzmann machines (CRBMs) to the task of autotagging music. The first consists of training a CRBM to predict tags that a user would apply to a clip of a song based on tags already applied by other users. By learning the relationships between tags, this model is able to pre-process training data to significantly improve the performance of a support vector machine (SVM) autotagging. The second is the use of a discriminative RBM, a type of CRBM, to autotag music. By simultaneously exploiting the relationships among tags and between tags and audio-based features, this model is able to significantly outperform SVMs, logistic regression, and multi-layer perceptrons. In order to be applied to this problem, the discriminative RBM was generalized to the multi-label setting and four different learning algorithms for it were evaluated, the first such in-depth analysis of which we are aware.
Lattice Boltzmann 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.
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. PMID:26986435
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.
Scattering theory for the linearized Boltzmann equation
International Nuclear Information System (INIS)
Scattering theory for a cloud of mutually non-interacting particles that in its passage through R3 undergoes absorption and production in a region D is contained in R3 through interaction with the medium in D is investigated. The motion for such a model is given by the linearized Boltzmann equation. Let n(x,v,t) denote the particle density in phase space at time t. The dynamics is described by a 1-parameter semigroup, W(t), which is in general not isometric. The existence of the wave operators Ω/sub +/ = s - lim W0(-t)W(t) (t →+infinity) and Ω/sub -/ = s - lim W(-t)W0(t) (t →-infinity), where W0(t) is the free dynamics, is examined at length
Thermal lattice Boltzmann method for complex microflows
Yasuoka, Haruka; Kaneda, Masayuki; Suga, Kazuhiko
2016-07-01
A methodology to simulate thermal fields in complex microflow geometries is proposed. For the flow fields, the regularized multiple-relaxation-time lattice Boltzmann method (LBM) is applied coupled with the diffusive-bounce-back boundary condition for wall boundaries. For the thermal fields, the regularized lattice Bhatnagar-Gross-Krook model is applied. For the thermal wall boundary condition, a newly developed boundary condition, which is a mixture of the diffuse scattering and constant temperature conditions, is applied. The proposed set of schemes is validated by reference data in the Fourier flows and square cylinder flows confined in a microchannel. The obtained results confirm that it is essential to apply the regularization to the thermal LBM for avoiding kinked temperature profiles in complex thermal flows. The proposed wall boundary condition is successful to obtain thermal jumps at the walls with good accuracy.
Tsallis, Constantino
2006-03-01
Boltzmann-Gibbs ( BG) statistical mechanics is, since well over one century, successfully used for many nonlinear dynamical systems which, in one way or another, exhibit strong chaos. A typical case is a classical many-body short-range-interacting Hamiltonian system (e.g., the Lennard-Jones model for a real gas at moderately high temperature). Its Lyapunov spectrum (which characterizes the sensitivity to initial conditions) includes positive values. This leads to ergodicity, the stationary state being thermal equilibrium, hence standard applicability of the BG theory is verified. The situation appears to be of a different nature for various phenomena occurring in living organisms. Indeed, such systems exhibit a complexity which does not really accommodate with this standard dynamical behavior. Life appears to emerge and evolve in a kind of delicate situation, at the frontier between large order (low adaptability and long memory; typically characterized by regular dynamics, hence only nonpositive Lyapunov exponents) and large disorder (high adaptability and short memory; typically characterized by strong chaos, hence at least one positive Lyapunov exponent). Along this frontier, the maximal relevant Lyapunov exponents are either zero or close to that, characterizing what is currently referred to as weak chaos. This type of situation is shared by a great variety of similar complex phenomena in economics, linguistics, to cite but a few. BG statistical mechanics is built upon the entropy S=-k∑plnp. A generalization of this form, S=k(1-∑piq)/(q-1) (with S=S), has been proposed in 1988 as a basis for formulating what is nowadays currently called nonextensive statistical mechanics. This theory appears to be particularly adapted for nonlinear dynamical systems exhibiting, precisely, weak chaos. Here, we briefly review the theory, its dynamical foundation, its applications in a variety of disciplines (with special emphasis to living systems), and its connections with
International Nuclear Information System (INIS)
Vortex patches of intense density generated by the diocotron instability in a magnetized pure electron plasma merge each other accompanied by the production of filaments and finally relax to a bell shape distribution surrounded by a halo of low-density electrons. Here we reexamine the vortical dynamics in terms of the time evolution of the power spectrum in the mode-number space. Triggered by the instability, the initial axisymmetric ring distribution is deformed and torn into mesoscopic blobs, and a distribution of radial flux is generated around the blobs. In the merging process between vortex patches, the energy spectrum expands toward higher mode-number space, while the dominant mode shifts downward to lower mode numbers as this process proceeds. The turbulent period characterized by the repeated mergers is accompanied by a fast reduction of the enstrophy. During this relaxation the energy and the angular momentum of the whole plasma system remain conserved. In a slow process after the rapid relaxation a convex profile appears in the density distribution accompanied by the recovery of a symmetric distribution of the azimuthal flux. The spectra in the final state concentrate at symmetric modes with a slight contribution from orbiting motion of the plasma column
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.
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.
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
International Nuclear Information System (INIS)
This work studies the behaviour of radionuclides when it produce a desintegration activity,decay and the isotopes stable creation. It gives definitions about the equilibrium between activity of parent and activity of the daughter, radioactive decay,isotope stable and transient equilibrium and maxim activity time. Some considerations had been given to generators that permit a disgregation of two radioisotopes in equilibrium and its good performance. Tabs
Guo, Xiaohui
Fluid and thermal problems are widely encountered in micro/nano-scale devices, the characteristic lengths of which are from hundreds of microns down to tens of nanometers. A great number of such devices involve fundamental components like microchannels, capillaries, membranes and cantilever beams. Continuum assumptions that lead to classical governing equations such as Navier-Stokes equations and Fourier Laws break down when the characteristic size shrinks by an order of millions. In addition, conventional sensors, actuators and controllers turn to be insufficient to depict the flow, thermal, or electrical fields in micro-devices without impacting the original conditions greatly. Therefore, the development of numerical methods becomes indispensable in design and performance analysis of micro-electro-mechanical systems (MEMS). The main goal of this PhD research is the development, implementation and application of comprehensive deterministic Boltzmann-ESBGK modeling framework to micro-scale fluid-thermal phenomena. Investigation of gas flows in short rectangular microchannels has been carried out to understand the rarefaction effects on the reduced mass-flow-rate as well as the non-equilibrium effects on the temperature components. At high Knudsen numbers, the reduced mass-flow-rate only depends on the pressure ratio and the temperature components deviate at the channel exit. For gas flows in long microchannels with and without constrictions, the Navier-Stokes equations with first-order slip boundary conditions are solved. Numerical results accurately predict the entrance pressure drop comparing to high-resolution experimental data using pressure-sensitive-paint (PSP). Simultions show clearly that the compressibility effects become less important than the rarefaction effects at low pressures. The coupled gas-phonon Boltzmann solver has been developed. The reduced distribution functions are used in the two-dimensional code to reduce the computational cost. The
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.
International Nuclear Information System (INIS)
Calculations and comparisons with experimental data indicate that the Boltzmann transport equation provides a comprehensive treatment of the general ion implantation problem. The primary ion distribution in a multilayer target can be calculated directly and is found to be in good agreement with experiments. The transport equation predicts the spatial distribution of recoils and thus provides the theoretical information needed to determine the fractional atomic displacement necessary for amorphization of silicon and the degree of stoichiometric imbalance that is produced when energetic ions are incident on a target having more than one type of host atom
Range profile calculations by direct numerical solution of linearized Boltzmann transport equations
International Nuclear Information System (INIS)
A new method to determine the depth distributions of implanted ions and recoil target atoms in amorphous targets is developed. Our procedure is based on the direct numerical solution of one-dimensional linearized Boltzmann transport equations for the scalar fluxes of the ions and the recoils. We consider characteristic examples of ion implantation into homogeneous and layered targets. The profiles calculated by the new method are compared with range distributions obtained from TRIM Monte Carlo simulations. Our program BOTE is up to two orders of magnitude faster than the TRIM calculations. (author)
Pakpicha Pathompituknukoon; Purich Khingthong; Komsan Suriya
2012-01-01
This study applies CGE model to investigate the effects of rising tourism income and fading agricultural income in Mae Kam Pong village in Chiang Mai, Thailand, on 4 issues: the expansion and recession of major economic sectors, income distribution, social welfare of the village, and welfare of the poorest households. Simulations show that services and construction sectors will expand while tea, commerce and tourism sectors will face the recession. Tourism sector will fade out from the villag...
Ultrafast non-equilibrium dynamics in conventional and unconventional superconductors
Energy Technology Data Exchange (ETDEWEB)
Schnyder, Andreas; Manske, Dirk [Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, D-70569 Stuttgart (Germany)
2010-07-01
We present simulations of the ultrafast dynamics of conventional and unconventional superconductors using density-matrix theory. In particular, we study how the optical conductivity evolves in response to ultrashort optical pulses in the frequency range of the superconducting gap, i.e., in the terahertz regime. The dominant relaxation process is assumed to be due to electron-phonon collisions. Employing a second order cluster expansion and assuming that the phonons remain equilibrated, Boltzmann type equations for the dynamics of the quasiparticle occupations and coherences are derived. We apply our theoretical model to the study of non-equilibrium dynamics in the two-gap superconductor MgB{sub 2}.
Pre-equilibrium decay processes in energetic heavy ion reactions
International Nuclear Information System (INIS)
The Boltzmann master equation (BME) is defined for application to precompound decay in heavy ion reactions in the 10 100 MeV/nucleon regime. Predicted neutron spectra are compared with measured results for central collisions of 20Ne and 12C with 165Ho target nuclei. Comparisons are made with subthreshold π0 yields in heavy ion reactions between 35 and 84 MeV/nucleon, and with the π0 spectra. The BME is found to be an excellent tool for investigating these experimentally observed aspects of non-equilibrium heavy ion reactions. 18 refs., 8 figs
Simplex characterization of equilibrium
International Nuclear Information System (INIS)
Minimization of the reaction isotherm absolute value by the sequential simplex method may be used to characterize the equilibrium valence state distribution of plutonium in aqueous solutions. Sequential simplex procedure is an empirical method of locating maxima or minima in the response of a function of several variables. Where the objective function is entirely mathematical, a computer may be used to perform the simplex operations in a rapid and accurate manner, so that maxima and minima can often be located quickly and easily. The disproportionation of tetravalent plutonium is considered to be the consequence of two sequential reactions: 2Pu4+ + 2HOH = Pu3+ + PuO2+ + 4H+ P (1). Pu4+ + PuO2+ = Pu3+ + PuO2+ Q (2). If P is the frequency of occurrence of Eq. (1), and Q is the frequency of occurrence of Eq. (2), then it is assumed, that P=Q, and Eqs (1) and (2) may be added directly. 3Pu4+ + 2HOH = 2Pu3+ + PuO22+ + 4H+ (3). The persistence of pentavalent plutonium in aqueous plutonium solutions suggests that reactions 1 and 2 are not of equal frequency, and that their proportion for purposes of addition is not exactly equal to 1:1. (T.I.)
International Nuclear Information System (INIS)
Application of the lattice Boltzmann method (LBM) recently proposed by Asinari et al. [Asinari P, Mishra SC, Borchiellini R. A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium. Numer Heat Transfer B 2010; 57:126–146] is extended to the analysis of transport of collimated radiation in a planar participating medium. To deal with azimuthally symmetric radiation in planar medium, a new lattice structure for the LBM is used. The transport of the collimated component in the medium is analysed by two different, viz., flux splitting and direct approaches. For different angles of incidence of the collimated radiation, the LBM formulation is tested for the effects of the extinction coefficient, the anisotropy factor, and the boundary emissivities on heat flux and emissive power distributions. Results are compared with the benchmark results obtained using the finite volume method. Both the approaches in LBM provide accurate results. -- Highlights: ► Transport of collimated radiation in participating media is studied. ► Usage of Lattice Boltzmann method (LBM) is extended in this study. ► In LBM, flux splitting and direct approaches are proposed. ► Effects of various parameters are studied on heat flux and temperature profiles. ► In all cases, LBM provides correct results.
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...
Langevin theory of fluctuations in the discrete Boltzmann equation
Gross, M; Varnik, F; Adhikari, R
2010-01-01
The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, the fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.
An extension of the Boltzmann relation to collisionless magnetized plasma
International Nuclear Information System (INIS)
The neutralization of positive space charge is studied for density perturbations of limited spatial extent in a collisionfree magnetized plasma. It is found that a local density maximum gets a positive potential which depends only on the ambient electron temperature Te and the relative increase in density ne/ne0. For small density increases, below 5%, the resulting relation between potential and plasma density agrees closely with the Boltzmann relation, which applies in the presence of collisions. For larger density increases, the difference from the Boltzmann relation rapidly becomes large, e.g. a factor 2 for a 50% density increase, and a factor 3 for a 100% density increase. The result constitutes (1) a justification for using the Boltzmann relation also in collisionless magnetized plasma, provided that the density perturbations are small, and (2) a general relation which replaces the Boltzmann relation for large-amplitude perturbations. (au)
Fluctuations around equilibrium laws in ergodic continuous-time random walks
Schulz, Johannes H. P.; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
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...
A Boltzmann model for rod alignment and schooling fish
Carlen, Eric A.; Carvalho, Maria C.; Degond, Pierre; Wennberg, Bernt
2014-01-01
We consider a Boltzmann model introduced by Bertin, Droz and Greegoire as a binary interaction model of the Vicsek alignment interaction. This model considers particles lying on the circle. Pairs of particles interact by trying to reach their mid-point (on the circle) up to some noise. We study the equilibria of this Boltzmann model and we rigorously show the existence of a pitchfork bifurcation when a parameter measuring the inverse of the noise intensity crosses a critical threshold. The an...
Advanced Mean Field Theory of Restricted Boltzmann Machine
Huang, Haiping; Toyoizumi, Taro
2015-01-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message passing based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those...
Linearized Boltzmann Equation and Hydrodynamics for Granular Gases
Brey, J. Javier; Dufty, James W.; Ruiz-Montero, M. J.
2003-01-01
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as the basis for a hydrodynamic description. Hydrodynamics is defined in terms of the spectrum of the generator for the dynamics of the linearized Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are calculated in the long wavelength limit....
A new lattice Boltzmann model for incompressible magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
Chen Xing-Wang; Shi Bao-Chang
2005-01-01
Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.
A Simple Method for Modeling Collision Processes in Plasmas with a Kappa Energy Distribution
Hahn, M.; Savin, D. W.
2015-08-01
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 3%. This is equal to or better than the accuracy of rate coefficients generated using “reverse-engineering” methods, which attempt to extract the needed cross sections from the published Maxwellian rate coefficient data and then reconvolve the extracted cross sections with the desired kappa distribution. Our approach of summing Maxwellian rate coefficients is easy to implement using existing spectral analysis software. Moreover, the weights in the sum of the Maxwell-Boltzmann distribution rate coefficients can be found for any value of the parameter κ, thereby enabling one to model plasmas with a time-varying κ. Tabulated Maxwellian fitting parameters are given for specific values of κ from 1.7 to 100. We also provide polynomial fits to these parameters over this entire range. Several applications of our technique are presented, including the plasma equilibrium charge state distribution (CSD), predicting line ratios, modeling the influence of electron impact multiple ionization on the equilibrium CSD of kappa-distribution plasmas, and calculating the time-varying CSD of plasmas during a solar flare.
Lattice Boltzmann modeling of three-phase incompressible flows
Liang, H.; Shi, B. C.; Chai, Z. H.
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
Lattice Boltzmann modeling of three-phase incompressible flows.
Liang, H; Shi, B C; Chai, Z H
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems. PMID:26871191
Lattice Boltzmann method for one-dimensional vector radiative transfer.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2016-02-01
A one-dimensional vector radiative transfer (VRT) model based on lattice Boltzmann method (LBM) that considers polarization using four Stokes parameters is developed. The angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by LBM. LBM has such attractive properties as simple calculation procedure, straightforward and efficient handing of boundary conditions, and capability of stable and accurate simulation. To validate the performance of LBM for vector radiative transfer, four various test problems are examined. The first case investigates the non-scattering thermal-emitting atmosphere with no external collimated solar. For the other three cases, the external collimated solar and three different scattering types are considered. Particularly, the LBM is extended to solve VRT in the atmospheric aerosol system where the scattering function contains singularities and the hemisphere space distributions for the Stokes vector are presented and discussed. The accuracy and computational efficiency of this algorithm are discussed. Numerical results show that the LBM is accurate, flexible and effective to solve one-dimensional polarized radiative transfer problems. PMID:26906779
Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls.
Šamaj, Ladislav; Trizac, Emmanuel
2016-01-01
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system). PMID:26871116
Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow
Huang, Rongzong
2016-01-01
In this work, a third-order Chapman-Enskog analysis of the multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for multiphase flow is performed for the first time. The leading terms on the interaction force, consisting of an anisotropic and an isotropic term, are successfully identified in the third-order macroscopic equation recovered by the lattice Boltzmann equation (LBE), and then new mathematical insights into the pseudopotential LB model are provided. For the third-order anisotropic term, numerical tests show that it can cause the stationary droplet to become out-of-round, which suggests the isotropic property of the LBE needs to be seriously considered in the pseudopotential LB model. By adopting the classical equilibrium moment or setting the so-called "magic" parameter to 1/12, the anisotropic term can be eliminated, which is found from the present third-order analysis and also validated numerically. As for the third-order isotropic term, when and only when it is considered, a...
Relaxation of hot and massive tracers using numerical solutions of the Boltzmann equation
Khurana, Saheba; Thachuk, Mark
2016-03-01
A numerical method using B-splines is used to solve the linear Boltzmann equation describing the energy relaxation of massive tracer particles moving through a dilute bath gas. The smooth and rough hard sphere and Maxwell molecule models are used with a variety of mass ratios and initial energies to test the capability of the numerical method. Massive tracers are initialized with energies typically found in energy loss experiments in mass spectrometry using biomolecules. The method is also used to examine the applicability of known expressions for the kinetic energy decay from the Fokker-Planck equation for the Rayleigh gas, where we find that results are generally good provided that the initial energy is properly bounded. Otherwise, the energy decay is not constant and a more complex behaviour occurs. The validity of analytical expressions for drag coefficients for spherical particles under specular and diffuse scattering is also tested. We find such expressions are generally good for hard spheres but cannot account, as expected, for the softer repulsive walls of the Maxwell (and real) molecules. Overall, the numerical method performed well even when tracers more than 400 times as massive as the bath were initialized with energies very far from equilibrium. This is a range of applicability beyond many of the standard methods for solving the Boltzmann equation.
Relaxation of hot and massive tracers using numerical solutions of the Boltzmann equation.
Khurana, Saheba; Thachuk, Mark
2016-03-14
A numerical method using B-splines is used to solve the linear Boltzmann equation describing the energy relaxation of massive tracer particles moving through a dilute bath gas. The smooth and rough hard sphere and Maxwell molecule models are used with a variety of mass ratios and initial energies to test the capability of the numerical method. Massive tracers are initialized with energies typically found in energy loss experiments in mass spectrometry using biomolecules. The method is also used to examine the applicability of known expressions for the kinetic energy decay from the Fokker-Planck equation for the Rayleigh gas, where we find that results are generally good provided that the initial energy is properly bounded. Otherwise, the energy decay is not constant and a more complex behaviour occurs. The validity of analytical expressions for drag coefficients for spherical particles under specular and diffuse scattering is also tested. We find such expressions are generally good for hard spheres but cannot account, as expected, for the softer repulsive walls of the Maxwell (and real) molecules. Overall, the numerical method performed well even when tracers more than 400 times as massive as the bath were initialized with energies very far from equilibrium. This is a range of applicability beyond many of the standard methods for solving the Boltzmann equation. PMID:26979675
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).
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere. PMID:26382548
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...
Marcozzi, M.; Nota, A.
2016-03-01
We consider a test particle moving in a random distribution of obstacles in the plane, under the action of a uniform magnetic field, orthogonal to the plane. We show that, in a weak coupling limit, the particle distribution behaves according to the linear Landau equation with a magnetic transport term. Moreover, we show that, in a low density regime, when each obstacle generates an inverse power law potential, the particle distribution behaves according to the linear Boltzmann equation with a magnetic transport term. We provide an explicit control of the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. We compare these results with those ones obtained for a system of hard disks in Bobylev et al. (Phys Rev Lett 75:2, 1995), which show instead that the memory effects are not negligible in the Boltzmann-Grad limit.
Equilibrium solubilities of iodine vapor in water
International Nuclear Information System (INIS)
Equilibrium solubilities of iodine vapor in water were measured by introducing iodine vapor, in equilibrium with solid iodine, into water and by circulating it in a closed system, and Henry's law constants were determined. Equilibrium distributions of iodine vapor between a gas phase and an aqueous phase were also measured by another method, and partition coefficients were determined. The solubilities of iodine vapor in water estimated from both the Henry's law constants and the partition coefficients are compared with those of solid iodine reported in the literature. Thermodynamic parameters for the hydration of iodine vapor are evaluated experimentally. (author)
International Nuclear Information System (INIS)
We propose to check and validate the approximations made in dissipative quantum transport (QT) simulations solved in the Non-equilibrium Green's Function formalism by comparing them with the exact solution of the linearized Boltzmann Transport Equation (LB) in the stationary regime. For that purpose, we calculate the phonon-limited electron and hole mobility in bulk Si and ultra-scaled Si nanowires for different crystal orientations 〈100〉, 〈110〉, and 〈111〉. In both QT and LB simulations, we use the same sp3d5s* tight-binding model to describe the electron/hole properties and the same valence-force-field approach to account for the phonon properties. It is found that the QT simplifications work well for electrons, but are less accurate for holes, where a renormalization of the phonon scattering strength is proved useful to improve the results
Rhyner, Reto; Luisier, Mathieu
2013-12-01
We propose to check and validate the approximations made in dissipative quantum transport (QT) simulations solved in the Non-equilibrium Green's Function formalism by comparing them with the exact solution of the linearized Boltzmann Transport Equation (LB) in the stationary regime. For that purpose, we calculate the phonon-limited electron and hole mobility in bulk Si and ultra-scaled Si nanowires for different crystal orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩. In both QT and LB simulations, we use the same sp3d5s* tight-binding model to describe the electron/hole properties and the same valence-force-field approach to account for the phonon properties. It is found that the QT simplifications work well for electrons, but are less accurate for holes, where a renormalization of the phonon scattering strength is proved useful to improve the results.
On the search of more stable second-order lattice-Boltzmann schemes in confined flows
Golbert, D. R.; Blanco, P. J.; Clausse, A.; Feijóo, R. A.
2015-08-01
The von Neumann linear analysis, restricted by a heuristic selection of wave-number vectors was applied to the search of explicit lattice Boltzmann schemes which exhibit more stability than existing methods. The relative stability of the family members of quasi-incompressible collision kernels, for the Navier-Stokes equations in confined flows, was analyzed. The linear stability analysis was simplified by assuming a uniform velocity level over the whole domain, where only the wave numbers of the first harmonic normal to the flow direction were permitted. A singular equilibrium function that maximizes the critical velocity level was identified, which was afterwards tested in particular cases of confined flows of interest, validating the resulting procedure.
Ripszam, Matyas; Haglund, Peter
2015-02-01
Dissolved organic carbon (DOC) plays a key role in determining the environmental fate of semivolatile organic environmental contaminants. The goal of the present study was to develop a method using commercially available hardware to rapidly characterize the sorption properties of DOC in water samples. The resulting method uses negligible-depletion direct immersion solid-phase microextraction (SPME) and gas chromatography-mass spectrometry. Its performance was evaluated using Nordic reference fulvic acid and 40 priority environmental contaminants that cover a wide range of physicochemical properties. Two SPME fibers had to be used to cope with the span of properties, 1 coated with polydimethylsiloxane and 1 coated with polystyrene divinylbenzene polydimethylsiloxane, for nonpolar and semipolar contaminants, respectively. The measured DOC-water distribution constants showed reasonably good reproducibility (standard deviation ≤ 0.32) and good correlation (R(2) = 0.80) with log octanol-water partition coefficients for nonpolar persistent organic pollutants. The sample pretreatment is limited to filtration, and the method is easy to adjust to different DOC concentrations. These experiments also utilized the latest SPME automation that largely decreases total cycle time (to 20 min or shorter) and increases sample throughput, which is advantageous in cases when many samples of DOC must be characterized or when the determinations must be performed quickly, for example, to avoid precipitation, aggregation, and other changes of DOC structure and properties. The data generated by this method are valuable as a basis for transport and fate modeling studies. PMID:25393710
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.
DIAGNOSIS OF FINANCIAL EQUILIBRIUM
Directory of Open Access Journals (Sweden)
SUCIU GHEORGHE
2013-04-01
Full Text Available The analysis based on the balance sheet tries to identify the state of equilibrium (disequilibrium that exists in a company. The easiest way to determine the state of equilibrium is by looking at the balance sheet and at the information it offers. Because in the balance sheet there are elements that do not reflect their real value, the one established on the market, they must be readjusted, and those elements which are not related to the ordinary operating activities must be eliminated. The diagnosis of financial equilibrium takes into account 2 components: financing sources (ownership equity, loaned, temporarily attracted. An efficient financial equilibrium must respect 2 fundamental requirements: permanent sources represented by ownership equity and loans for more than 1 year should finance permanent needs, and temporary resources should finance the operating cycle.
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.
Hammou, H.; Ginzburg, I.; Boulerhcha, M.
2011-06-01
We develop two-relaxation-times Lattice Boltzmann schemes (TRT) with two relaxation functions Λ±(r→,t) for solving highly non-linear equations for groundwater modeling in d-dimensions, namely, the Richards equation for water content distribution θ(r→,t) in unsaturated flow and the associated transport equation for solute concentration C(r→,t), advected by the local Darcian water flux. The method is verified against the analytical solutions and the HYDRUS code where the TRT schemes behave more robustly for small diffusion coefficients and sharp infiltration profiles. The focus is on the stability and efficiency of two transport schemes. The first scheme conventionally prescribes C for diffusive flux equilibrium variable while conserving θC. The second scheme prescribes θC for both variables, expecting to retain the stable parameter areas and velocity amplitudes recently predicted by linear von Neumann stability analysis. We show that the first scheme reduces the stable diffusion range, e.g. from Λ-/ d to θΛ-/ d for simplest velocity sets, but it also modifies the linearized numerical diffusion, from - Λ-UαUβ to - θΛ-UαUβ, giving rise to possible enhancement of stable velocity U2, max by a factor 1/ θ. This analysis indicates that the first scheme is most efficient for infiltration into dry soil. When the product Λ+Λ- is kept constant, we find a good agreement between the attainable velocity and our predictions providing that Λ- does not exceed ≈5. Otherwise, approaching two opposite stability limits, Λ+ → 0 when Λ- → ∞ , the stable velocity amplitude drastically falls for the two transport TRT schemes. At the same time, their BGK submodels Λ+ = Λ- may keep the optimal stability for diffusion-dominant problems but their boundary and bulk approximations are completely destroyed. The analysis presented here may serve as a starting point for construction of the suitable equilibrium transformations, based on the analytical stability
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
Affine General Equilibrium Models
Bjørn Eraker
2008-01-01
No-arbitrage models are extremely flexible modelling tools but often lack economic motivation. This paper describes an equilibrium consumption-based CAPM framework based on Epstein-Zin preferences, which produces analytic pricing formulas for stocks and bonds under the assumption that macro growth rates follow affine processes. This allows the construction of equilibrium pricing formulas while maintaining the same flexibility of state dynamics as in no-arbitrage models. In demonstrating the a...
Computing Equilibrium Chemical Compositions
Mcbride, Bonnie J.; Gordon, Sanford
1995-01-01
Chemical Equilibrium With Transport Properties, 1993 (CET93) computer program provides data on chemical-equilibrium compositions. Aids calculation of thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93/PC is version of CET93 specifically designed to run within 640K memory limit of MS-DOS operating system. CET93/PC written in FORTRAN.
hanjoon michael, jung/j
2010-01-01
We propose a revised version of the perfect Bayesian equilibrium in general multi-period games with observed actions. In finite games, perfect Bayesian equilibria are weakly consistent and subgame perfect Nash equilibria. In general games that allow a continuum of types and strategies, however, perfect Bayesian equilibria might not satisfy these criteria of rational solution concepts. To solve this problem, we revise the definition of the perfect Bayesian equilibrium by replacing Bayes' rule ...
Symmetry-energy dependence of the dynamical dipole mode in the Boltzmann-Uehling-Uhlenbeck model
Ye, S Q; Ma, Y G; Shen, W Q
2013-01-01
Using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we have studied the connection between the symmetry energy and features of the dynamical dipole mode in fusion reactions with charge-asymmetric entrance channel. The yield and angular distribution of the prompt photon emission are extracted by a bremsstrahlung approach. The experimental data of $^{36}$Ar+$^{96}$Zr at 16 MeV/nucleon and $^{32}$S + $^{100}$Mo at 9.3 MeV/nucleon are compared with IBUU model calculations, and the soft symmetry energy is found to describe the data reasonably well.
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.
The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates
Marklof, Jens
2010-01-01
The dynamics of a point particle in a periodic array of spherical scatterers converges, in the limit of small scatterer size, to a random flight process, whose paths are piecewise linear curves generated by a Markov process with memory two. The corresponding transport equation is distinctly different from the linear Boltzmann equation observed in the case of a random configuration of scatterers. In the present paper we provide asymptotic estimates for the transition probabilities of this Markov process. Our results in particular sharpen previous upper and lower bounds on the distribution of free path lengths obtained by Bourgain, Golse and Wennberg.
Riaud, Antoine; Zhao, Shufang; Wang, Kai; Cheng, Yi; Luo, Guangsheng
2014-05-01
Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds. PMID:25353915
Mouhot, Clément; Neumann, Lukas
2006-01-01
For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard and moderately soft potentials and the semi-classical linearized fermionic and bosonic relaxation models, we prove explicit coercivity estimates on the associated integro-differential operator for some modified Sobolev norms. We deduce existence of classical solutions near equilibrium for the full non-linear...
Electrostatic interaction of two charged macroparticles in an equilibrium plasma
Filippov, A. V.; Pal', A. F.; Starostin, A. N.
2015-11-01
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.
Electrostatic interaction of two charged macroparticles in an equilibrium plasma
International Nuclear Information System (INIS)
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
The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein
International Nuclear Information System (INIS)
These four men were influential in the transition from classical to modern physics. They interacted as scientists, often antagonistically. Thus Boltzmann was the greatest champion of the atom, while Mach remained unconvinced all his life. As a aphysicist, Einstein was greatly influenced by both Mach and Boltzmann, although Mach in the end rejected relativity as well. Because of his work on statistical mechanics, fluctuations, and quantum theory, Einstein has been called the natural successor to Boltzmann. Planck also was influenced by Mach at first. Hence he and Boltzmann were adversaries antil Planck converted to atomistics in 1900 and used the statistical interpretation of entropy to establish his radiation law. Planck accepted relativity early, but in quantum theory he was for a long time partly opposed to Einstein, and vice versa - Einstein considered Planck's derivation of his radiation law as unsound, while Planck could not accept the light quantum. In the case of all four physicists, science was interwoven with philosophy. Boltzmann consistently fought Mach's positivism, while Planck and Einstein moved from positivism to realism. All were also, though in very different ways, actively interested in public affairs. (orig.)
Cumulant solution of the elastic Boltzmann transport equation in an infinite uniform medium
International Nuclear Information System (INIS)
We consider an analytical solution of the time-dependent elastic Boltzmann transport equation in an infinite uniform isotropic medium with an arbitrary phase function. We obtain (1) the exact distribution in angle, (2) the exact first and second spatial cumulants at any angle, and (3) an approximate combined distribution in position and angle and a spatial distribution whose central position and half-width of spread are always exact. The resulting Gaussian distribution has a center that advances in time, and an ellipsoidal contour that grows and changes shape providing a clear picture of the time evolution of the particle migration from near ballistic, through snakelike and into the final diffusive regime. (c) 2000 The American Physical Society
International Nuclear Information System (INIS)
This thesis looks into some qualitative properties, of dynamical systems occurring as ordinary differential equations. Essential information about the structure of the solution can be obtained without explicitly solving a linear system of differential equations with constant coefficients. This can be achieved by decomposing the operator of such a system into a semisimple and a nilpotent part. Fundamental theorems, concerning the existence of the solutions are discussed as well as the problem of stability of equilibrium points in dynamical systems (Liapunov's theorem). Gradient systems, special forms of dynamical systems, have particular properties that simplify the analysis of their flow. Finally, by applying the theory of dynamical systems to the Boltzmann equation with constant collision frequencies an investigation of equilibrium points is carried out. A mixture of three gases consisting of particles that interact through different collision mechanisms serves as the physical model. (Suda)
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.
Systematic Study of the Boundary Composition in Poisson Boltzmann Calculations
Kar, P; Hansmann, U H E; Hoefinger, S
2007-01-01
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but our results are also of interest to finite difference techniques of Poisson Boltzmann calculations. At first, we identify the critical size of the geometrical elements for discretizing the boundary, and thus the necessary resolution required to establish numerical convergence. In the following two steps we perform reference calculations on a set of dipeptides in different conformations using the Polarizable Continuum Model and a high-level Density Functional as well as a high-quality basis set. Afterwards, we propose a mechanism for defining appropriate boundary geometries. Finally, we compare the classic Poisson Boltzmann description with the Quantum Chemical description, and aim at finding appropriate fitting parameters to get a close match to the reference data. Surprisi...
Microcanonical Foundation for Systems with Power-Law Distributions
Abe, Sumiyoshi; Rajagopal, and A. K.
2000-01-01
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can also be derived.
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.
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.
Multiphase lattice Boltzmann simulations for porous media applications -- a review
Liu, Haihu; Leonardi, Christopher R; Jones, Bruce D; Schmieschek, Sebastian; Narváez, Ariel; Williams, John R; Valocchi, Albert J; Harting, Jens
2014-01-01
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.
Asymptotic-preserving Boltzmann model equations for binary gas mixture
Liu, Sha; Liang, Yihua
2016-02-01
An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations.
Jet propagation within a Linearized Boltzmann Transport Model
Luo, Tan; Wang, Xin-Nian; Zhu, Yan
2015-01-01
A Linear Boltzmann Transport (LBT) model has been developed for the study of jet propagation inside a quark-gluon plasma. Both leading and thermal recoiled partons are transported according to the Boltzmann equations to account for jet-induced medium excitations. In this talk, we present our study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate elastic energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons are found to have significant influences on the jet energy loss and transverse profile.
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Boltzmann learning of parameters in cellular neural networks
DEFF Research Database (Denmark)
Hansen, Lars Kai
1992-01-01
The use of Bayesian methods to design cellular neural networks for signal processing tasks and the Boltzmann machine learning rule for parameter estimation is discussed. The learning rule can be used for models with hidden units, or for completely unsupervised learning. The latter is exemplified ...... unsupervised adaptation of an image segmentation cellular network. The learning rule is applied to adaptive segmentation of satellite imagery......The use of Bayesian methods to design cellular neural networks for signal processing tasks and the Boltzmann machine learning rule for parameter estimation is discussed. The learning rule can be used for models with hidden units, or for completely unsupervised learning. The latter is exemplified by...
A tripartite equilibrium for carbon emission allowance allocation in the power-supply industry
International Nuclear Information System (INIS)
In the past decades, there has been a worldwide multilateral efforts to reduce carbon emissions. In particular, the “cap-and-trade” mechanism has been regarded as an effective way to control emissions. This is a market-based approach focused on the efficient allocation of initial emissions allowances. Based on the “grandfather” allocation method, this paper develops an alternative method derived from Boltzmann distribution to calculate the allowances. Further, with fully considering the relationship between the regional authority, power plants and grid company, a three-level multi-objective model for carbon emission allowance allocations in the power-supply industry is presented. To achieve tripartite equilibrium, the impacts on electricity output, carbon emissions and carbon intensity of the allocation method, allocation cap, and emission limits are assessed. The results showed that the greatest impact was seen in the emission limits rather than the allocation cap or allocation method. It also indicated that to effectively achieve reduction targets, it is necessary to allocate greater allowances to lower carbon intensity power plants. These results demonstrated the practicality and efficiency of the proposed model in seeking optimal allocation policies. -- Highlights: •A three-level decision model is proposed for allowance allocation policy-making. •The relationship between the regional authority, power plants and grid company is considered. •GA is combined with KKT conditions to search for the tripartite equilibrium. •Appropriate emission limits have a great effect on achieving the reduction target. •Power plants with lower carbon intensity should be allocated more allowances
Hierarchical condensation near phase equilibrium
Olemskoi, A. I.; Yushchenko, O. V.; Borisyuk, V. N.; Zhilenko, T. I.; Kosminska, Yu. O.; Perekrestov, V. I.
2012-06-01
A novel mechanism of new phase formation is studied both experimentally and theoretically in the example of quasi-equilibrium stationary condensation in an ion-plasma sputterer. Copper condensates are obtained to demonstrate that a specific network structure is formed as a result of self-assembly in the course of deposition. The fractal pattern related is inherent in the phenomena of diffusion limited aggregation. Condensate nuclei are shown to form statistical ensemble of hierarchically subordinated objects distributed in ultrametric space. The Langevin equation and the Fokker-Planck equation related are found to describe stationary distribution of thermodynamic potential variations at condensation. Time dependence of the formation probability of branching structures is found to clarify the experimental situation.
Determination of nonaxisymmetric equilibrium
International Nuclear Information System (INIS)
The Princeton Equilibrium Code is modified to determine the equilibrium surfaces for a large aspect ratio toroidal system with helical magnetic fields. The code may easily be made to include any variety of modes. Verification of the code is made by comparison with an analytic solution for l = 3. Previously observed shifting of the magnetic axis with increasing pressure or with a changed externally applied vertical field is obtained. The case l = 0, a bumpy torus, gives convergence only for the lenient convergence tolerance of epsilon/sub b/ = 1.0 x 10-2
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution). PMID:24182245
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.
Lattice Boltzmann model for free-surface flow and its application to filling process in casting
Ginzburg, I
2003-01-01
A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities at the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial ...
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...
Rukolaine, Sergey A.
2016-05-01
In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential
Lattice Boltzmann Simulation of One Particle Migrating in a Pulsating Flow in Microvessel
International Nuclear Information System (INIS)
A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel. The particle is as big as a red blood cell, and the micro vessel is four times as wide as the diameter of the particle. It is found that Segré-Silberberg effect will not respond to the pulsation of the flow when the Reynolds number is relatively high. However, when the Reynolds number is low enough, Segré-Silberberg effect disappears. In the steady flow, different initial position leads to different equilibrium positions. In a pulsating flow, different frequencies of pulsation also cause different equilibrium positions. Particularly, when the frequency of pulsation is closed to the human heart rate, Segré-Silberberg effect presents again. The evolutions of velocity, rotation, and trajectory of the particle are investigated to find the dynamics of such abnormal phenomenon. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Shibata, Tatsuo; Sasa, Shin-ichi
1997-01-01
An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot efficiency. Relevance to the study of protein motors is discussed. KEYWORDS: Chemical thermodynamics, Engine, Efficiency, Molecular machine.
An Updated Equilibrium Machine
Schultz, Emeric
2008-01-01
A device that can demonstrate equilibrium, kinetic, and thermodynamic concepts is described. The device consists of a leaf blower attached to a plastic container divided into two chambers by a barrier of variable size and form. Styrofoam balls can be exchanged across the barrier when the leaf blower is turned on and various air pressures are…
Study of equilibrium using collision dynamics
International Nuclear Information System (INIS)
Full text: The heavy-ion collisions at low, intermediate and relativistic energies provide a unique possibility to investigate the different questions ranging from the fusion at low incident energies to the formation of quark-gluon-plasma at higher incident energies. The intermediate energy heavy-ion collisions are excellent tool to study the nuclear equation of state which depends on the temperature as well on the density of the matter. Another important question associated with heavy-ion collision is the degree of equilibrium reached in a reaction. The answer of this question is important as there are several models employed at intermediate energy that assume global (or local) equilibrium. We shall study this question with two different aims. First, we would like to see whether a equilibrium is reached in a heavy-ion collision or not. Secondly, one is interested to know the number of collisions one needs to thermalized the matter. This study is attempted within Quantum Molecular Dynamics (QMD) model [1]. The QMD model is based on molecular dynamics picture where nucleons propagate under the influence of two and three body interactions. Here nucleon-nucleon potential is represented by the Skyrme, Coulomb and Yukawa forces. The question of equilibrium is addressed with the help of rapidity distribution which is defined as: Yi = 1/2 Ln E(i) + pz (i) c / E(i) - pz (i) c Here E(i) and pz(i) denote, respectively, the total energy and longitudinal momentum of the with particle. For a complete equilibrium, one should get a single peak in the distribution at mid rapidity. We calculated the rapidity distribution of Sn-Xe reaction at incident of 50, 400 and 2000 MeV/nucleon. We find that central collisions lead to better global equilibrium whereas peripheral collisions lack equilibrium. Further, one needs 10 collisions for complete equilibrium i.e. for a single peak at mid rapidity distribution. Whereas, if the number of collisions is less than 10, one obtains two peaks
International Nuclear Information System (INIS)
To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms. (paper)
Bouchard, Hugo; Bielajew, Alex
2015-07-01
To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.
A new scheme for solving inhomogeneous Boltzmann equation for electrons in weakly ionised gases
International Nuclear Information System (INIS)
In the case of weakly ionized gases, the numerical treatment of non-hydrodynamic regime involving spatial variation of distribution function due to boundaries (walls, electrodes, electron source, etc hor-ellipsis) by using direct Boltzmann equation always constitute a challenge if the main collisional processes occurring in non thermal plasmas are to be considered (elastic, inelastic and super-elastic collisions, Penning ionisation, Coulomb interactions, etc hor-ellipsis). In the non-thermal discharge modelling, the inhomogeneous electron Boltzmann equation is needed in order to be coupled for example to a fluid model to take into account the electron non-hydrodynamic effects. This is for example the case of filamentary discharge, in which the space charge electric field due to streamer propagation has a very sharp spatial profile thus leading to important space non-hydrodynamic effects. It is also the case of the cathodic zone of glow discharge where electric field has a rapid spatial decrease until the negative glow. In the present work, a new numerical scheme is proposed to solve the inhomogeneous Boltzmann equation for electrons in the framework of two-term approximation (TTA) taking into account elastic and inelastic processes. Such a method has the usual drawbacks associated with the TTA i.e. not an accurate enough at high E/N values or in presence of high inelastic processes. But the accuracy of this method is considered sufficient because in a next step it is destinated to be coupled to fluid model for charged particles and a chemical kinetic model where the accuracy is of the same order of magnitude or worse. However there are numerous advantages of this method concerning time computing, treatment of non-linear collision processes (Coulomb, Penning, etc hor-ellipsis)
The Boltzmann-Hamel Equations for Optimal Control
Maruskin, Jared M.; Bloch, Anthony M.
2007-01-01
We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In particular, we will show the dynamic optimal control problem can be written as a minimal set of 4n-2m first order differential equations of motion.
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...
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.
Lattice Boltzmann simulations of attenuation-driven acoustic streaming
International Nuclear Information System (INIS)
We show that lattice Boltzmann simulations can be used to model the attenuation-driven acoustic streaming produced by a travelling wave. Comparisons are made to analytical results and to the streaming pattern produced by an imposed body force approximating the Reynolds stresses. We predict the streaming patterns around a porous material in an attenuating acoustic field
On the linearized relativistic Boltzmann equation. II. Existence of hydrodynamics
International Nuclear Information System (INIS)
Solutions are analyzed of the linearized relativistic Boltzmann equation for initial data from L2(r, p) in long-time and/or small-mean-free-path limits. In both limits solutions of this equation converge to approximate ones constructed with solutions of the set of differential equations called the equations of relativistic hydrodynamics
Existence of the scattering operator for the linear Boltzmann equation
International Nuclear Information System (INIS)
Existence theorems are proven in a study of the scattering problem for the linear Boltzmann equation (transport equation), describing the motion of a cloud of nonself-interacting particles (neutrons) in phase space. Also Simon's weak coupling result is discussed, and a meaningful wave operator in the presence of trapped particles is defined and its existence proven. 7 references
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…
Modeling of non-equilibrium phenomena in expanding flows by means of a collisional-radiative model
International Nuclear Information System (INIS)
The effects of non-equilibrium in a quasi-one-dimensional nozzle flow are investigated by means of a collisional-radiative model. The gas undergoing the expansion is an air plasma and consists of atoms, molecules, and free electrons. In the present analysis, the electronic excited states of atomic and molecular species are treated as separate pseudo-species. Rotational and vibrational energy modes are assumed to be populated according to Boltzmann distributions. The coupling between radiation and gas dynamics is accounted for, in simplified manner, by using escape factors. The flow governing equations for the steady quasi-one-dimensional flow are written in conservative form and discretized in space by means of a finite volume method. Steady-state solutions are obtained by using a fully implicit time integration scheme. The analysis of the evolution of the electronic distribution functions reveals a substantial over-population of the high-lying excited levels of atoms and molecules in correspondence of the nozzle exit. The influence of optical thickness is also studied. The results clearly demonstrate that the radiative transitions, within the optically thin approximation, drastically reduce the over-population of high-lying electronic levels
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.
Wei, Linsheng; Xu, Min; Yuan, Dingkun; Zhang, Yafang; Hu, Zhaoji; Tan, Zhihong
2014-10-01
The electron drift velocity, electron energy distribution function (EEDF), density-normalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SF6-Air mixtures. The experimental results from a pulsed Townsend discharge are plotted for comparison with the numerical results. The reduced field strength varies from 40 Td to 500 Td (1 Townsend=10-17 V·cm2) and the SF6 concentration ranges from 10% to 100%. A Boltzmann equation associated with the two-term spherical harmonic expansion approximation is utilized to gain the swarm parameters in steady-state Townsend. Results show that the accuracy of the Boltzmann solution with a two-term expansion in calculating the electron drift velocity, electron energy distribution function, and density-normalized effective ionization coefficient is acceptable. The effective ionization coefficient presents a distinct relationship with the SF6 content in the mixtures. Moreover, the E/Ncr values in SF6-Air mixtures are higher than those in SF6-O2 mixtures and the calculated value E/Ncr in SF6-O2 and SF6-Air mixtures is lower than the measured value in SF6-N2. Parametric studies conducted on these parameters using the Boltzmann analysis offer substantial insight into the plasma physics, as well as a basis to explore the ozone generation process.
International Nuclear Information System (INIS)
The electron drift velocity, electron energy distribution function (EEDF), density-normalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SF6-Air mixtures. The experimental results from a pulsed Townsend discharge are plotted for comparison with the numerical results. The reduced field strength varies from 40 Td to 500 Td (1 Townsend=10−17 V·cm2) and the SF6 concentration ranges from 10% to 100%. A Boltzmann equation associated with the two-term spherical harmonic expansion approximation is utilized to gain the swarm parameters in steady-state Townsend. Results show that the accuracy of the Boltzmann solution with a two-term expansion in calculating the electron drift velocity, electron energy distribution function, and density-normalized effective ionization coefficient is acceptable. The effective ionization coefficient presents a distinct relationship with the SF6 content in the mixtures. Moreover, the E/Ncr values in SF6-Air mixtures are higher than those in SF6-O2 mixtures and the calculated value E/Ncr in SF6-O2 and SF6-Air mixtures is lower than the measured value in SF6-N2. Parametric studies conducted on these parameters using the Boltzmann analysis offer substantial insight into the plasma physics, as well as a basis to explore the ozone generation process. (low temperature plasma)
Mohammadipoor, O R; Niazmand, H; Mirbozorgi, S A
2014-01-01
Since the lattice Boltzmann method originally carries out the simulations on the regular Cartesian lattices, curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved-boundary problems is extrapolating or interpolating macroscopic properties of boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation or interpolation in boundary conditions potentially causes abrupt changes in particle distributions. Therefore, a curved-boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to potential fields. The proposed treatment is tested against several well-established problems and the solutions order of accuracy is evaluated. Numerical results show that the present treatment is of second-order accuracy and has reliable stability characteristics. PMID:24580362
Dopita, Michael A; Nicholls, David C; Kewley, Lisa J; Vogt, Frédéric P A
2013-01-01
Recently, \\citet{Nicholls12}, inspired by \\emph{in situ} observations of solar system astrophysical plasmas, suggested that the electrons in \\HII regions are characterised by a $\\kappa$-distribution of electron energies rather than by a simple Maxwell-Boltzmann distribution. Here we have collected together the new atomic data within a modified photoionisation code to explore the effects of both the new atomic data and the $\\kappa$-distribution on the strong-line techniques used to determine chemical abundances in \\HII regions. By comparing the recombination temperatures ($T_{\\rm rec}$) with the forbidden line temperatures ($T_{\\rm FL}$) we conclude that $ \\kappa \\sim 20$. While representing only a mild deviation from equilibrium, this is sufficient to strongly influence abundances determined using methods which depend on measurements of the electron temperature from forbidden lines. We present a number of new emission line ratio diagnostics which cleanly separate the two parameters determining the optical spe...
International Nuclear Information System (INIS)
Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not
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.
International Nuclear Information System (INIS)
Determinations of many possible equilibrium configurations in a device is one of the most important phases of the project in the sense that plasma configurations basically determine the details of the machine project. Details as limiters, vacuum vessel configuration and the position of vertical field or shapping field coils. Recent progress of tokamaks with non circular poloidal section in the formation of different plasma shapes compared to traditional circular ones, made the determination of MHD equilibrium and becomes more essential. Tokamak TBR-2, to be constructed at the Institute of Physics of the University of Sao Paulo, is a device with this non-traditional quality. This paper shows the simulation results obtained for the TBR-2. (Author)
Gated equilibrium bloodpool scintigraphy
International Nuclear Information System (INIS)
This thesis deals with the clinical applications of gated equilibrium bloodpool scintigraphy, performed with either a gamma camera or a portable detector system, the nuclear stethoscope. The main goal has been to define the value and limitations of noninvasive measurements of left ventricular ejection fraction as a parameter of cardiac performance in various disease states, both for diagnostic purposes as well as during follow-up after medical or surgical intervention. Secondly, it was attempted to extend the use of the equilibrium bloodpool techniques beyond the calculation of ejection fraction alone by considering the feasibility to determine ventricular volumes and by including the possibility of quantifying valvular regurgitation. In both cases, it has been tried to broaden the perspective of the observations by comparing them with results of other, invasive and non-invasive, procedures, in particular cardiac catheterization, M-mode echocardiography and myocardial perfusion scintigraphy. (Auth.)
Yongmin Chen; Ron Smith
2001-01-01
Cost overruns are endemic in military procurement projects and pervasive in other areas. This paper studies a model in which the apparent cost overruns arise not as systematic expectational errors but as equilibrium phenomena. The possibility of renegotiating payments when cost overruns occur results in firms bidding below their true estimate of expected project costs. This can cause the initial price for a project to be consistently lower than its expected cost, and hence the persistence of ...
DEFF Research Database (Denmark)
Bollerslev, Tim; Sizova, Natalia; Tauchen, George
Stock market volatility clusters in time, carries a risk premium, is fractionally inte- grated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast i......, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes....
Bluffing: an equilibrium strategy
Fabrice Rousseau
1999-01-01
The present work studies the behavior of a monopolistic informed trader in a two-period competitive dealer market. We show that the informed trader may engage in stock price manipulation as a result of the exploitation of his informational advantage (sufficient conditions are provided). The informed trader achieves this manipulation by not trading in the first period according to the information received. This trader attempts to jam his signal or to bluff. In equilibrium this behavior is anti...
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
Travaillé, G.; Peyrusse, O.; Bousquet, B.; Canioni, L.; Pierres, K. Michel-Le; Roy, S.
2009-10-01
We present a collisional-radiative approach of the theoretical analysis of laser-induced breakdown spectroscopy (LIBS) plasmas. This model, which relies on an optimized effective potential atomic structure code, was used to simulate a pure aluminum plasma. The description of aluminum involved a set of 220 atomic levels representative of three different stages of ionization (Al 0, Al + and Al ++). The calculations were carried for stationary plasmas, with input parameters ( ne and Te) ranging respectively between 10 13-18 cm - 3 and 0.3-2 eV. A comparison of our atomic data with some existing databases is made. The code was mainly developed to address the validity of the local thermodynamic equilibrium (LTE) assumption. For usual LIBS plasma parameters, we did not reveal a sizeable discrepancy of the radiative equilibrium of the plasma towards LTE. For cases where LTE was firmly believed to stand, the Boltzmann plot outputs of this code were used to check the physical accuracy of the Boltzmann temperature, as it is currently exploited in several calibration-free laser-induced breakdown spectroscopy (CF-LIBS) studies. In this paper, a deviation ranging between 10 and 30% of the measured Boltzmann temperature to the real excitation temperature is reported. This may be due to the huge dispersion induced on the line emissivities, on which the Boltzmann plots are based to extract this parameter. Consequences of this fact on the CF-LIBS procedure are discussed and further insights to be considered for the future are introduced.
International Nuclear Information System (INIS)
We present a collisional-radiative approach of the theoretical analysis of laser-induced breakdown spectroscopy (LIBS) plasmas. This model, which relies on an optimized effective potential atomic structure code, was used to simulate a pure aluminum plasma. The description of aluminum involved a set of 220 atomic levels representative of three different stages of ionization (Al0, Al+ and Al++). The calculations were carried for stationary plasmas, with input parameters (ne and Te) ranging respectively between 1013-18 cm-3 and 0.3-2 eV. A comparison of our atomic data with some existing databases is made. The code was mainly developed to address the validity of the local thermodynamic equilibrium (LTE) assumption. For usual LIBS plasma parameters, we did not reveal a sizeable discrepancy of the radiative equilibrium of the plasma towards LTE. For cases where LTE was firmly believed to stand, the Boltzmann plot outputs of this code were used to check the physical accuracy of the Boltzmann temperature, as it is currently exploited in several calibration-free laser-induced breakdown spectroscopy (CF-LIBS) studies. In this paper, a deviation ranging between 10 and 30% of the measured Boltzmann temperature to the real excitation temperature is reported. This may be due to the huge dispersion induced on the line emissivities, on which the Boltzmann plots are based to extract this parameter. Consequences of this fact on the CF-LIBS procedure are discussed and further insights to be considered for the future are introduced.