Multispeed models in off-lattice Boltzmann simulations

NARCIS (Netherlands)

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

2008-01-01

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

Thermal equilibrium properties of surface hopping with an implicit Langevin bath

International Nuclear Information System (INIS)

Sherman, M. C.; Corcelli, S. A.

2015-01-01

The ability of fewest switches surface hopping (FSSH) approach, where the classical degrees of freedom are coupled to an implicit Langevin bath, to establish and maintain an appropriate thermal equilibrium was evaluated in the context of a three site model for electron transfer. The electron transfer model consisted of three coupled diabatic states that each depends harmonically on the collective bath coordinate. This results in three states with increasing energy in the adiabatic representation. The adiabatic populations and distributions of the collective solvent coordinate were monitored during the course of 250 ns FSSH-Langevin (FSSH-L) simulations performed at a broad range of temperatures and for three different nonadiabatic coupling strengths. The agreement between the FSSH-L simulations and numerically exact results for the adiabatic population ratios and solvent coordinate distributions was generally favorable. The FSSH-L method produces a correct Boltzmann distribution of the solvent coordinate on each of the adiabats, but the integrated populations are slightly incorrect because FSSH does not rigorously obey detailed balance. The overall agreement is better at high temperatures and for high nonadiabatic coupling, which agrees with a previously reported analytical and simulation analysis [J. R. Schmidt, P. V. Parandekar, and J. C. Tully, J. Chem. Phys. 129, 044104 (2008)] on a two-level system coupled to a classical bath

From hard thermal loops to Langevin dynamics

International Nuclear Information System (INIS)

Boedeker, Dietrich

1999-01-01

In hot non-Abelian gauge theories, processes characterized by the momentum scale g 2 T (such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft (vertical bar p vertical bar ∼ g 2 T) field modes is obtained by integrating out momenta larger than than g 2 T. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale T, it is shown how to integrate out the scale gT in an expansion in the gauge coupling g. At leading order in g, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as Γ = κg 10 log(1/g)gT 4 , and it allows for a calculation for κ on the lattice

Progress on Complex Langevin simulations of a finite density matrix model for QCD

Energy Technology Data Exchange (ETDEWEB)

Bloch, Jacques [Univ. of Regensburg (Germany). Inst. for Theorectical Physics; Glesaan, Jonas [Swansea Univ., Swansea U.K.; Verbaarschot, Jacobus [Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Zafeiropoulos, Savvas [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik

2018-04-01

We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.

Langevin modelling of high-frequency Hang-Seng index data

Science.gov (United States)

Tang, Lei-Han

2003-06-01

Accurate statistical characterization of financial time series, such as compound stock indices, foreign currency exchange rates, etc., is fundamental to investment risk management, pricing of derivative products and financial decision making. Traditionally, such data were analyzed and modeled from a purely statistics point of view, with little concern on the specifics of financial markets. Increasingly, however, attention has been paid to the underlying economic forces and the collective behavior of investors. Here we summarize a novel approach to the statistical modeling of a major stock index (the Hang Seng index). Based on mathematical results previously derived in the fluid turbulence literature, we show that a Langevin equation with a variable noise amplitude correctly reproduces the ubiquitous fat tails in the probability distribution of intra-day price moves. The form of the Langevin equation suggests that, despite the extremely complex nature of financial concerns and investment strategies at the individual's level, there exist simple universal rules governing the high-frequency price move in a stock market.

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

Science.gov (United States)

Luo, Li-Shi

1998-01-01

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Model reduction of multiscale chemical langevin equations: a numerical case study.

Science.gov (United States)

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

Pruning Boltzmann networks and hidden Markov models

DEFF Research Database (Denmark)

Pedersen, Morten With; Stork, D.

1996-01-01

We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...

Boltzmann machines as a model for parallel annealing

NARCIS (Netherlands)

Aarts, E.H.L.; Korst, J.H.M.

1991-01-01

The potential of Boltzmann machines to cope with difficult combinatorial optimization problems is investigated. A discussion of various (parallel) models of Boltzmann machines is given based on the theory of Markov chains. A general strategy is presented for solving (approximately) combinatorial

On the Langevin approach to particle transport

International Nuclear Information System (INIS)

Bringuier, Eric

2006-01-01

In the Langevin description of Brownian motion, the action of the surrounding medium upon the Brownian particle is split up into a systematic friction force of Stokes type and a randomly fluctuating force, alternatively termed noise. That simple description accounts for several basic features of particle transport in a medium, making it attractive to teach at the undergraduate level, but its range of applicability is limited. The limitation is illustrated here by showing that the Langevin description fails to account realistically for the transport of a charged particle in a medium under crossed electric and magnetic fields and the ensuing Hall effect. That particular failure is rooted in the concept of the friction force rather than in the accompanying random force. It is then shown that the framework of kinetic theory offers a better account of the Hall effect. It is concluded that the Langevin description is nothing but an extension of Drude's transport model subsuming diffusion, and so it inherits basic limitations from that model. This paper thus describes the interrelationship of the Langevin approach, the Drude model and kinetic theory, in a specific transport problem of physical interest

On a Boltzmann-type price formation model

KAUST Repository

Burger, Martin; Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie Therese

2013-01-01

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.

On a Boltzmann-type price formation model

KAUST Repository

Burger, Martin

2013-06-26

In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann-type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore, we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

Generalized Langevin quantization

International Nuclear Information System (INIS)

Defendi, A.; Roncadelli, M.

1994-01-01

The recently proposed Langevin formulation of quantum dynamics yields the quantum mechanical propagator at imaginary time as a noise average which involves the solutions of a Langevin equation in configuration space with a Gaussian white noise. This strategy does not require any knowledge about the ground-state quantum dynamics and has been successful in dealing with certain as yet unsolved problems. Here we sketch a generalization of this approach which is based on a similar Langevin equation, whose drift however contains an arbitrary function. As it turns out, this freedom leads to a great simplification in the treatment of several quantum mechanical systems as compared to the original Langevin formulation (this point is illustrated by taking the forced harmonic oscillator as an example). We also show that when the above-mentioned arbitrary function obeys the imaginary-time Hamilton-Jacobi equation, then the new formulation of quantum dynamics exhibits a manifest connection with classical mechanics (at imaginary time). (orig.)

On some asymptotic relations in the Boltzmann-Enskog model

International Nuclear Information System (INIS)

Sadovnikov, B.I.; Inozemtseva, N.G.

1977-04-01

The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

The Langevin equation

Science.gov (United States)

Pomeau, Yves; Piasecki, Jarosław

2017-11-01

The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.

A lattice Boltzmann model for solute transport in open channel flow

Science.gov (United States)

Wang, Hongda; Cater, John; Liu, Haifei; Ding, Xiangyi; Huang, Wei

2018-01-01

A lattice Boltzmann model of advection-dispersion problems in one-dimensional (1D) open channel flows is developed for simulation of solute transport and pollutant concentration. The hydrodynamics are calculated based on a previous lattice Boltzmann approach to solving the 1D Saint-Venant equations (LABSVE). The advection-dispersion model is coupled with the LABSVE using the lattice Boltzmann method. Our research recovers the advection-dispersion equations through the Chapman-Enskog expansion of the lattice Boltzmann equation. The model differs from the existing schemes in two points: (1) the lattice Boltzmann numerical method is adopted to solve the advection-dispersion problem by meso-scopic particle distribution; (2) and the model describes the relation between discharge, cross section area and solute concentration, which increases the applicability of the water quality model in practical engineering. The model is verified using three benchmark tests: (1) instantaneous solute transport within a short distance; (2) 1D point source pollution with constant velocity; (3) 1D point source pollution in a dam break flow. The model is then applied to a 50-year flood point source pollution accident on the Yongding River, which showed good agreement with a MIKE 11 solution and gauging data.

Chaotic Boltzmann machines

Science.gov (United States)

Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

2013-01-01

The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425

Navier-Stokes Dynamics by a Discrete Boltzmann Model

Science.gov (United States)

Rubinstein, Robet

2010-01-01

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

Entropic multirelaxation lattice Boltzmann models for turbulent flows

Science.gov (United States)

Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.

2015-10-01

We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

Immiscible multicomponent lattice Boltzmann model for fluids with ...

Indian Academy of Sciences (India)

College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, ... was developed from a discretized fluid model known as the lattice gas automata ... of two immiscible fluids, several lattice Boltzmann (LB) models have been ...

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

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

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

Galilean-Invariant Lattice-Boltzmann Models with H Theorem

National Research Council Canada - National Science Library

Boghosian, Bruce

2003-01-01

The authors demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations...

Langevin dynamics for ramified structures

Science.gov (United States)

Méndez, Vicenç; Iomin, Alexander; Horsthemke, Werner; Campos, Daniel

2017-06-01

We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. The mean square displacement (MSD) along the backbone characterizes the transport through the ramified structure. We derive a general analytical expression for this observable in terms of the probability distribution function of the motion along the secondary branches. We apply our result to various types of motion along the secondary branches of finite or infinite length, such as subdiffusion, superdiffusion, and Langevin dynamics with colored Gaussian noise and with non-Gaussian white noise. Monte Carlo simulations show excellent agreement with the analytical results. The MSD for the case of Gaussian noise is shown to be independent of the noise color. We conclude by generalizing our analytical expression for the MSD to the case where each secondary branch is n dimensional.

Paul Langevin

Indian Academy of Sciences (India)

tions not only in physics but also in various other fields such as chemistry, biology and ... the required tools for the development of t~e special theory of relativity and would ... During the second world war Langevin became a vocal anti-.

Three-dimensional lattice Boltzmann model for compressible flows.

Science.gov (United States)

Sun, Chenghai; Hsu, Andrew T

2003-07-01

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

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

Science.gov (United States)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed

Grid refinement model in lattice Boltzmann method for stream function-vorticity formulations

Energy Technology Data Exchange (ETDEWEB)

Shin, Myung Seob [Dept. of Mechanical Engineering, Dongyang Mirae University, Seoul (Korea, Republic of)

2015-03-15

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

Numerical simulations of the O(3) and CP1 models using the Langevin equations and the Metropolis algorithm

International Nuclear Information System (INIS)

Abdalla, E.; Carneiro, C.E.I.

1988-12-01

The O(3) model, the pure CP 1 model and the CP 1 model minimally coupled to fermions are numerically simulated. The equivalence between the O(3) and the bound state of the pure CP 1 model is investigated. It is shown that: the relations g O(3 ) = 2 g CP 1 and E O(3 )= 2E CP 1 + 2, for the coupling constants and energies hold beyond the classical level; the mass gap as a function of the coupling is the same for both models. The mass gap for the CP 1 minimally coupled to fermions is also calculated. The calculations are performed using different techniques. The proposal by Namiki and colaborators to enforce constraints on Langevin equations and Parisi's technique to calculate correlation functions via Langevin equations is tested. The results are compared with those obtained using the multi-hit Metropolis algorithm. (author) [pt

Fast-forward Langevin dynamics with momentum flips

Science.gov (United States)

Hijazi, Mahdi; Wilkins, David M.; Ceriotti, Michele

2018-05-01

Stochastic thermostats based on the Langevin equation, in which a system is coupled to an external heat bath, are popular methods for temperature control in molecular dynamics simulations due to their ergodicity and their ease of implementation. Traditionally, these thermostats suffer from sluggish behavior in the limit of high friction, unlike thermostats of the Nosé-Hoover family whose performance degrades more gently in the strong coupling regime. We propose a simple and easy-to-implement modification to the integration scheme of the Langevin algorithm that addresses the fundamental source of the overdamped behavior of high-friction Langevin dynamics: if the action of the thermostat causes the momentum of a particle to change direction, it is flipped back. This fast-forward Langevin equation preserves the momentum distribution and so guarantees the correct equilibrium sampling. It mimics the quadratic behavior of Nosé-Hoover thermostats and displays similarly good performance in the strong coupling limit. We test the efficiency of this scheme by applying it to a 1-dimensional harmonic oscillator, as well as to water and Lennard-Jones polymers. The sampling efficiency of the fast-forward Langevin equation thermostat, measured by the correlation time of relevant system variables, is at least as good as the traditional Langevin thermostat, and in the overdamped regime, the fast-forward thermostat performs much better, improving the efficiency by an order of magnitude at the highest frictions we considered.

Lattice gas cellular automata and lattice Boltzmann models an introduction

CERN Document Server

Wolf-Gladrow, Dieter A

2000-01-01

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

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Langevin formulation of quantum dynamics

International Nuclear Information System (INIS)

Roncadelli, M.

1989-03-01

We first show that nonrelativistic quantum mechanics formulated at imaginary-(h/2 π) can formally be viewed as the Fokker-Planck description of a frictionless brownian motion, which occurs (in general) in an absorbing medium. We next offer a new formulation of quantum mechanics, which is basically the Langevin treatment of this brownian motion. Explicitly, we derive a noise-average representation for the transition probability W(X'',t''|X',t'), in terms of the solutions to a Langevin equation with a Gaussian white-noise. Upon analytic continuation back to real-(h/2 π),W(X'',t''|X',t') becomes the propagator of the original Schroedinger equation. Our approach allows for a straightforward application to quantum dynamical problems of the mathematical techniques of classical stochastic processes. Moreover, computer simulations of quantum mechanical systems can be carried out by using numerical programs based on the Langevin dynamics. (author). 19 refs, 1 tab

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

Science.gov (United States)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Poisson-Boltzmann-Nernst-Planck model

International Nuclear Information System (INIS)

Zheng Qiong; Wei Guowei

2011-01-01

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 model for three-phase viscoelastic fluid flow

Science.gov (United States)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics

Energy Technology Data Exchange (ETDEWEB)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2017-02-15

The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from the Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

International Nuclear Information System (INIS)

Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai

2014-01-01

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Boltzmann

International Nuclear Information System (INIS)

Lin, X.

1991-01-01

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

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

International Nuclear Information System (INIS)

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

2016-01-01

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. (paper)

Poisson-Boltzmann-Nernst-Planck model.

Science.gov (United States)

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

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 model capable of mesoscopic vorticity computation

Science.gov (United States)

Peng, Cheng; Guo, Zhaoli; Wang, Lian-Ping

2017-11-01

It is well known that standard lattice Boltzmann (LB) models allow the strain-rate components to be computed mesoscopically (i.e., through the local particle distributions) and as such possess a second-order accuracy in strain rate. This is one of the appealing features of the lattice Boltzmann method (LBM) which is of only second-order accuracy in hydrodynamic velocity itself. However, no known LB model can provide the same quality for vorticity and pressure gradients. In this paper, we design a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice. A detailed Chapman-Enskog analysis is presented to illustrate all the necessary constraints in reproducing the isothermal Navier-Stokes equations. The remaining degrees of freedom are carefully analyzed to derive a model that accommodates mesoscopic computation of all the velocity and pressure gradients from the nonequilibrium moments. This way of vorticity calculation naturally ensures a second-order accuracy, which is also proven through an asymptotic analysis. We thus show, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM. The resulting model is then validated in simulations of a three-dimensional decaying Taylor-Green flow, a lid-driven cavity flow, and a uniform flow passing a fixed sphere. Furthermore, it is shown that the mesoscopic vorticity computation can be realized even with single relaxation parameter.

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

International Nuclear Information System (INIS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-01-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O(N) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalism. (orig.)

Langevin diffusions on the torus

DEFF Research Database (Denmark)

García-Portugués, Eduardo; Sørensen, Michael; Mardia, Kanti V.

2018-01-01

We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues......) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate...

Exploring cluster Monte Carlo updates with Boltzmann machines.

Science.gov (United States)

Wang, Lei

2017-11-01

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

Exploring cluster Monte Carlo updates with Boltzmann machines

Science.gov (United States)

Wang, Lei

2017-11-01

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

Dynamical scenario of intermediary mass fragments formation in heavy ion collisions

International Nuclear Information System (INIS)

Ayik, S.; Belkacem, M.; Gregoire, C.; Stryjewski, J.; Suraud, E.

1989-01-01

We briefly remind the possible dynamical scenario of fragments formation in heavy-ion collisions at some tens fo MeV/A. We discuss how present day dynamical models can describe fragment formation. We next turn to the Boltzmann-Langevin formalism which provides a well defined theoretical framework for the understanding of the growing of the dynamical instabilities leading to multifragmentation. We present a first numerical solution of the Boltzmann-Langevin equation and we apply the formalism to the onset of multifragmentation of the 40 Ca + 40 Ca system between 20 and 60 MeV/A beam energy [fr

Topology optimization and lattice Boltzmann methods

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund

This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

The convergence of parallel Boltzmann machines

NARCIS (Netherlands)

Zwietering, P.J.; Aarts, E.H.L.; Eckmiller, R.; Hartmann, G.; Hauske, G.

1990-01-01

We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular

Studies of fluctuation processes in nuclear collisions

International Nuclear Information System (INIS)

Ayik, S.

1992-02-01

This report discusses the following topics: Relativistic Boltzmann-Langevin model for heavy-ion collision; K+ production far below free neucleon-nucleon threshold and damping of collective vibrations in a memory-dependent transport model

Nonequilibrium Langevin dynamics: A demonstration study of shear flow fluctuations in a simple fluid

Science.gov (United States)

Belousov, Roman; Cohen, E. G. D.; Rondoni, Lamberto

2017-08-01

The present paper is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic molecular dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which then is simulated numerically and compared directly with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems theoretically and computationally. We find an intriguing relation between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of an athermal cumulant ratio, an apposite quantity introduced here. In addition, we discuss how the order of a given Langevin dynamics can be raised systematically by introducing colored noise.

Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation

Science.gov (United States)

Rossi, Mariana; Kapil, Venkat; Ceriotti, Michele

2018-03-01

Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. We develop quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, and show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modeling of vibrational dynamics of molecules, liquids, and solids.

An introduction to the theory of the Boltzmann equation

CERN Document Server

Harris, Stewart

2011-01-01

Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes

Lorentz Covariance of Langevin Equation

International Nuclear Information System (INIS)

Koide, T.; Denicol, G.S.; Kodama, T.

2008-01-01

Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)

Lattice Boltzmann model for simulating immiscible two-phase flows

International Nuclear Information System (INIS)

Reis, T; Phillips, T N

2007-01-01

The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

Flavored quantum Boltzmann equations

International Nuclear Information System (INIS)

Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

2010-01-01

We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

Coupling Langevin Dynamics With Continuum Mechanics: Exposing the Role of Sarcomere Stretch Activation Mechanisms to Cardiac Function

Directory of Open Access Journals (Sweden)

Takumi Washio

2018-04-01

Full Text Available High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with overcoming the large spatial (from 1 nm to 10 cm and temporal (from 1 ns to 1 ms gaps between the two scales. In this paper, we propose an efficient parallel scheme to couple a microscopic model using Langevin dynamics for a protein motor with a finite element continuum model of a beating heart. The proposed scheme allows us to use a macroscale time step that is an order of magnitude longer than the microscale time step of the Langevin model, without loss of stability or accuracy. This reduces the overhead required by the imbalanced loads of the microscale computations and the communication required when switching between scales. An example of the Langevin dynamics model that demonstrates the usefulness of the coupling approach is the molecular mechanism of the actomyosin system, in which the stretch-activation phenomenon can be successfully reproduced. This microscopic Langevin model is coupled with a macroscopic finite element ventricle model. In the numerical simulations, the Langevin dynamics model reveals that a single sarcomere can undergo spontaneous oscillation (15 Hz accompanied by quick lengthening due to cooperative movements of the myosin molecules pulling on the common Z-line. Also, the coupled simulations using the ventricle model show that the stretch-activation mechanism contributes to the synchronization of the quick lengthening of the sarcomeres at the end of the systolic phase. By comparing the simulation results given by the molecular model with and without the stretch-activation mechanism, we see that this synchronization contributes to

Essentially Entropic Lattice Boltzmann Model

Science.gov (United States)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Numerical study of Langevin equation in twisted Eguchi-Kawai model: distribution of eigenvalues of the plaquette matrix

International Nuclear Information System (INIS)

Migdal, A.A.; Polikarpov, M.I.; Veselov, A.I.; Yurov, V.P.

1983-01-01

The Langevin equation for the lattice theory with arbitrary gauge group is derived. The four-dimensional twisted Eguchi-Kawai model is investigated numerically. The results for the plaquette energy agree with those of the known Monte Carlo calculations. The new result is the distribution of eigenvalues of the plaquette matrix. In the strong coupling phase this distribution is smooth, whereas in the weak coupling phase a gap is clearly seen

The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems

CERN Document Server

Snook, Ian

2007-01-01

The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book.* Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

International Nuclear Information System (INIS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

Using x-ray tomography and lattice Boltzmann modeling to evaluate pore-scale processes in porous media

DEFF Research Database (Denmark)

Christensen, Britt Stenhøj Baun

-teknik (Computed Tomography) til at visualisere og kvantificere de eksperimentelle poreskala systemer. Både en medicinsk CT-scanner og et synkrotron baseret skanningssystem med høj billede opløselighed blev anvendt. Numerisk modellering af poreskala processerne blev gjort ved hjælp af en lattice Boltzmann model...... for testning af en Shan-Chen lattice Boltzmann model. Ved anvendelse af simple veldefinerede to-fase systemer blev en kalibreringsprocedure skitseret til identificering af de dimensionsløse modelparametre og deres kobling til overfladespænding og kontaktvinkel egenskaberne af det fysiske system. Det blev taget...

NMR signals within the generalized Langevin model for fractional Brownian motion

Science.gov (United States)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

On the Langevin equation for stochastic quantization of gravity

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-10-01

We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations leads to stochastic quantization of gravity including an unique superspace metric. (author)

Lattice Boltzmann simulations of the permeability and capillary adsorption of cement model microstructures

Energy Technology Data Exchange (ETDEWEB)

Zalzale, M. [Laboratory of Construction Materials, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne (Switzerland); McDonald, P.J., E-mail: p.mcdonald@surrey.ac.uk [Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH (United Kingdom)

2012-12-15

The lattice Boltzmann method is used to investigate the permeability of microstructures of cement pastes generated using the numerical models CEMHYD3D (Bentz, 1997) and {mu}IC (Bishnoi and Scrivener, 2009). Results are reported as a function of paste water-to-cement ratio and degree of hydration. The permeability decreases with increasing hydration and decreasing water-to-cement ratio in agreement with experiment. However the permeability is larger than the experimental data recorded using beam bending methods (Vichit-Vadakan and Scherer, 2002). Notwithstanding, the lattice Boltzmann results compare favourably with alternate numerical methods of permeability calculation for cement model microstructures. In addition, we show early results for the liquid/vapour capillary adsorption and desorption isotherms in the same model {mu}IC structures. The broad features of the experimental capillary porosity isotherm are reproduced, although further work is required to adequately parameterise the model.

A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids.

Science.gov (United States)

Ginzburg, Irina; Steiner, Konrad

2002-03-15

The filling process of viscoplastic metal alloys and plastics in expanding cavities is modelled using the lattice Boltzmann method in two and three dimensions. These models combine the regularized Bingham model for viscoplastic fluids with a free-interface algorithm. The latter is based on a modified immiscible lattice Boltzmann model in which one species is the fluid and the other one is considered to be a vacuum. The boundary conditions at the curved liquid-vacuum interface are met without any geometrical front reconstruction from a first-order Chapman-Enskog expansion. The numerical results obtained with these models are found in good agreement with available theoretical and numerical analysis.

On a class of quantum Langevin equations and the question of approach to equilibrium

International Nuclear Information System (INIS)

Maassen, J.D.M.

1982-01-01

This thesis is concerned with a very simple 'open' quantum system, i.e. being in contact with the outer world. It is asked whether the motion of this system shows frictional behaviour in that it tends to thermal equilibrium. A partial positive answer is given to this question, more precisely, to the question if the solution of the quantum mechanical Langevin equation that describes the Lamb-model (a harmonic oscillator damped by coupling with a string), approaches an equilibrium state. In two sections, the classical and quantum Langevin equations are treated analogously. (Auth.)

A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics.

Science.gov (United States)

Smith, E R; Müller, E A; Craster, R V; Matar, O K

2016-12-06

Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.

Mesoscopic modelling and simulation of soft matter.

Science.gov (United States)

Schiller, Ulf D; Krüger, Timm; Henrich, Oliver

2017-12-20

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows.

Science.gov (United States)

Munafò, A; Panesi, M; Magin, T E

2014-02-01

A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

Suitability of the double Langevin function for description of anhysteretic magnetization curves in NO and GO electrical steel grades

Directory of Open Access Journals (Sweden)

Simon Steentjes

2017-05-01

Full Text Available This paper compares the match obtained using the classical Langevin function, the tanh function as well as a recently by the authors proposed double Langevin function with the measured anhysteretic magnetization curve of three different non-oriented electrical steel grades and one grain-oriented grade. Two standard non-oriented grades and a high-silicon grade (Si content of 6.5% made by CVD are analyzed. An excellent match is obtained using the double Langevin function, whereas the classical solutions are less appropriate. Thereby, problems such as those due to propagation of approximation errors observed in hysteresis modeling can be bypassed.

A numerical model for simulating electroosmotic micro- and nanochannel flows under non-Boltzmann equilibrium

Energy Technology Data Exchange (ETDEWEB)

Kim, Kyoungjin; Kwak, Ho Sang [School of Mechanical Engineering, Kumoh National Institute of Technology, 1 Yangho, Gumi, Gyeongbuk 730-701 (Korea, Republic of); Song, Tae-Ho, E-mail: kimkj@kumoh.ac.kr, E-mail: hskwak@kumoh.ac.kr, E-mail: thsong@kaist.ac.kr [Department of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong, Yuseong, Daejeon 305-701 (Korea, Republic of)

2011-08-15

This paper describes a numerical model for simulating electroosmotic flows (EOFs) under non-Boltzmann equilibrium in a micro- and nanochannel. The transport of ionic species is represented by employing the Nernst-Planck equation. Modeling issues related to numerical difficulties are discussed, which include the handling of boundary conditions based on surface charge density, the associated treatment of electric potential and the evasion of nonlinearity due to the electric body force. The EOF in the entrance region of a straight channel is examined. The numerical results show that the present model is useful for the prediction of the EOFs requiring a fine resolution of the electric double layer under either the Boltzmann equilibrium or non-equilibrium. Based on the numerical results, the correlation between the surface charge density and the zeta potential is investigated.

Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

Science.gov (United States)

Boozer, A. D.

2011-01-01

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

Science.gov (United States)

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

CERN Document Server

Farhat, Hassan; Kondaraju, Sasidhar

2014-01-01

Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

Directory of Open Access Journals (Sweden)

Liping Chen

2018-05-01

Full Text Available A sub-grid multiple relaxation time (MRT lattice Boltzmann model with curvilinear coordinates is applied to simulate an artificial meandering river. The method is based on the D2Q9 model and standard Smagorinsky sub-grid scale (SGS model is introduced to simulate meandering flows. The interpolation supplemented lattice Boltzmann method (ISLBM and the non-equilibrium extrapolation method are used for second-order accuracy and boundary conditions. The proposed model was validated by a meandering channel with a 180° bend and applied to a steady curved river with piers. Excellent agreement between the simulated results and previous computational and experimental data was found, showing that MRT-LBM (MRT lattice Boltzmann method coupled with a Smagorinsky sub-grid scale (SGS model in a curvilinear coordinates grid is capable of simulating practical meandering flows.

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Energy Technology Data Exchange (ETDEWEB)

Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

2016-06-01

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

Boltzmann equations for a binary one-dimensional ideal gas.

Science.gov (United States)

Boozer, A D

2011-09-01

We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

Lattice Boltzmann modeling an introduction for geoscientists and engineers

CERN Document Server

Sukop, Michael C

2005-01-01

Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.

Boltzmann hierarchy for interacting neutrinos I: formalism

International Nuclear Information System (INIS)

Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y.Y.

2015-01-01

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c eff 2 ,c vis 2 )-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles

Axisymmetric multiphase lattice Boltzmann method for generic equations of state

NARCIS (Netherlands)

Reijers, S.A.; Gelderblom, H.; Toschi, F.

2016-01-01

We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Science.gov (United States)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

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

NARCIS (Netherlands)

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

2013-01-01

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

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

Science.gov (United States)

Chu, Weiqi; Li, Xiantao

2018-01-01

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

Complex saddle points and the sign problem in complex Langevin simulation

International Nuclear Information System (INIS)

Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya

2016-01-01

We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.

Hot electrons in superlattices: quantum transport versus Boltzmann equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

1999-01-01

A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

Ultrafine particles dispersion modeling in a street canyon: development and evaluation of a composite lattice Boltzmann model.

Science.gov (United States)

Habilomatis, George; Chaloulakou, Archontoula

2013-10-01

Recently, a branch of particulate matter research concerns on ultrafine particles found in the urban environment, which originate, to a significant extent, from traffic sources. In urban street canyons, dispersion of ultrafine particles affects pedestrian's short term exposure and resident's long term exposure as well. The aim of the present work is the development and the evaluation of a composite lattice Boltzmann model to study the dispersion of ultrafine particles, in urban street canyon microenvironment. The proposed model has the potential to penetrate into the physics of this complex system. In order to evaluate the model performance against suitable experimental data, ultrafine particles levels have been monitored on an hourly basis for a period of 35 days, in a street canyon, in Athens area. The results of the comparative analysis are quite satisfactory. Furthermore, our modeled results are in a good agreement with the results of other computational and experimental studies. This work is a first attempt to study the dispersion of an air pollutant by application of the lattice Boltzmann method. Copyright © 2013 Elsevier B.V. All rights reserved.

Study of fission dynamics with the three-dimensional Langevin equations

Energy Technology Data Exchange (ETDEWEB)

Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)

2011-11-15

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei {sup 210}Po and {sup 224}Th formed in the fusion-fission reactions {sup 4}He+{sup 206}Pb, {sup 16}O+{sup 208}Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data. (orig.)

Modeling of flow of particles in a non-Newtonian fluid using lattice Boltzmann method

DEFF Research Database (Denmark)

Skocek, Jan; Svec, Oldrich; Spangenberg, Jon

2011-01-01

is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

International Nuclear Information System (INIS)

Xu Hui; Tao Wenquan; Zhang Yan

2009-01-01

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM

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

Science.gov (United States)

Schmitt, Richard Henry

2011-01-01

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

Improvement of the instability of compressible lattice Boltzmann model by shockdetecting sensor

International Nuclear Information System (INIS)

Esfahanian, Vahid; Ghadyani, Mohsen

2015-01-01

Recently, lattice Boltzmann method (LBM) has drawn attention as an alternative and promising numerical technique for simulating fluid flows. The stability of LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. This study, proposes a complementary scheme for simulating inviscid flows by a compressible lattice Boltzmann model in order to improve the instability using a shock-detecting procedure. The advantages and disadvantages of using a numerical hybrid filter on the primitive or conservative variables, in addition to, macroscopic or mesoscopic variables are investigated. The study demonstrates that the robustness of the utilized LB model is improved for inviscid compressible flows by implementation of the complementary scheme on mesoscopic variables. The validity of the procedure to capture shocks and resolve contact discontinuity and rarefaction waves in well-known benchmark problems is investigated. The numerical results show that the scheme is capable of generating more robust solutions in the simulation of compressible flows and prevents the formation of oscillations. Good agreements are obtained for all test cases.

Improvement of the instability of compressible lattice Boltzmann model by shockdetecting sensor

Energy Technology Data Exchange (ETDEWEB)

Esfahanian, Vahid [University of Tehran, Tehran (Iran, Islamic Republic of); Ghadyani, Mohsen [Islamic Azad University, Tehran (Iran, Islamic Republic of)

2015-05-15

Recently, lattice Boltzmann method (LBM) has drawn attention as an alternative and promising numerical technique for simulating fluid flows. The stability of LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. This study, proposes a complementary scheme for simulating inviscid flows by a compressible lattice Boltzmann model in order to improve the instability using a shock-detecting procedure. The advantages and disadvantages of using a numerical hybrid filter on the primitive or conservative variables, in addition to, macroscopic or mesoscopic variables are investigated. The study demonstrates that the robustness of the utilized LB model is improved for inviscid compressible flows by implementation of the complementary scheme on mesoscopic variables. The validity of the procedure to capture shocks and resolve contact discontinuity and rarefaction waves in well-known benchmark problems is investigated. The numerical results show that the scheme is capable of generating more robust solutions in the simulation of compressible flows and prevents the formation of oscillations. Good agreements are obtained for all test cases.

A Langevin simulation of the Gross-Neveu spectrum

International Nuclear Information System (INIS)

Lacaze, R.; Morel, A.; Petersson, B.

1989-01-01

We study the order parameter of Chiral symmetry, and fermion and boson masses in the Gross-Neveu model as a function of the flavour number N and of the Langevin time step ε in the scaling region. The 1/N dependence of the ε=0 value of the order parameter is in excellent agreement with an analytical calculation up to second order. Care is taken of the important two fermion contribution in the bosonic correlation functions. Mass ratios are found to be ε dependent, but their ε=0 extrapolation is compatible with the analytic expectation

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

DEFF Research Database (Denmark)

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

2006-01-01

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

Langevin theory of anomalous Brownian motion made simple

International Nuclear Information System (INIS)

Tothova, Jana; Vasziova, Gabriela; Lisy, VladimIr; Glod, Lukas

2011-01-01

During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.

Thermal equation of state for lattice Boltzmann gases

International Nuclear Information System (INIS)

Zheng, Ran

2009-01-01

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

Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids: II. Symmetrical top molecules

CERN Document Server

Coffey, W T; Titov, S V

2003-01-01

A theory of orientational relaxation for the inertial rotational Brownian motion of a symmetric top molecule is developed using the Langevin equation rather than the Fokker-Planck equation. The infinite hierarchy of differential-recurrence relations for the orientational correlation functions for the relaxation behaviour is derived by averaging the corresponding Euler-Langevin equations. The solution of this hierarchy is obtained using matrix continued fractions allowing the calculation of the correlation times and the spectra of the orientational correlation functions for typical values of the model parameters.

Correlated continuous-time random walks—scaling limits and Langevin picture

International Nuclear Information System (INIS)

Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr

2012-01-01

In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations

Exact solutions for a discrete unidimensional Boltzmann model satisfying all conservation laws

International Nuclear Information System (INIS)

Cornille, H.

1989-01-01

We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions [fr

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

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

Kinetic Boltzmann, Vlasov and Related Equations

CERN Document Server

Sinitsyn, Alexander; Vedenyapin, Victor

2011-01-01

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

Numerical integration of the Langevin equation: Monte Carlo simulation

International Nuclear Information System (INIS)

Ermak, D.L.; Buckholz, H.

1980-01-01

Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation which uses a memory function in the friction force term. General simulation techniques are derived which are independent of the form of the memory function. A special method requiring less storage space is presented for the case of the exponential memory function

Lattice Boltzmann model for melting with natural convection

International Nuclear Information System (INIS)

Huber, Christian; Parmigiani, Andrea; Chopard, Bastien; Manga, Michael; Bachmann, Olivier

2008-01-01

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

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

Science.gov (United States)

Nuraiman, Dian

2017-10-01

In this paper, we present on modeling and simulation of ocean wave propagation from the deep sea to the shoreline. This requires high computational cost for simulation with large domain. We propose to couple a 1D shallow water equations (SWE) model with a 2D incompressible Navier-Stokes equations (NSE) model in order to reduce the computational cost. The coupled model is solved using the lattice Boltzmann method (LBM) with the lattice Bhatnagar-Gross-Krook (BGK) scheme. Additionally, a special method is implemented to treat the complex behavior of free surface close to the shoreline. The result shows the coupled model can reduce computational cost significantly compared to the full NSE model.

Operational derivation of Boltzmann distribution with Maxwell's demon model.

Science.gov (United States)

Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka

2015-11-24

The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.

Tomography and generative training with quantum Boltzmann machines

Science.gov (United States)

Kieferová, Mária; Wiebe, Nathan

2017-12-01

The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP , provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995), 10.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012), 10.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies.

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

On the interpretations of Langevin stochastic equation in different coordinate systems

International Nuclear Information System (INIS)

Martinez, E.; Lopez-Diaz, L.; Torres, L.; Alejos, O.

2004-01-01

The stochastic Langevin Landau-Lifshitz equation is usually utilized in micromagnetics formalism to account for thermal effects. Commonly, two different interpretations of the stochastic integrals can be made: Ito and Stratonovich. In this work, the Langevin-Landau-Lifshitz (LLL) equation is written in both Cartesian and Spherical coordinates. If Spherical coordinates are employed, the noise is additive, and therefore, Ito and Stratonovich solutions are equal. This is not the case when (LLL) equation is written in Cartesian coordinates. In this case, the Langevin equation must be interpreted in the Stratonovich sense in order to reproduce correct statistical results. Nevertheless, the statistics of the numerical results obtained from Euler-Ito and Euler-Stratonovich schemes are equivalent due to the additional numerical constraint imposed in Cartesian system after each time step, which itself assures that the magnitude of the magnetization is preserved

Ludwig Boltzmann, mechanics and vitalism

International Nuclear Information System (INIS)

Broda, E.

1990-01-01

During most of his life Boltzmann considered classical mechanics, based on the ideas of material points and central forces, as the fundament of physics. On this basis he became one of the founders of Statistical Mechanics, through which thermodynamics was interpreted on an atomistic basis. In this work, Boltzmann was opposed by his colleague, Ernst Mach. Boltzmann also devoted much work to attempts to interpret Maxwell's theory of the electromagnetic field, of which he was a main protagonist in Central Europe, through mechanics. However, as a supporter of mechanics Boltzmann was by no means dogmatic. While he was adamant in his rejection of Wilhelm Ostwald's energism, he was openminded in respect to the relationship of mechanics, electromagnetism and atomistics. Personally, Boltzmann wanted to conserve and transmit the enormous achievements of mechanics, especially in connection with the mechanical theory of heat, so that these results should not be lost to future generations, but he encouraged attempts to proceed in new directions. While within the framework of statistical mechanics the atoms were treated like the material points of classical mechanics, Boltzmann resisted the initial, unwarranted, ideas about the structure and the properties of the atoms. When later valid ideas were evolved, Boltzmann warmly welcomed this progress, without however personally taking part in the new developments. In his later years, Boltzmann took an intense interest in biology. He supported Darwin's theories, and he contributed to them. He may be called an 'absolute Darwinist'. In his search for a natural explanation of the phenomena of life, he used the term 'mechanical', without meaning to limit them to the realm of classical mechanics. This terminological laxity is considered as unfortunate. Extending his application of Darwinian principles to advanced species, including man, Boltzmann put forward 'mechanical' explanations of thought, of morality, of the sense of beauty, and of

An Analysis of Vehicular Traffic Flow Using Langevin Equation

Directory of Open Access Journals (Sweden)

Çağlar Koşun

2015-08-01

Full Text Available Traffic flow data are stochastic in nature, and an abundance of literature exists thereof. One way to express stochastic data is the Langevin equation. Langevin equation consists of two parts. The first part is known as the deterministic drift term, the other as the stochastic diffusion term. Langevin equation does not only help derive the deterministic and random terms of the selected portion of the city of Istanbul traffic empirically, but also sheds light on the underlying dynamics of the flow. Drift diagrams have shown that slow lane tends to get congested faster when vehicle speeds attain a value of 25 km/h, and it is 20 km/h for the fast lane. Three or four distinct regimes may be discriminated again from the drift diagrams; congested, intermediate, and free-flow regimes. At places, even the intermediate regime may be divided in two, often with readiness to congestion. This has revealed the fact that for the selected portion of the highway, there are two main states of flow, namely, congestion and free-flow, with an intermediate state where the noise-driven traffic flow forces the flow into either of the distinct regimes.

Langevin- Science and vigilance

International Nuclear Information System (INIS)

Bensaude-Vincent, B.

1987-01-01

Paul Langevin personifies the figure of popular scientist, buried in the Pantheon, because he was in all great fights: to diffuse knowledge, for improvement and democratization of teaching, for justice and peace. Great theoretician of physics, comparable to Einstein whom he rejoined the approach, he was a fertile discoverer, author, in particular, of a proceeding to detect submarines. He fought politically, regardless of his career, in the ranges of pacifists and opponents of fascism. This book reveals, in his warm diversity, a badly known personality, in spite of the legend in his lifetime. (N.C.)

Classifying images using restricted Boltzmann machines and convolutional neural networks

Science.gov (United States)

Zhao, Zhijun; Xu, Tongde; Dai, Chenyu

2017-07-01

To improve the feature recognition ability of deep model transfer learning, we propose a hybrid deep transfer learning method for image classification based on restricted Boltzmann machines (RBM) and convolutional neural networks (CNNs). It integrates learning abilities of two models, which conducts subject classification by exacting structural higher-order statistics features of images. While the method transfers the trained convolutional neural networks to the target datasets, fully-connected layers can be replaced by restricted Boltzmann machine layers; then the restricted Boltzmann machine layers and Softmax classifier are retrained, and BP neural network can be used to fine-tuned the hybrid model. The restricted Boltzmann machine layers has not only fully integrated the whole feature maps, but also learns the statistical features of target datasets in the view of the biggest logarithmic likelihood, thus removing the effects caused by the content differences between datasets. The experimental results show that the proposed method has improved the accuracy of image classification, outperforming other methods on Pascal VOC2007 and Caltech101 datasets.

Ludwig Boltzmann - pioneer of atomistics and evolution

International Nuclear Information System (INIS)

Stiller, W.

1986-01-01

At first a short introduction to Ludwig Boltzmann's life (1844 - 1906) and work is given. Some theoretical results of his work (H-theorem, classical Boltzmann statistics, Boltzmann's kinetic equation) are treated in detail. His experimental work is briefly discussed. In addition Boltzmann's philosophical work is characterized. Finally, the influence of Boltzmann's ideas on our time is investigated. (author)

Invasion percolation of single component, multiphase fluids with lattice Boltzmann models

International Nuclear Information System (INIS)

Sukop, M.C.; Or, Dani

2003-01-01

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elements on a lattice. In reality, fluid interfaces and connectivity in porous media are naturally controlled by the details of the pore geometry, its dynamic interaction with the fluid, and the ambient fluid potential. The multiphase LBM approach admits realistic pore geometry derived from imaging techniques and incorporation of realistic hydrodynamics into invasion percolation models

Complex Langevin simulation of real time quantum evolution

International Nuclear Information System (INIS)

Ilgenfritz, E.M.; Kripfganz, J.

1986-07-01

Complex Langevin methods are used to study the time evolution of quantum mechanical wave packets. We do not need any Feynman ε regularization for the numerical evaluation of the double time path integral. (author)

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

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

KAUST Repository

Burger, Martin; Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese

2014-01-01

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

Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions

International Nuclear Information System (INIS)

Kwok, Sau Fa

2012-01-01

A Langevin equation with multiplicative white noise and its corresponding Fokker–Planck equation are considered in this work. From the Fokker–Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: ► Fokker–Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. ► Transformation of diffusion processes into the Wiener process in different prescriptions is provided. ► The prescription parameter is associated with the growth rate for a Gompertz-type model.

A lattice Boltzmann model for the Burgers-Fisher equation.

Science.gov (United States)

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Boltzmann, Einstein, Natural Law and Evolution

International Nuclear Information System (INIS)

Broda, E.

1980-01-01

Like Boltzmann, Einstein was a protagonist of atomistics. As a physicist, he has been called Boltzmann's true successor. Also in epistemology, after overcoming the positivist influence of Mach, Einstein approached Boltzmann. Any difference between Boltzmann's realism, or even materialism, and Einstein's pantheism may be merely a matter of emphasis. Yet a real difference exists in another respect. Boltzmann explained man's power of thinking and feeling, his morality and his esthetic sense, on an evolutionary, Darwinian, basis. In contrast, evolution had no role in Einstein's thought, though Darwin was accepted by him. This lack of appreciation of the importance of evolution is now attributed to socio-political factors. (author)

Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

International Nuclear Information System (INIS)

Yotsuji, K.; Tachi, Y.; Nishimaki, Y.

2012-01-01

Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3

Lattice Boltzmann method with the cell-population equilibrium

International Nuclear Information System (INIS)

Zhou Xiaoyang; Cheng Bing; Shi Baochang

2008-01-01

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

Entropic lattice Boltzmann model for charged leaky dielectric multiphase fluids in electrified jets.

Science.gov (United States)

Lauricella, Marco; Melchionna, Simone; Montessori, Andrea; Pisignano, Dario; Pontrelli, Giuseppe; Succi, Sauro

2018-03-01

We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of nonlinear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.

Modeling heat transfer in supercritical fluid using the lattice Boltzmann method.

Science.gov (United States)

Házi, Gábor; Márkus, Attila

2008-02-01

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

Modelling of electric characteristics of 150-watt peak solar panel using Boltzmann sigmoid function under various temperature and irradiance

Science.gov (United States)

Sapteka, A. A. N. G.; Narottama, A. A. N. M.; Winarta, A.; Amerta Yasa, K.; Priambodo, P. S.; Putra, N.

2018-01-01

Solar energy utilized with solar panel is a renewable energy that needs to be studied further. The site nearest to the equator, it is not surprising, receives the highest solar energy. In this paper, a modelling of electrical characteristics of 150-Watt peak solar panels using Boltzmann sigmoid function under various temperature and irradiance is reported. Current, voltage, temperature and irradiance data in Denpasar, a city located at just south of equator, was collected. Solar power meter is used to measure irradiance level, meanwhile digital thermometer is used to measure temperature of front and back panels. Short circuit current and open circuit voltage data was also collected at different temperature and irradiance level. Statistically, the electrical characteristics of 150-Watt peak solar panel can be modelled using Boltzmann sigmoid function with good fit. Therefore, it can be concluded that Boltzmann sigmoid function might be used to determine current and voltage characteristics of 150-Watt peak solar panel under various temperature and irradiance.

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

OpenAIRE

Song-Gui Chen; Chuan-Hu Zhang; Yun-Tian Feng; Qi-Cheng Sun; Feng Jin

2016-01-01

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-L...

Evolution of a neutral-ion 2 fluid system using thermal lattice Boltzmann model

International Nuclear Information System (INIS)

Vahala, L.; Vahala, G.; Carter, J.; Pavlo, P.

2000-01-01

The 2D evolution of a 2-species system is examined using the thermal lattice Boltzmann model (TLBM). The effects of velocity shear layers on sharp heat fronts are considered for a neutral-ion system in the case where both species are turbulent. The rate at which the species velocities and temperatures equilibrate no longer follow the Morse estimate. (author)

Limitations of Boltzmann's principle

International Nuclear Information System (INIS)

Lavenda, B.H.

1995-01-01

The usual form of Boltzmann's principle assures that maximum entropy, or entropy reduction, occurs with maximum probability, implying a unimodal distribution. Boltzmann's principle cannot be applied to nonunimodal distributions, like the arcsine law, because the entropy may be concave only over a limited portion of the interval. The method of subordination shows that the arcsine distribution corresponds to a process with a single degree of freedom, thereby confirming the invalidation of Boltzmann's principle. The fractalization of time leads to a new distribution in which arcsine and Cauchy distributions can coexist simultaneously for nonintegral degrees of freedom between √2 and 2

Ludwig Boltzmann: Atomic genius

Energy Technology Data Exchange (ETDEWEB)

Cercignani, C. [Department of Mathematics, Politecnico di Milano (Italy)]. E-mail: carcer@mate.polimi.it

2006-09-15

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.)

Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

International Nuclear Information System (INIS)

Brett, Tobias; Galla, Tobias

2014-01-01

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period

Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system.

Science.gov (United States)

Brett, Tobias; Galla, Tobias

2014-03-28

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

Multiple-relaxation-time lattice Boltzmann model for compressible fluids

International Nuclear Information System (INIS)

Chen Feng; Xu Aiguo; Zhang Guangcai; Li Yingjun

2011-01-01

We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version. - Highlights: → We present an energy-conserving MRT finite-difference LB model. → The moment space is constructed according to the group representation theory. → The new model works for both low and high speeds compressible flows. → It has better numerical stability and wider applicable range than its SRT version.

Signals for the QCD phase transition and critical point in a Langevin dynamical model

International Nuclear Information System (INIS)

Herold, Christoph; Bleicher, Marcus; Yan, Yu-Peng

2013-01-01

The search for the critical point is one of the central issues that will be investigated in the upcoming FAIR project. For a profound theoretical understanding of the expected signals we go beyond thermodynamic studies and present a fully dynamical model for the chiral and deconfinement phase transition in heavy ion collisions. The corresponding order parameters are propagated by Langevin equations of motions on a thermal background provided by a fluid dynamically expanding plasma of quarks. By that we are able to describe nonequilibrium effects occurring during the rapid expansion of a hot fireball. For an evolution through the phase transition the formation of a supercooled phase and its subsequent decay crucially influence the trajectories in the phase diagram and lead to a significant reheating of the quark medium at highest baryon densities. Furthermore, we find inhomogeneous structures with high density domains along the first order transition line within single events.

Langevin description of fission fragment charge distribution from excited nuclei

CERN Document Server

Karpov, A V

2002-01-01

A stochastic approach to fission dynamics based on a set of three-dimensional Langevin equations was applied to calculate fission-fragment charge distribution of compound nucleus sup 2 sup 3 sup 6 U. The following collective coordinates have been chosen - elongation coordinate, neck-thickness coordinate, and charge-asymmetry coordinate. The friction coefficient of charge mode has been calculated in the framework of one-body and two-body dissipation mechanisms. Analysis of the results has shown that Langevin approach is appropriate for investigation of isobaric distribution. Moreover, the dependences of the variance of the charge distribution on excitation energy and on the two-body viscosity coefficient has been studied

Gli atomi di Boltzmann

CERN Document Server

Lindley, David

2002-01-01

Ludwig Boltzmann (1844-1906) è il fisico e matematico austriaco che negli ultimi decenni dell'Ottocento e ancora ai primi del Novecento lottò contro l'opinione dominante tra gli scienziati dell'epoca per affermare la teoria atomica della materia. È noto come con Albert Einstein e fino a oggi la fisica si sia sviluppata e abbia celebrato i propri trionfi lungo le linee anticipate da Boltzmann. La controversia con Mach non riguardava soltanto l'esistenza degli atomi, ma l'intero modo di fare fisica che Boltzmann non riteneva di dover limitare allo studio di quantità misurabili, introducendo invece spiegazioni più elaborate basate su ipotesi più ampie.

Heat dissipation and information flow for delayed bistable Langevin systems near coherence resonance.

Science.gov (United States)

Xiao, Tiejun

2016-11-01

In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.

Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

PDF models and synthetic model for the wind speed fluctuations based on the resolution of Langevin equation

International Nuclear Information System (INIS)

Calif, Rudy

2012-01-01

Highlights: ► Probability Density Functions are proposed to fit the wind speed fluctuations distributions for three representative classes. ► Stochastic simulations are performed using a Langevin equation for each class. ► The properties of simulated and measured wind speed sequences are close. -- Abstract: Wind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1 h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each class.

Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

International Nuclear Information System (INIS)

Diestler, D.J.; Riley, M.E.

1985-01-01

We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed

Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process

Directory of Open Access Journals (Sweden)

Song Wenyu

2017-06-01

Full Text Available In the current study, a macroscopic lattice Boltzmann model for simulating the heat and moisture transport phenomenon in unsaturated porous media during the freezing process was proposed. The proposed model adopted percolation threshold to reproduce the extra resistance in frozen fringe during the freezing process. The freezing process in Kanagawa sandy loam soil was demonstrated by the proposed model. The numerical result showed good agreement with the experimental result. The proposed model also offered higher computational efficiency and better agreement with the experimental result than the existing numerical models. Lattice Boltzmann method is suitable for simulating complex heat and mass transfer process in porous media at macroscopic scale under proper dimensionless criterion, which makes it a potentially powerful tool for engineering application.

Riemann-Theta Boltzmann Machine arXiv

CERN Document Server

Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

Modelling viscoacoustic wave propagation with the lattice Boltzmann method.

Science.gov (United States)

Xia, Muming; Wang, Shucheng; Zhou, Hui; Shan, Xiaowen; Chen, Hanming; Li, Qingqing; Zhang, Qingchen

2017-08-31

In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.

Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases

OpenAIRE

Cates, M. E.; Henrich, O.; Marenduzzo, D.; Stratford, K.

2010-01-01

Lattice Boltzmann simulations have become a method of choice to solve the hydrodynamic equations of motion of a number of complex fluids. Here we review some recent applications of lattice Boltzmann to study the hydrodynamics of liquid crystalline materials. In particular, we focus on the study of (a) the exotic blue phases of cholesteric liquid crystals, and (b) active gels - a model system for actin plus myosin solutions or bacterial suspensions. In both cases lattice Boltzmann studies have...

Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

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Guo, Yangyu; Wang, Moran

2017-10-01

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

A pore-scale model for the cathode electrode of a proton exchange membrane fuel cell by lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Molaeimanesh, Gholam Reza; Akbari, Mohammad Hadi [Shiraz University, Shiraz (Iran, Islamic Republic of)

2015-03-15

A pore-scale model based on the lattice Boltzmann method (LBM) is proposed for the cathode electrode of a PEM fuel cell with heterogeneous and anisotropic porous gas diffusion layer (GDL) and interdigitated flow field. An active approach is implemented to model multi-component transport in GDL, which leads to enhanced accuracy, especially at higher activation over-potentials. The core of the paper is the implementation of an electrochemical reaction with an active approach in a multi-component lattice Boltzmann model for the first time. After model validation, the capability of the presented model is demonstrated through a parametric study. Effects of activation over-potential, pressure differential between inlet and outlet gas channels, land width to channel width ratio, and channel width are investigated. The results show the significant influence of GDL microstructure on the oxygen distribution and current density profile.

Understanding price discovery in interconnected markets: Generalized Langevin process approach and simulation

Science.gov (United States)

Schenck, Natalya A.; Horvath, Philip A.; Sinha, Amit K.

2018-02-01

While the literature on price discovery process and information flow between dominant and satellite market is exhaustive, most studies have applied an approach that can be traced back to Hasbrouck (1995) or Gonzalo and Granger (1995). In this paper, however, we propose a Generalized Langevin process with asymmetric double-well potential function, with co-integrated time series and interconnected diffusion processes to model the information flow and price discovery process in two, a dominant and a satellite, interconnected markets. A simulated illustration of the model is also provided.

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

Science.gov (United States)

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Comparison of Einstein-Boltzmann solvers for testing general relativity

Science.gov (United States)

Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.

2018-01-01

We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

The Boltzmann project

Science.gov (United States)

Fischer, J.; Fellmuth, B.; Gaiser, C.; Zandt, T.; Pitre, L.; Sparasci, F.; Plimmer, M. D.; de Podesta, M.; Underwood, R.; Sutton, G.; Machin, G.; Gavioso, R. M.; Madonna Ripa, D.; Steur, P. P. M.; Qu, J.; Feng, X. J.; Zhang, J.; Moldover, M. R.; Benz, S. P.; White, D. R.; Gianfrani, L.; Castrillo, A.; Moretti, L.; Darquié, B.; Moufarej, E.; Daussy, C.; Briaudeau, S.; Kozlova, O.; Risegari, L.; Segovia, J. J.; Martín, M. C.; del Campo, D.

2018-04-01

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649  ×  10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7  ×  10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Phase space dynamics and collective variable fluctuations

International Nuclear Information System (INIS)

Benhassine, B.; Farine, M.; Idier, D.; Remaud, B.; Sebille, F.; Schuck, P.

1995-01-01

A dynamical study of collective variable fluctuations in heavy ion reactions is performed within the framework of the Boltzmann-Langevin theory. A general method to extract dispersions on collective variables from numerical simulations based on test particles models is presented and its validity is checked by comparison with analytical equilibrium results. (authors)

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

Directory of Open Access Journals (Sweden)

Stuart Bartlett

2017-08-01

Full Text Available The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

Lattice Boltzmann method for weakly ionized isothermal plasmas

International Nuclear Information System (INIS)

Li Huayu; Ki, Hyungson

2007-01-01

In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values

Asymmetrically extremely dilute neural networks with Langevin dynamics and unconventional results

International Nuclear Information System (INIS)

Hatchett, J P L; Coolen, A C C

2004-01-01

We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the binary neurons case) that even in statics, for T > 0 or large α, one cannot eliminate the non-persistent order parameters, atypically for recurrent neural network models. The macroscopic dynamics is driven by the (non-trivial) joint distribution of neurons and fields, rather than just the (Gaussian) field distribution. We calculate phase transition lines and find, as may be expected for this asymmetric model, that there is no spin-glass phase, only recall and paramagnetic phases. We present simulation results in support of our theory

Stable lattice Boltzmann model for Maxwell equations in media

Science.gov (United States)

Hauser, A.; Verhey, J. L.

2017-12-01

The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Science.gov (United States)

Sofonea, V.; Biciuşcǎ, T.; Busuioc, S.; Ambruş, Victor E.; Gonnella, G.; Lamura, A.

2018-02-01

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 ×6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca≳0.2 .

Phase space dynamics and collective variable fluctuations

Energy Technology Data Exchange (ETDEWEB)

Benhassine, B.; Farine, M.; Idier, D.; Remaud, B.; Sebille, F. [Laboratoire de Physique Nucleaire de Nantes, 44 (France); Schuck, P. [Institut des Sciences Nucleaires, 38 - Grenoble (France)

1995-12-31

A dynamical study of collective variable fluctuations in heavy ion reactions is performed within the framework of the Boltzmann-Langevin theory. A general method to extract dispersions on collective variables from numerical simulations based on test particles models is presented and its validity is checked by comparison with analytical equilibrium results. (authors) 10 refs.

Nuclear fission with a Langevin equation

International Nuclear Information System (INIS)

Boilley, D.; Suraud, E.; Abe, Yasuhisa

1992-01-01

A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs

A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation

NARCIS (Netherlands)

Hoitinga, W.; Brummelen, van E.H.

2011-01-01

To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly

Langevin approach to synchronization of hyperchaotic time-delay dynamics

Energy Technology Data Exchange (ETDEWEB)

Budini, Adrian A [Consejo Nacional de Investigaciones CientIficas y Tecnicas, Centro Atomico Bariloche, Av. E Bustillo Km 9.5, (8400) Bariloche (Argentina); Consortium of the Americas for Interdisciplinary Science and Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131 (United States)

2008-11-07

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar nonlinear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the nonlinear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second-order differential delay equations associated with synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated with the hyperchaotic dynamics support the formalism.

A topological insight into restricted Boltzmann machines

NARCIS (Netherlands)

Mocanu, D.C.; Mocanu, E.; Nguyen, H.P.; Gibescu, M.; Liotta, A.

Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as density estimators. Thus, their generative and discriminative

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

Science.gov (United States)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

Lattice Boltzmann heat transfer model for permeable voxels

Science.gov (United States)

Pereira, Gerald G.; Wu, Bisheng; Ahmed, Shakil

2017-12-01

We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

Science.gov (United States)

Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

2015-04-01

We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.

Science.gov (United States)

Li, Q; Luo, K H; Li, X J

2012-07-01

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

QSPR models based on molecular mechanics and quantum chemical calculations. 1. Construction of Boltzmann averaged descriptors for alkanes, alcohols, diols, ethers and cyclic compounds

DEFF Research Database (Denmark)

Dyekjær, Jane Dannow; Rasmussen, Kjeld; Jonsdottir, Svava Osk

2002-01-01

Values for nine descriptors for QSPR (quantitative structure-property relationships) modeling of physical properties of 96 alkanes, alcohols, ethers, diols, triols and cyclic alkanes and alcohols in conjunction with the program Codessa are presented. The descriptors are Boltzmann-averaged by sele......Values for nine descriptors for QSPR (quantitative structure-property relationships) modeling of physical properties of 96 alkanes, alcohols, ethers, diols, triols and cyclic alkanes and alcohols in conjunction with the program Codessa are presented. The descriptors are Boltzmann...

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

International Nuclear Information System (INIS)

Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin

2014-01-01

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body

Relativistic Boltzmann theory for a plasma

International Nuclear Information System (INIS)

Erkelens, H. van.

1984-01-01

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.)

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

Science.gov (United States)

Farhat, Hassan

Colloids are ubiquitous in the food, medical, cosmetic, polymer, water purification and pharmaceutical industries. Colloids thermal, mechanical and storage properties are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a cheap and reliable virtual laboratory for the study of colloids. However efficiency is a major concern to address when using numerical methods for practical applications. This work introduces the main building-blocks for an improved lattice Boltzmann-based numerical tool designed for the study of colloidal rheology and interface morphology. The efficiency of the proposed model is enhanced by using the recently developed and validated migrating multi-block algorithms for the lattice Boltzmann method (LBM). The migrating multi-block was used to simulate single component, multi-component, multiphase and single component multiphase flows. Results were validated by experimental, numerical and analytical solutions. The contamination of the fluid-fluid interface influences the colloids morphology. This issue was addressed by the introduction of the hybrid LBM for surfactant-covered droplets. The module was used for the simulation of surfactant-covered droplet deformation under shear and uniaxial extensional flows respectively and under buoyancy. Validation with experimental and theoretical results was provided. Colloids are non-Newtonian fluids which exhibit rich rheological behavior. The suppression of coalescence module is the part of the proposed model which facilitates the study of colloids rheology. The model results for the relative viscosity were in agreement with some theoretical results. Biological suspensions such as blood are macro-colloids by nature. The study of the blood flow in the microvasculature was heuristically approached by assuming the red blood cells as surfactant covered droplets. The effects of interfacial tension on the flow velocity and the droplet exclusion from the walls

Electronic transport in VO2—Experimentally calibrated Boltzmann transport modeling

International Nuclear Information System (INIS)

Kinaci, Alper; Rosenmann, Daniel; Chan, Maria K. Y.; Kado, Motohisa; Ling, Chen; Zhu, Gaohua; Banerjee, Debasish

2015-01-01

Materials that undergo metal-insulator transitions (MITs) are under intense study, because the transition is scientifically fascinating and technologically promising for various applications. Among these materials, VO 2 has served as a prototype due to its favorable transition temperature. While the physical underpinnings of the transition have been heavily investigated experimentally and computationally, quantitative modeling of electronic transport in the two phases has yet to be undertaken. In this work, we establish a density-functional-theory (DFT)-based approach with Hubbard U correction (DFT + U) to model electronic transport properties in VO 2 in the semiconducting and metallic regimes, focusing on band transport using the Boltzmann transport equations. We synthesized high quality VO 2 films and measured the transport quantities across the transition, in order to calibrate the free parameters in the model. We find that the experimental calibration of the Hubbard correction term can efficiently and adequately model the metallic and semiconducting phases, allowing for further computational design of MIT materials for desirable transport properties

Etude d'un modele de Boltzmann sur reseau pour la simulation assistee par ordinateur des fluides a plusieurs phases immiscibles

Science.gov (United States)

Leclaire, Sebastien

The computer assisted simulation of the dynamics of fluid flow has been a highly rewarding topic of research for several decades now, in terms of the number of scientific problems that have been solved as a result, both in the academic world and in industry. In the fluid dynamics field, simulating multiphase immiscible fluid flow remains a challenge, because of the complexity of the interactions at the flow phase interfaces. Various numerical methods are available to study these phenomena, and, the lattice Boltzmann method has been shown in recent years to be well adapted to solving this type of complex flow. In this thesis, a lattice Boltzmann model for the simulation of two-phase immiscible flows is studied. The main objective of the thesis is to develop this promising method further, with a view to enhancing its validity. To achieve this objective, the research is divided into five distinct themes. The first two focus on correcting some of the deficiencies of the original model. The third generalizes the model to support the simulation of N-phase immiscible fluid flows. The fourth is aimed at modifying the model itself, to enable the simulation of immiscible fluid flows in which the density of the phases varies. With the lattice Boltzmann class of models studied here, this density variation has been inadequately modeled, and, after 20 years, the issue still has not been resolved. The fifth, which complements this thesis, is connected with the lattice Boltzmann method, in that it generalizes the theory of 2D and 3D isotropic gradients for a high order of spatial precision. These themes have each been the subject of a scientific article, as listed in the appendix to this thesis, and together they constitute a synthesis that explains the links between the articles, as well as their scientific contributions, and satisfy the main objective of this research. Globally, a number of qualitative and quantitative test cases based on the theory of multiphase fluid flows

Large Time Behavior of the Vlasov-Poisson-Boltzmann System

Directory of Open Access Journals (Sweden)

Li Li

2013-01-01

Full Text Available The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005. The improvement of the present paper is the removal of condition on parameter λ as in the work of Li (2008.

Soft-Deep Boltzmann Machines

OpenAIRE

Kiwaki, Taichi

2015-01-01

We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs over RBMs has not ever been validated in a theoretical fashion. In this paper, we provide both theoretical and empirical evidences that the representational power of DBMs can be a...

Non-linear effects in the Boltzmann equation

International Nuclear Information System (INIS)

Barrachina, R.O.

1985-01-01

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.) [es

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

Science.gov (United States)

Berglund, Mathias; Raiko, Tapani; Cho, Kyunghyun

2015-04-01

Restricted Boltzmann machines (RBMs) and deep Boltzmann machines (DBMs) are important models in deep learning, but it is often difficult to measure their performance in general, or measure the importance of individual hidden units in specific. We propose to use mutual information to measure the usefulness of individual hidden units in Boltzmann machines. The measure is fast to compute, and serves as an upper bound for the information the neuron can pass on, enabling detection of a particular kind of poor training results. We confirm experimentally that the proposed measure indicates how much the performance of the model drops when some of the units of an RBM are pruned away. We demonstrate the usefulness of the measure for early detection of poor training in DBMs. Copyright © 2014 Elsevier Ltd. All rights reserved.

Joint Training of Deep Boltzmann Machines

OpenAIRE

Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua

2012-01-01

We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.

Singularities in the nonisotropic Boltzmann equation

International Nuclear Information System (INIS)

Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

1987-09-01

We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

Institut Max von Laue-Paul Langevin

International Nuclear Information System (INIS)

This part of the annual report is concerned with the external and internal organization of the ILL (Institut Laue-Langevin), and a general presentation of the activities of the ILL during 1975. A first part is concerned with measurement and control instruments: three axis spectrometers,, time-of-flight, crystallography, diffuse scattering, powder spectrometers, polarized neutrons, monochromators, nuclear physics. In the second part the fields of research are reviewed by College: theory, nuclear physics, excitations, structures, liquids, gas and amorphous materials, imperfections, physical biochemistry, and chemistry, reactor exploitation [fr

Institut Max von Laue-Paul Langevin

International Nuclear Information System (INIS)

Whereas the first volume of the Annual Report gives a general survey of the activities of the different sections of the ILL (Institut Laue-Langevin), this second volume titled Annex to the 1975 annual report is dealing in more details with the scientific work carried out at the ILL from November the 1st 1974 to October the 1st 1975. Scientific works for which reports are available are presented grouped as possible, by college: theory; nuclear physics; excitations; structures; liquids, gas and amorphous materials; imperfections; physical biochemistry; and chemistry [fr

A topological insight into restricted Boltzmann machines (extented abstract)

NARCIS (Netherlands)

Mocanu, D.C.; Mocanu, E.; Nguyen, H.P.; Gibescu, M.; Liotta, A.

2016-01-01

Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep neural networks for automatic features extraction, unsupervised weights initialization, but also as standalone models for density estimation, activity recognition and so on.

Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

DEFF Research Database (Denmark)

Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

2015-01-01

A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall. It is sh......A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall...

Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

Science.gov (United States)

Dalgamoni, Hussein; Yong, Xin

2017-11-01

Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.

Combinatorial optimization on a Boltzmann machine

NARCIS (Netherlands)

Korst, J.H.M.; Aarts, E.H.L.

1989-01-01

We discuss the problem of solving (approximately) combinatorial optimization problems on a Boltzmann machine. It is shown for a number of combinatorial optimization problems how they can be mapped directly onto a Boltzmann machine by choosing appropriate connection patterns and connection strengths.

Quantum linear Boltzmann equation

International Nuclear Information System (INIS)

Vacchini, Bassano; Hornberger, Klaus

2009-01-01

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

Langevin equation in effective theory of interacting QCD pomerons in the limit of large Nc

International Nuclear Information System (INIS)

Bondarenko, S.

2007-01-01

Effective field theory of interacting BFKL pomerons is investigated and Langevin equation for the theory, which arises after the introduction of additional auxiliary field, is obtained. The Langevin equations are considered for the case of interacting BFKL pomerons with both splitting and merging vertexes and for the interaction which includes additional 'toy' four pomeron interaction vertex. In the latest case an analogy with the Regge field theory in zero dimensions (RFT-0) was used in order to obtain this 'toy' vertex, which coincided with the four point function of two-dimensional conformal field theory obtained in [G.P. Korchemsky, Nucl. Phys. B 550 (1999) 397]. The comparison between the Langevin equations obtained in the frameworks of dipole and RFT approaches is performed, the interpretation of results is given and possible application of obtained equations is discussed

Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method

Directory of Open Access Journals (Sweden)

Muneki Yasuda

2018-04-01

Full Text Available The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning problems in the Boltzmann machine are NP-hard. The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning. In this paper, we study Boltzmann machine learning based on the (first-order spatial Monte Carlo integration method, referred to as the 1-SMCI learning method, which was proposed in the author’s previous paper. In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is more effective than the MPLE. In the latter part, we compare the 1-SMCI learning method with other effective methods, ratio matching and minimum probability flow, using a numerical experiment, and show the 1-SMCI learning method outperforms them.

Numerical simulations of generalized Langevin equations with deeply asymptotic parameters

International Nuclear Information System (INIS)

Bao Jingdong; Li Rongwu; Wu Wei

2004-01-01

A unified algorithm for solving Langevin equations with deeply asymptotic parameters is proposed and tested. The method consists of identifying solvable linear friction and implementing the force evaluations by use of the Runge-Kutta method. We apply the present scheme to the periodic motion of an overdamped particle subjected to a multiplicative white noise. The accurate calculations for the temporal velocity of the particle and its correlation function can be realized by introducing an inertial term. It is shown that the fluctuation around the steady quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift, and the result can converge to the correct value if the added inertia approaches zero. The other application is the simulation of generalized Langevin equation with an exponential memory friction, this allows us to treat a weak non-Markovian process

On the non-stationary generalized Langevin equation

Science.gov (United States)

Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

2017-12-01

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations

International Nuclear Information System (INIS)

Xu Kun; He Xiaoyi

2003-01-01

Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented

Ethic and Evolution in Boltzmann's and Einstein's Thought

Energy Technology Data Exchange (ETDEWEB)

Broda, E.

1980-07-01

In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

Ethic and Evolution in Boltzmann's and Einstein's Thought

International Nuclear Information System (INIS)

Broda, E.

1980-01-01

In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

Langevin equation of a fluid particle in wall-induced turbulence

NARCIS (Netherlands)

Brouwers, J.J.H.

2010-01-01

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-inducedturbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer).The analysis is based on the asymptotic behavior at a large Reynolds number. We use

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Directory of Open Access Journals (Sweden)

Nikolai N. Bogoliubov (Jr.

2007-01-01

Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

Deviations from the Boltzmann distribution in vibrationally excited gas flows

International Nuclear Information System (INIS)

Offenhaeuser, F.; Frohn, A.

1986-01-01

A new model for the exchange of vibrational energy in one-dimensional flows of CO 2 -H 2 O-N 2 -O 2 -He gas mixtures is presented. In contrast to previous models, the assumption of local Boltzmann distributions for the vibrational degrees of freedom is not required. This generalization was achieved by the assumption that the molecules are harmonic oscillators with one or more degrees of freedom represented by finite numbers of energy levels. The population densities of these energy levels are coupled by a set of rate equations. It is shown that in some cases of molecular gas flow the Boltzmann distribution for the vibrational degrees of freedom may be disturbed. 12 references

Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

Science.gov (United States)

Cadilhe, A.; Voter, Arthur F.

2018-02-01

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

International Nuclear Information System (INIS)

Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad

2014-01-01

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion

Large Eddy Simulation of Wall-Bounded Turbulent Flows with the Lattice Boltzmann Method: Effect of Collision Model, SGS Model and Grid Resolution

Science.gov (United States)

Pradhan, Aniruddhe; Akhavan, Rayhaneh

2017-11-01

Effect of collision model, subgrid-scale model and grid resolution in Large Eddy Simulation (LES) of wall-bounded turbulent flows with the Lattice Boltzmann Method (LBM) is investigated in turbulent channel flow. The Single Relaxation Time (SRT) collision model is found to be more accurate than Multi-Relaxation Time (MRT) collision model in well-resolved LES. Accurate LES requires grid resolutions of Δ+ LBM requires either grid-embedding in the near-wall region, with grid resolutions comparable to DNS, or a wall model. Results of LES with grid-embedding and wall models will be discussed.

A note on Boltzmann brains

Energy Technology Data Exchange (ETDEWEB)

Nomura, Yasunori, E-mail: ynomura@berkeley.edu

2015-10-07

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.

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

International Nuclear Information System (INIS)

Mozolevski, I.E.

2001-01-01

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

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

Science.gov (United States)

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Another higher order Langevin algorithm for QCD

International Nuclear Information System (INIS)

Kronfeld, A.S.

1986-01-01

This note provides an algorithm for integrating the Langevin equation which is second order. It introduces a term into the drift force which is a product of the Gaussian noise and a second derivative of the action. The specific application presented here is for nonabelian gauge theories interacting with fermions, e.g. QCD, for which it requires less memory than the Runge-Kutta algorithm of the same order. The memory and computational requirements of Euler, Runge-Kutta, and the present algorithm are compared. (orig.)

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

Science.gov (United States)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

International Nuclear Information System (INIS)

Zergani, Sara; Aziz, Z A; Viswanathan, K K

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory

Optimising Boltzmann codes for the PLANCK era

International Nuclear Information System (INIS)

Hamann, Jan; Lesgourgues, Julien; Balbi, Amedeo; Quercellini, Claudia

2009-01-01

High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the PLANCK satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical error in the output of the Boltzmann codes used to calculate angular power spectra. In this work, we carry out an extensive study of the numerical accuracy of the public Boltzmann code CAMB, and identify a set of parameters which determine the error of its output. We show that at the current default settings, the cosmological parameters extracted from data of future experiments like Planck can be biased by several tenths of a standard deviation for the six parameters of the standard ΛCDM model, and potentially more seriously for extended models. We perform an optimisation procedure that leads the code to achieve sufficient precision while at the same time keeping the computation time within reasonable limits. Our conclusion is that the contribution of numerical errors to the theoretical uncertainty of model predictions is well under control—the main challenges for more accurate calculations of CMB spectra will be of an astrophysical nature instead

Contact angle determination in multicomponent lattice Boltzmann simultations

NARCIS (Netherlands)

Schmieschek, S.M.P.; Harting, J.D.R.

2011-01-01

Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications and there exists a number of commonly used multicomponent and multiphase lattice Boltzmann schemes to study such systems. In this paper we focus on a popular implementation of a multicomponent model as introduced by Shan

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...

The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein

International Nuclear Information System (INIS)

Broda, E.

1981-01-01

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.)

Inelastic X-ray scattering on liquid benzene analyzed using a generalized Langevin equation

Science.gov (United States)

Yoshida, Koji; Fukuyama, Nami; Yamaguchi, Toshio; Hosokawa, Shinya; Uchiyama, Hiroshi; Tsutsui, Satoshi; Baron, Alfred Q. R.

2017-07-01

The dynamic structure factor, S(Q,ω), of liquid benzene was measured by meV-resolved inelastic X-ray scattering (IXS) and analyzed using a generalized Langevin model with a memory function including fast, μ-relaxation and slow, structural, α-relaxation. The model well reproduced the experimental S(Q,ω) of liquid benzene. The dispersion relation of the collective excitation energy yields the high-frequency sound velocity for liquid benzene as related to the α-relaxation. The ratio of the high-frequency to the adiabatic sound velocity is approximately 1.5, larger to that of carbon tetrachloride and smaller than those of methanol and water, reflecting the nature of intermolecular interactions.

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

Science.gov (United States)

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

Volumetric formulation of lattice Boltzmann models with energy conservation

OpenAIRE

Sbragaglia, M.; Sugiyama, K.

2010-01-01

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. ...

Monte Carlo variance reduction approaches for non-Boltzmann tallies

International Nuclear Information System (INIS)

Booth, T.E.

1992-12-01

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

Brownian motion of spins; generalized spin Langevin equation

International Nuclear Information System (INIS)

Jayannavar, A.M.

1990-03-01

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concomitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature. (author). 16 refs

Boltzmann und das Ende des mechanistischen Weltbildes

CERN Document Server

Renn, Jürgen

2007-01-01

Der Wissenschaftshistoriker und Physiker Jürgen Renn untersucht die Rolle des österreichischen Physikers und Philosophen Ludwig Boltzmann (18441906) bei der Entwicklung der modernen Physik. Boltzmann war einer der letzen Vertreter des mechanistischen Weltbildes und stand somit am Ende eines Zeitalters. Renn porträtiert den Wissenschaftler aber als einen Pionier der modernen Physik, dessen Beschäftigung mit den inneren Spannungen der klassischen Physik ihn visionär zukünftige Fragestellungen aufgreifen ließ. So befasste sich Boltzmann etwa mit den Grenzproblemen zwischen Mechanik und Thermodynamik, die ihn zur Entwicklung immer raffinierterer Instrumente der statistischen Physik antrieb, die schließlich zu Schlüsselinstrumenten der modernen Physik wurden. Boltzmanns Werk steht somit am Übergang vom mechanistischen Weltbild zur Relativitäts- und Quantentheorie. Der Aussage des viel bekannteren Physikers Albert Einstein, dass Fantasie wichtiger sei als Wissen, hält Jürgen Renn im Hinblick auf Leben ...

Towards a physical interpretation of the entropic lattice Boltzmann method

Science.gov (United States)

Malaspinas, Orestis; Deville, Michel; Chopard, Bastien

2008-12-01

The entropic lattice Boltzmann method (ELBM) is one among several different versions of the lattice Boltzmann method for the simulation of hydrodynamics. The collision term of the ELBM is characterized by a nonincreasing H function, guaranteed by a variable relaxation time. We propose here an analysis of the ELBM using the Chapman-Enskog expansion. We show that it can be interpreted as some kind of subgrid model, where viscosity correction scales like the strain rate tensor. We confirm our analytical results by the numerical computations of the relaxation time modifications on the two-dimensional dipole-wall interaction benchmark.

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

International Nuclear Information System (INIS)

Green, B I; Vedula, Prakash

2013-01-01

An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)

Application of the lattice Boltzmann model to simulated stenosis growth in a two-dimensional carotid artery

International Nuclear Information System (INIS)

Boyd, J; Buick, J; Cosgrove, J A; Stansell, P

2005-01-01

The lattice Boltzmann model is used to observe changes in the velocity flow and shear stress in a carotid artery model during a simulated stenosis growth. Near wall shear stress in the unstenosed artery is found to agree with literature values. The model also shows regions of low velocity, rotational flow and low near wall shear stress along parts of the walls of the carotid artery that have been identified as being prone to atherosclerosis. These regions persist during the simulated stenosis growth, suggesting that atherosclerotic plaque build-up creates regions of flow with properties that favour atherosclerotic progression

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

Science.gov (United States)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

Trap-assisted and Langevin-type recombination in organic light-emitting diodes

Science.gov (United States)

Wetzelaer, G. A. H.; Kuik, M.; Nicolai, H. T.; Blom, P. W. M.

2011-04-01

Trapping of charges is known to play an important role in the charge transport of organic semiconductors, but the role of traps in the recombination process has not been addressed. Here we show that the ideality factor of the current of organic light-emitting diodes (OLEDs) in the diffusion-dominated regime has a temperature-independent value of 2, which reveals that nonradiative trap-assisted recombination dominates the current. In contrast, the ideality factor of the light output approaches unity, demonstrating that luminance is governed by recombination of the bimolecular Langevin type. This apparent contradiction can be resolved by measuring the current and luminance ideality factor for a white-emitting polymer, where both free and trapped charge carriers recombine radiatively. With increasing bias voltage, Langevin recombination becomes dominant over trap-assisted recombination due to its stronger dependence on carrier density, leading to an enhancement in OLED efficiency.

Boltzmann-Gaussian transition under specific noise effect

International Nuclear Information System (INIS)

Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai

2014-01-01

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.

Polar-coordinate lattice Boltzmann modeling of compressible flows

Science.gov (United States)

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

2014-01-01

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

Dissipative Boltzmann-Robertson-Walker cosmologies

International Nuclear Information System (INIS)

Hiscock, W.A.; Salmonson, J.

1991-01-01

The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that ''bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory

Non-Gaussian statistics, classical field theory, and realizable Langevin models

International Nuclear Information System (INIS)

Krommes, J.A.

1995-11-01

The direct-interaction approximation (DIA) to the fourth-order statistic Z ∼ left-angle λψ 2 ) 2 right-angle, where λ is a specified operator and ψ is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z DIA already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (''spurious vertices'') is described. It is shown how to derive an improved representation, that realizes cumulants through O(ψ 4 ), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z DIA M to Z DIA is derived. Both Z DIA and Z DIA M incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example

Study of nonequilibrium work distributions from a fluctuating lattice Boltzmann model.

Science.gov (United States)

Nasarayya Chari, S Siva; Murthy, K P N; Inguva, Ramarao

2012-04-01

A system of ideal gas is switched from an initial equilibrium state to a final state not necessarily in equilibrium, by varying a macroscopic control variable according to a well-defined protocol. The distribution of work performed during the switching process is obtained. The equilibrium free energy difference, ΔF, is determined from the work fluctuation relation. Some of the work values in the ensemble shall be less than ΔF. We term these as ones that "violate" the second law of thermodynamics. A fluctuating lattice Boltzmann model has been employed to carry out the simulation of the switching experiment. Our results show that the probability of violation of the second law increases with the increase of switching time (τ) and tends to one-half in the reversible limit of τ→∞.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Ludwig Boltzmann - The Man and His Work

International Nuclear Information System (INIS)

Broda, E.

1982-01-01

It is argued that Ludwig Boltzmann was, along with Newton and Maxwell, one of the three greatest theoretical physicists of classical times. It is less generally known that he was also a powerful realist-materialist philosopher and a keen opponent of Ernst Mach's positivism and of the philosophical idealism of Berkeley, Hegel and Schopenhauer. Boltzmann was also opposed to Kant. Moreover, he had a lively interest in biology and especially in Darwinian evolution, and he should be taken as one of the founders of biophysics. Boltzmann discussed the origin of life and of the mind. Finally, he also was a most vigorous, colourful and attractive person. (author)

Electronic transport in VO{sub 2}—Experimentally calibrated Boltzmann transport modeling

Energy Technology Data Exchange (ETDEWEB)

Kinaci, Alper; Rosenmann, Daniel; Chan, Maria K. Y., E-mail: debasish.banerjee@toyota.com, E-mail: mchan@anl.gov [Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Kado, Motohisa [Higashifuji Technical Center, Toyota Motor Corporation, Susono, Shizuoka 410-1193 (Japan); Ling, Chen; Zhu, Gaohua; Banerjee, Debasish, E-mail: debasish.banerjee@toyota.com, E-mail: mchan@anl.gov [Materials Research Department, Toyota Motor Engineering and Manufacturing North America, Inc., Ann Arbor, Michigan 48105 (United States)

2015-12-28

Materials that undergo metal-insulator transitions (MITs) are under intense study, because the transition is scientifically fascinating and technologically promising for various applications. Among these materials, VO{sub 2} has served as a prototype due to its favorable transition temperature. While the physical underpinnings of the transition have been heavily investigated experimentally and computationally, quantitative modeling of electronic transport in the two phases has yet to be undertaken. In this work, we establish a density-functional-theory (DFT)-based approach with Hubbard U correction (DFT + U) to model electronic transport properties in VO{sub 2} in the semiconducting and metallic regimes, focusing on band transport using the Boltzmann transport equations. We synthesized high quality VO{sub 2} films and measured the transport quantities across the transition, in order to calibrate the free parameters in the model. We find that the experimental calibration of the Hubbard correction term can efficiently and adequately model the metallic and semiconducting phases, allowing for further computational design of MIT materials for desirable transport properties.

Lattice Boltzmann simulation of flow across a staggered tube bundle array

Energy Technology Data Exchange (ETDEWEB)

Tiftikçi, A.; Kocar, C., E-mail: ckocar@hacettepe.edu.tr

2016-04-15

Highlights: • Large eddy simulation of the cross-flow in a staggered tube bundle array in 3D was made. • LBM and FVM are used separately as numerical solvers and the results of each method compared with experimental data. • Effect of lattice model is studied for tube bundle flow. • Filter size effects, mesh size effects are studied for VLES turbulence model. - Abstract: The decision on the magnitude of the grid size is a crucial problem in large eddy simulations. Finer mesh requires excessive memory and causes long simulation time. Large eddy simulation model becomes inefficient when the extent of the flow geometry to be simulated with the lattice-Boltzmann method is large. Thus, in this study, it is proposed to investigate the capabilities of three turbulence models, namely, very large eddy simulation, Van Driest and Smagorinsky–Lilly. As a test case, a staggered tube bundle flow experiment is used for the validation and comparison purposes. Sensitivity analyses (including mesh and filter size) have been made. Furthermore, the effect of lattice model is investigated and it is showed that the D3Q27 and D3Q19 models do not differ significantly in lattice-Boltzmann method for this type of flow. The results of turbulence model comparisons for staggered tube bundle flow showed that very large eddy simulation is superior at low resolution. This paper might be considered as a good validation of the lattice-Boltzmann method. In turbulent flow conditions, the code successfully captures the velocity and stress profiles even if the flow is quite complicated.

Emergence of nonwhite noise in Langevin dynamics with magnetic Lorentz force

Science.gov (United States)

Chun, Hyun-Myung; Durang, Xavier; Noh, Jae Dong

2018-03-01

We investigate the low mass limit of Langevin dynamics for a charged Brownian particle driven by a magnetic Lorentz force. In the low mass limit, velocity variables relaxing quickly are coarse-grained out to yield effective dynamics for position variables. Without the Lorentz force, the low mass limit is equivalent to the high friction limit. Both cases share the same Langevin equation that is obtained by setting the mass to zero. The equivalence breaks down in the presence of the Lorentz force. The low mass limit cannot be achieved by setting the mass to zero. The limit is also distinct from the large friction limit. We derive the effective equations of motion in the low mass limit. The resulting stochastic differential equation involves a nonwhite noise whose correlation matrix has antisymmetric components. We demonstrate the importance of the nonwhite noise by investigating the heat dissipation by a driven Brownian particle, where the emergent nonwhite noise has a physically measurable effect.

Quantum Difference Langevin System with Nonlocal q-Derivative Conditions

Directory of Open Access Journals (Sweden)

Surang Sitho

2016-01-01

Full Text Available We introduce a new class of boundary value problems for Langevin quantum difference systems. Some new existence and uniqueness results for coupled systems are obtained by using fixed point theorems. The existence and uniqueness of solutions are established by Banach’s contraction mapping principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The obtained results are well illustrated with the aid of examples.

Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

Directory of Open Access Journals (Sweden)

Y. Peng

2017-01-01

Full Text Available Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

Topology optimization of unsteady flow problems using the lattice Boltzmann method

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

2016-01-01

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

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

2010-09-15

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

Global existence proof for relativistic Boltzmann equation

International Nuclear Information System (INIS)

Dudynski, M.; Ekiel-Jezewska, M.L.

1992-01-01

The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions

Quantum Heat Engine and Negative Boltzmann Temperature

International Nuclear Information System (INIS)

Xi Jing-Yi; Quan Hai-Tao

2017-01-01

To clarify the ambiguity on negative Boltzmann temperature in literature, we study the Carnot and the Otto cycle with one of the heat reservoirs at the negative Boltzmann temperature based on a canonical ensemble description. The work extraction, entropy production and the efficiency of these cycles are explored. Conditions for constructing and properties of these thermodynamic cycles are elucidated. We find that the apparent “violation” of the second law of thermodynamics in these cycles are due to the fact that the traditional definition of thermodynamic efficiency is inappropriate in this situation. When properly understanding the efficiency and the adiabatic processes, in which the system crosses over “absolute ZERO” in a limit sense, the Carnot cycle with one of the heat reservoirs at a negative Boltzmann temperature can be understood straightforwardly, and it contradicts neither the second nor the third law of thermodynamics. Hence, negative Boltzmann temperature is a consistent concept in thermodynamics. We use a two-level system and an Ising spin system to illustrate our central results. (paper)

The Lattice Boltzmann Method applied to neutron transport

International Nuclear Information System (INIS)

Erasmus, B.; Van Heerden, F. A.

2013-01-01

In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Training Restricted Boltzmann Machines

DEFF Research Database (Denmark)

Fischer, Asja

relies on sampling based approximations of the log-likelihood gradient. I will present an empirical and theoretical analysis of the bias of these approximations and show that the approximation error can lead to a distortion of the learning process. The bias decreases with increasing mixing rate......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...... of the applied sampling procedure and I will introduce a transition operator that leads to faster mixing. Finally, a different parametrisation of RBMs will be discussed that leads to better learning results and more robustness against changes in the data representation....

Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

KAUST Repository

Burger, Martin

2016-11-18

In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.

Lattice Boltzmann simulations of attenuation-driven acoustic streaming

International Nuclear Information System (INIS)

Haydock, David; Yeomans, J M

2003-01-01

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

Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons

DEFF Research Database (Denmark)

Olsen, Thomas; Schiøtz, Jakob

2010-01-01

We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain...... quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum...... mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution...

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

KAUST Repository

Allen, Rebecca

2013-01-01

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

A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

Science.gov (United States)

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods

International Nuclear Information System (INIS)

Klassen, Alexander; Scharowsky, Thorsten; Körner, Carolin

2014-01-01

Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti–6Al–4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects. (paper)

Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

Science.gov (United States)

Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

2007-03-01

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

Quantum Non-Markovian Langevin Equations and Transport Coefficients

International Nuclear Information System (INIS)

Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.

2005-01-01

Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed

Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

Science.gov (United States)

Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

2014-12-26

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

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.

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

International Nuclear Information System (INIS)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.

2015-01-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

Energy Technology Data Exchange (ETDEWEB)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

2015-07-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model

International Nuclear Information System (INIS)

Scheinine, A.L.

1992-01-01

The frustrated XY model was studied on a lattice, primarily to test Fourier transform acceleration technique for a phase transition having more field structure than just spinwaves and vortices. Also, the spinless Hubbard model without hopping was simulated using continuous variables for the auxiliary field that mediates coupling between fermions. Finally, spin one-half Hubbard model was studied with a technique that sampled the fermion occupation configurations. The frustrated two-dimensional XY model was simulated using the Langevin equation with Fourier transform acceleration. Speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. The unfrustrated XY model was also studied. For the frustrated case, only long-distance spin correlation and the autocorrelation of the spin showed significant speedup. The frustrated case has Ising-like domains. It was found that Fourier acceleration speeds the evolution of spinwaves but has negligible effect on the Ising-like domains. In the Hubbard model, fermion determinant weight factor in the partition function changes sign, causing large statistical fluctuations of observables. A technique was found for sampling configuration space using continuous auxiliary fields, despite energy barriers where the fermion determinant changes sign. For two-dimensional spinless Hubbard model with no hopping, an exact solution was found for a 4 x 4 lattice; which could be compared to numerical simulations. The sign problem remained, and was found to be related to the sign problem encountered when a discrete variable is used for the auxiliary field. For spin one-half Hubbard model, a Monte Carlo simulation was done in which the fermion occupation configurations were varied. Rather than integrate-out the fermions and make a numerical estimate of the sum over the auxiliary field, the auxiliary field was integrated-out and a numerical estimate was made of the sum over fermion configurations

Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

Science.gov (United States)

Bouzat, Sebastián

2016-01-01

One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

Analytical estimation of effective charges at saturation in Poisson-Boltzmann cell models

International Nuclear Information System (INIS)

Trizac, Emmanuel; Aubouy, Miguel; Bocquet, Lyderic

2003-01-01

We propose a simple approximation scheme for computing the effective charges of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression for the effective charge in the infinite-dilution limit which is asymptotically valid for large salt concentrations; this result is then extended to finite colloidal concentration, approximating the salt partitioning effect which relates the salt content in the suspension to that of a dialysing reservoir. This leads to an analytical expression for the effective charge as a function of colloid volume fraction and salt concentration. These results compare favourably with the effective charges at saturation (i.e. in the limit of large bare charge) computed numerically following the standard prescription proposed by Alexander et al within the cell model

General relativistic Boltzmann equation, II: Manifestly covariant treatment

NARCIS (Netherlands)

Debbasch, F.; van Leeuwen, W.A.

2009-01-01

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

Science.gov (United States)

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

International Nuclear Information System (INIS)

Menezes, G.; Svaiter, N.F.

2006-04-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

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Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Resonant behavior of the generalized Langevin system with tempered Mittag–Leffler memory kernel

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Chen, Yao; Wang, Xudong; Deng, Weihua

2018-05-01

The generalized Langevin equation describes anomalous dynamics. Noise is not only the origin of uncertainty but also plays a positive role in helping to detect signals with information, termed stochastic resonance (SR). This paper analyzes the anomalous resonant behaviors of the generalized Langevin system with a multiplicative dichotomous noise and an internal tempered Mittag–Leffler noise. For a system with a fluctuating harmonic potential, we obtain the exact expressions of several types of SR such as the first moment, the amplitude and autocorrelation function for the output signal as well as the signal–noise ratio. We analyze the influence of the tempering parameter and memory exponent on the bona fide SR and the general SR. Moreover, it is detected that the critical memory exponent changes regularly with the increase of the tempering parameter. Almost all the theoretical results are validated by numerical simulations.

Lattice Boltzmann methods for global linear instability analysis

Science.gov (United States)

Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

2017-12-01

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua

2018-01-01

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. Support of National Natural Science Foundation of China under Grant Nos. 11475028, 11772064, and 11502117 Science Challenge Project under Grant Nos. JCKY2016212A501 and TZ2016002

The Sagnac effect and its interpretation by Paul Langevin

Science.gov (United States)

Pascoli, Gianni

2017-11-01

The French physicist Georges Sagnac is nowdays frequently cited by the engineers who work on devices such as ring-laser gyroscopes. These systems operate on the principle of the Sagnac effect. It is less known that Sagnac was a strong opponent to the theory of special relativity proposed by Albert Einstein. He set up his experiment to prove the existence of the aether discarded by the Einsteinian relativity. An accurate explanation of the phenomenon was provided by Paul Langevin in 1921.

Langevin equations with multiplicative noise: application to domain growth

International Nuclear Information System (INIS)

Sancho, J.M.; Hernandez-Machado, A.; Ramirez-Piscina, L.; Lacasta, A.M.

1993-01-01

Langevin equations of Ginzburg-Landau form with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hilliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical productions of the linear analysis. We also present simulation results for spinodal decomposition at large times. (author). 28 refs, 2 figs

A lattice Boltzmann model for substrates with regularly structured surface roughness

Science.gov (United States)

Yagub, A.; Farhat, H.; Kondaraju, S.; Singh, T.

2015-11-01

Superhydrophobic surface characteristics are important in many industrial applications, ranging from the textile to the military. It was observed that surfaces fabricated with nano/micro roughness can manipulate the droplet contact angle, thus providing an opportunity to control the droplet wetting characteristics. The Shan and Chen (SC) lattice Boltzmann model (LBM) is a good numerical tool, which holds strong potentials to qualify for simulating droplets wettability. This is due to its realistic nature of droplet contact angle (CA) prediction on flat smooth surfaces. But SC-LBM was not able to replicate the CA on rough surfaces because it lacks a real representation of the physics at work under these conditions. By using a correction factor to influence the interfacial tension within the asperities, the physical forces acting on the droplet at its contact lines were mimicked. This approach allowed the model to replicate some experimentally confirmed Wenzel and Cassie wetting cases. Regular roughness structures with different spacing were used to validate the study using the classical Wenzel and Cassie equations. The present work highlights the strength and weakness of the SC model and attempts to qualitatively conform it to the fundamental physics, which causes a change in the droplet apparent contact angle, when placed on nano/micro structured surfaces.

On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier-Stokes equations

Science.gov (United States)

Zhao, Weifeng; Wang, Liang; Yong, Wen-An

2018-02-01

In this paper, we are concerned with the stability of some lattice kinetic schemes. First, we show that a recently proposed lattice kinetic scheme is a two-relaxation-time model different from those in the literature. Second, we analyze the stability of the model by verifying the Onsager-like relation. In addition, a necessary stability criterion for hyperbolic relaxation systems is adapted to the lattice Boltzmann method. As an application of this criterion, we find some necessary stability conditions for a previously proposed lattice kinetic scheme. Numerical experiments are conducted to validate the necessary stability conditions.

Study of fission dynamics of the excited nuclei produced in fusion reactions in the framework of the four-dimensional Langevin equations

Energy Technology Data Exchange (ETDEWEB)

Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)

2014-12-01

The dynamics of fission of excited nuclei has been studied by solving four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. The projection of the total spin of the compound nucleus to the symmetry axis, K, was considered as the fourth dimension in Langevin dynamical calculations. The average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy have been calculated in a wide range of fissile parameter for compound nuclei {sup 162}Yb, {sup 172}Yb, {sup 215}Fr, {sup 224}Th, {sup 248}Cf, {sup 260}Rf and results compared with the experimental data. Calculations were performed with a constant dissipation coefficient of K, {sub γK} (MeV zs){sup -1/2}, and with a non-constant dissipation coefficient. Comparison of the theoretical results for the average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy with the experimental data showed that the results of four-dimensional Langevin equations with a non-constant dissipation coefficient are in better agreement with the experimental data. Furthermore, the difference between the results of two models for compound nuclei with low fissile parameter is low whereas, for heavy compound nuclei, is high. (orig.)

Simulation of Micro-Channel and Micro-Orifice Flow Using Lattice Boltzmann Method with Langmuir Slip Model

Directory of Open Access Journals (Sweden)

A. R. Rahmati

2016-12-01

Full Text Available Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the accommodation coefficient significantly, but there is not an explicitly relationship between properties at wall and accommodation coefficient. In the present wok, Langmuir slip model is used beside LBM to simulate micro-channel and micro-orifice flows. Slip velocity and nonlinear pressure drop profiles are presented as two major effects in such flows. The results are in good agreement with existing results in the literature.

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

Science.gov (United States)

Xu, Ao; Shyy, Wei; Zhao, Tianshou

2017-06-01

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas-liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

Effects of nanoparticles on melting process with phase-change using the lattice Boltzmann method

Directory of Open Access Journals (Sweden)

Ahmed M. Ibrahem

Full Text Available In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM enthalpy-based is employed. The collision model of lattice Bhatnagar-Gross-Krook (LBGK is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0–2% added to water-base fluid and Rayleigh numbers of 103–105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied. Keywords: Lattice Boltzmann method, Nanofluids, Conduction melting, Convection melting, BGK collision model

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

Science.gov (United States)

Huang, Rongzong; Wu, Huiying; Adams, Nikolaus A.

2018-05-01

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3 ) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

Science.gov (United States)

Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele

2011-02-01

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

Accelerating the convergence of path integral dynamics with a generalized Langevin equation.

Science.gov (United States)

Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele

2011-02-28

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

Comparison of Langevin dynamics and direct energy barrier computation

International Nuclear Information System (INIS)

Dittrich, Rok; Schrefl, Thomas; Thiaville, Andre; Miltat, Jacques; Tsiantos, Vassilios; Fidler, Josef

2004-01-01

Two complementary methods to study thermal effects in micromagnetics are compared. On short time scales Langevin dynamics gives insight in the thermally activated dynamics. For longer time scales the 'nudged elastic band' method is applied. The method calculates a highly probable thermal switching path between two local energy minima of a micromagnetic system. Comparing the predicted thermal transition rates between ground states in small softmagnetic elements up to a size of 90x90x4.5 nm 3 gives good agreement of the methods

Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

Science.gov (United States)

Meng, Xuhui; Guo, Zhaoli

2015-10-01

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: I. Model and velocity analysis

Energy Technology Data Exchange (ETDEWEB)

Boyd, J [Cardiovascular Research Group Physics, University of New England, Armidale, NSW 2351 (Australia); Buick, J M [Department of Mechanical and Design Engineering, University of Portsmouth, Anglesea Building, Anglesea Road, Portsmouth PO1 3DJ (United Kingdom)

2008-10-21

Numerical modelling is a powerful tool in the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall velocity and shear are important in the pathogenesis and progression of atherosclerosis. In this paper results for a simulation of blood flow in a three-dimensional carotid artery geometry using the lattice Boltzmann method are presented. The velocity fields in the body of the fluid are analysed at six times of interest during a physiologically accurate velocity waveform. It is found that the three-dimensional model agrees well with previous literature results for carotid artery flow. Regions of low near wall velocity and circulatory flow are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery, which are regions that are typically prone to atherosclerosis.

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: I. Model and velocity analysis

International Nuclear Information System (INIS)

Boyd, J; Buick, J M

2008-01-01

Numerical modelling is a powerful tool in the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall velocity and shear are important in the pathogenesis and progression of atherosclerosis. In this paper results for a simulation of blood flow in a three-dimensional carotid artery geometry using the lattice Boltzmann method are presented. The velocity fields in the body of the fluid are analysed at six times of interest during a physiologically accurate velocity waveform. It is found that the three-dimensional model agrees well with previous literature results for carotid artery flow. Regions of low near wall velocity and circulatory flow are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery, which are regions that are typically prone to atherosclerosis.

CMB spectral distortions as solutions to the Boltzmann equations

Energy Technology Data Exchange (ETDEWEB)

Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

2017-01-01

We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem

Directory of Open Access Journals (Sweden)

Aizat Abas

2016-01-01

Full Text Available This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI. Three different types of Lattice Boltzmann (LB models are computed, namely, single relaxation time (SRT, multiple relaxation time (MRT, and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV- based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required.

Lattice Boltzmann approach for complex nonequilibrium flows.

Science.gov (United States)

Montessori, A; Prestininzi, P; La Rocca, M; Succi, S

2015-10-01

We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

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

International Nuclear Information System (INIS)

Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang

2013-01-01

We present a L 2 -stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L 2 -distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L 2 -stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L 2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L 2 -stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L 2 -stability estimate. This is the first result on the L 2 -stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: II. Shear analysis

Energy Technology Data Exchange (ETDEWEB)

Boyd, J [Cardiovascular Research Group, Physics, University of New England, Armidale, NSW 2351 (Australia); Buick, J M [Mechanical and Design Engineering, Anglesea Building, Anglesea Road, University of Portsmouth, Portsmouth, PO1 3DJ (United Kingdom)

2008-10-21

Near-wall shear is known to be important in the pathogenesis and progression of atherosclerosis. In this paper, the shear field in a three-dimensional model of the human carotid artery is presented. The simulations are performed using the lattice Boltzmann model and are presented at six times of interest during a physiologically accurate velocity waveform. The near-wall shear rate and von Mises effective shear are also examined. Regions of low near-wall shear rates are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery. These are regions where low near-wall velocity and circulatory flows have been observed and are regions that are typically prone to atherosclerosis.

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: II. Shear analysis

International Nuclear Information System (INIS)

Boyd, J; Buick, J M

2008-01-01

Near-wall shear is known to be important in the pathogenesis and progression of atherosclerosis. In this paper, the shear field in a three-dimensional model of the human carotid artery is presented. The simulations are performed using the lattice Boltzmann model and are presented at six times of interest during a physiologically accurate velocity waveform. The near-wall shear rate and von Mises effective shear are also examined. Regions of low near-wall shear rates are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery. These are regions where low near-wall velocity and circulatory flows have been observed and are regions that are typically prone to atherosclerosis.

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.

Characterization and visualization of RNA secondary structure Boltzmann ensemble via information theory.

Science.gov (United States)

Lin, Luan; McKerrow, Wilson H; Richards, Bryce; Phonsom, Chukiat; Lawrence, Charles E

2018-03-05

The nearest neighbor model and associated dynamic programming algorithms allow for the efficient estimation of the RNA secondary structure Boltzmann ensemble. However because a given RNA secondary structure only contains a fraction of the possible helices that could form from a given sequence, the Boltzmann ensemble is multimodal. Several methods exist for clustering structures and finding those modes. However less focus is given to exploring the underlying reasons for this multimodality: the presence of conflicting basepairs. Information theory, or more specifically mutual information, provides a method to identify those basepairs that are key to the secondary structure. To this end we find most informative basepairs and visualize the effect of these basepairs on the secondary structure. Knowing whether a most informative basepair is present tells us not only the status of the particular pair but also provides a large amount of information about which other pairs are present or not present. We find that a few basepairs account for a large amount of the structural uncertainty. The identification of these pairs indicates small changes to sequence or stability that will have a large effect on structure. We provide a novel algorithm that uses mutual information to identify the key basepairs that lead to a multimodal Boltzmann distribution. We then visualize the effect of these pairs on the overall Boltzmann ensemble.

On transient effects in violent nuclear collisions

International Nuclear Information System (INIS)

Suraud, E.; Belkacem, M.; Feng-Shou Zhang; Academia Sinica, Lanzhou, GS

1993-01-01

It is shown that the numerical simulations of the recently developed Boltzmann-Langevin model exhibit large dynamical fluctuations in momentum space during the early stages of heavy-ion collisions, which arise from an interplay between the nuclear meanfield and binary collisions. It is pointed out that this transient behaviour provides an initial seed for the development of density fluctuations, and could strongly influence the particle production cross-sections at subthreshold energies. (author) 13 refs.; 3 figs

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis; Mouhot, Clé ment

2011-01-01

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.

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis

2011-04-01

The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

Science.gov (United States)

Li, Qing; Zhou, P.; Yan, H. J.

2017-12-01

In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012), 10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇ .(λ ∇ T ) /∇.(λ ∇ T ) ρ cV ρ cV with ∇ .(χ ∇ T ) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂t 0(T v ) +∇ .(T vv ) , which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇ .(λ ∇ T ) /∇ .(λ ∇ T ) ρ cV ρ cV with ∇ .(χ ∇ T ) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS

International Nuclear Information System (INIS)

QIANG, J.; RYNE, R.; HABIB, S.

2000-01-01

In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the FR-iction and diffusion coefficients are computed FR-om first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators

A lattice Boltzmann coupled to finite volumes method for solving phase change problems

Directory of Open Access Journals (Sweden)

El Ganaoui Mohammed

2009-01-01

Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

Stabilizing the thermal lattice Boltzmann method by spatial filtering.

Science.gov (United States)

Gillissen, J J J

2016-10-01

We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

Analysis of a bubble coalescence in the multiphase lattice Boltzmann method

International Nuclear Information System (INIS)

Ryu, Seung Yeob; Park, Cheon Tae; Lee, Chung Chan; Kim, Keung Koo

2008-01-01

Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a 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. To study the effect of the mobility coefficient Γ and the width of the interface layer, two stationary bubbles without a collision are considered. The gap of the two bubbles is taken as 4, while the width of the interface (w) and the mobility coefficient Γ are varied. In the present work, the lattice Boltzmann model for multiphase flows proposed by Zheng et al. is used for simulating two stationary bubbles without a collision. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made smaller. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

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

Indian Academy of Sciences (India)

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 ...

Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution

International Nuclear Information System (INIS)

Tothova, J.; Lisy, V.

2015-01-01

The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)

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

Science.gov (United States)

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

2015-12-01

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

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

Science.gov (United States)

Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

2018-01-01

In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

Science.gov (United States)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Lattice Boltzmann simulation of flow around a confined circular cyclinder

International Nuclear Information System (INIS)

Ashrafizaadeh, M.; Zadehgol, A.

2002-01-01

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

Lattice Boltzmann model for free-surface flow and its application to filling process in casting

CERN Document Server

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 ...

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

KAUST Repository

Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.

2010-01-01

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

Science.gov (United States)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

Lattice Boltzmann methods for the simulation of heat transfer in particle suspensions

International Nuclear Information System (INIS)

McCullough, J.W.S.; Leonardi, C.R.; Jones, B.D.; Aminossadati, S.M.; Williams, J.R.

2016-01-01

Highlights: • Development of a lattice Boltzmann heat transfer model for curved boundaries. • Thermodynamic coupling aims to ensure continuity of both temperature and heat flux. • Good correlation found in transient comparison of results to analytical solutions. • Illustration of the developed model applied to a moving particle test case. - Abstract: This study examines the use of a lattice Boltzmann method framework to study heat transfer behaviours within particle suspensions. This has been done through the use of an adapted interface condition to attempt to resolve the required continuity of temperature and flux at the boundary between the solid and fluid phases. The proposed method is tested against analytical solutions for layered media in both a 1D bar and a radial layout. These tests showed that the model was able to generate results with first order convergence towards the analytical outcomes. The model was then used to examine the behaviour of two moving particles travelling along a channel to illustrate its potential for resolving complex suspension flows.

Celebrating Cercignani's conjecture for the Boltzmann equation

KAUST Repository

Villani, Cédric

2011-01-01

Cercignani\\'s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann\\'s nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.

On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

Science.gov (United States)

Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

2018-03-01

The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

Boltzmann Solver with Adaptive Mesh in Velocity Space

International Nuclear Information System (INIS)

Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.

2011-01-01

We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

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

International Nuclear Information System (INIS)

Protopopescu, V.

1975-01-01

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

Entropy à la Boltzmann

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...

Paul Langevin and french physics from 1900 to 1939

International Nuclear Information System (INIS)

Bensaude-Vincent, B.

1987-01-01

As a young physicist at the turn of this century, P. Langevin was one of the most promising figures in French science. His doctoral dissertation on gas ionization and his research on magnetic theory earned him international reputation. All along his career he championed the new physical theories and made efforts to spread them in France. Through his research and his teaching, he thus fostered the development of atomistics, of theory of relativity and of quantum physics. After a brief survey of his physicist's work the paper seeks to discuss his influence on French physics [fr

Nucleation theory in Langevin's approach and lifetime of a Brownian particle in potential wells.

Science.gov (United States)

Alekseechkin, N V

2008-07-14

The multivariable theory of nucleation suggested by Alekseechkin [J. Chem. Phys. 124, 124512 (2006)] is further developed in the context of Langevin's approach. The use of this approach essentially enhances the capability of the nucleation theory, because it makes possible to consider the cases of small friction which are not taken into account by the classical Zel'dovich-Frenkel theory and its multivariable extensions. The procedure for the phenomenological determination of the nucleation parameters is described. Using the similarity of the Kramers model with that of nucleation, the lifetime of a Brownian particle in potential wells in various dimensionalities is calculated with the help of the expression for the steady state nucleation rate.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad

2013-01-01

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.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

Flux Limiter Lattice Boltzmann for Compressible Flows

International Nuclear Information System (INIS)

Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

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

Langevin dynamics encapsulate the microscopic and emergent macroscopic properties of midge swarms

Science.gov (United States)

2018-01-01

In contrast to bird flocks, fish schools and animal herds, midge swarms maintain cohesion but do not possess global order. High-speed imaging techniques are now revealing that these swarms have surprising properties. Here, I show that simple models found on the Langevin equation are consistent with this wealth of recent observations. The models predict correctly that large accelerations, exceeding 10 g, will be common and they predict correctly the coexistence of core condensed phases surrounded by dilute vapour phases. The models also provide new insights into the influence of environmental conditions on swarm dynamics. They predict that correlations between midges increase the strength of the effective force binding the swarm together. This may explain why such correlations are absent in laboratory swarms but present in natural swarms which contend with the wind and other disturbances. Finally, the models predict that swarms have fluid-like macroscopic mechanical properties and will slosh rather than slide back and forth after being abruptly displaced. This prediction offers a promising avenue for future experimentation that goes beyond current quasi-static testing which has revealed solid-like responses. PMID:29298958

Measurement of the Boltzmann constant by Johnson noise thermometry using a superconducting integrated circuit

Science.gov (United States)

Urano, C.; Yamazawa, K.; Kaneko, N.-H.

2017-12-01

We report on our measurement of the Boltzmann constant by Johnson noise thermometry (JNT) using an integrated quantum voltage noise source (IQVNS) that is fully implemented with superconducting integrated circuit technology. The IQVNS generates calculable pseudo white noise voltages to calibrate the JNT system. The thermal noise of a sensing resistor placed at the temperature of the triple point of water was measured precisely by the IQVNS-based JNT. We accumulated data of more than 429 200 s in total (over 6 d) and used the Akaike information criterion to estimate the fitting frequency range for the quadratic model to calculate the Boltzmann constant. Upon detailed evaluation of the uncertainty components, the experimentally obtained Boltzmann constant was k=1.380 6436× {{10}-23} J K-1 with a relative combined uncertainty of 10.22× {{10}-6} . The value of k is relatively -3.56× {{10}-6} lower than the CODATA 2014 value (Mohr et al 2016 Rev. Mod. Phys. 88 035009).

Collision group and renormalization of the Boltzmann collision integral

Science.gov (United States)

Saveliev, V. L.; Nanbu, K.

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.

Science.gov (United States)

Liu, Haihu; Valocchi, Albert J; Kang, Qinjun

2012-04-01

We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35

A note on the Lattice Boltzmann Method Beyond the Chapman Enskog Limits

NARCIS (Netherlands)

Sbragaglia, M.; Succi, S.

2006-01-01

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also

Transport-level description of the 252Cf-source method using the Langevin technique

International Nuclear Information System (INIS)

Stolle, A.M.; Akcasu, A.Z.

1991-01-01

The fluctuations in the neutron number density and detector outputs in a nuclear reactor can be analyzed conveniently by using the Langevin equation approach. This approach can be implemented at any level of approximation to describe the time evolution of the neutron population, from the most complete transport-level description to the very basic point reactor analysis of neutron number density fluctuations. In this summary, the complete space- and velocity-dependent transport-level formulation of the Langevin equation approach is applied to the analysis of the 252 Cf-source-driven noise analysis (CSDNA) method, an experimental technique developed by J.T. Mihalczo at Oak Ridge National Laboratory, which makes use of noise analysis to determine the reactivity of subcritical media. From this analysis, a theoretical expression for the subcritical multiplication factor is obtained that can then be used to interpret the experimental data. Results at the transport level are in complete agreement with an independent derivation performed by Sutton and Doub, who used the probability density method to interpret the CSDNA experiment, but differed from other expressions that have appeared in the literature

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

Science.gov (United States)

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

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Florian Thüroff

2014-11-01

Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

Science.gov (United States)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

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

International Nuclear Information System (INIS)

Jakovac, A.

2002-01-01

A novel refinement of the conventional treatment of Kadanoff-Baym equations is suggested. In addition to the Boltzmann equation, another differential equation is used for calculating the evolution of the nonequilibrium 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 a smearing out of the nonanalytic threshold behavior of the spectral function. The possible consequences for the dilepton production are discussed

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

KAUST Repository

Allen, Rebecca; Reis, Tim; Sun, Shuyu

2013-01-01

-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE

Simulation of bubble motion under gravity by lattice Boltzmann method

International Nuclear Information System (INIS)

Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo

2001-01-01

We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method (LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single-and two-bubble motions, setting flow conditions according to the Eoetvoes and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two-bubble interaction of their approach and coalescence in circular tube. There results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity. (author)

Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows.

Science.gov (United States)

Li, Qing; Luo, K H

2014-05-01

The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB community for simulating multiphase flows. Recently, several thermal LB models, which are based on the pseudopotential LB model and constructed within the framework of the double-distribution-function LB method, were proposed to simulate thermal multiphase flows [G. Házi and A. Márkus, Phys. Rev. E 77, 026305 (2008); L. Biferale, P. Perlekar, M. Sbragaglia, and F. Toschi, Phys. Rev. Lett. 108, 104502 (2012); S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012); M. R. Kamali et al., Phys. Rev. E 88, 033302 (2013)]. The objective of the present paper is to show that the effect of the forcing term on the temperature equation must be eliminated in the pseudopotential LB modeling of thermal flows. First, the effect of the forcing term on the temperature equation is shown via the Chapman-Enskog analysis. For comparison, alternative treatments that are free from the forcing-term effect are provided. Subsequently, numerical investigations are performed for two benchmark tests. The numerical results clearly show that the existence of the forcing-term effect will lead to significant numerical errors in the pseudopotential LB modeling of thermal flows.

An efficient numerical method for solving the Boltzmann equation in multidimensions

Science.gov (United States)

Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

2018-01-01

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

KAUST Repository

Allen, Rebecca

2016-06-29

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

Langevin dynamics of A+A reactions in one dimension

International Nuclear Information System (INIS)

Sancho, J M; Romero, A H; Lacasta, A M; Lindenberg, Katja

2007-01-01

We propose a set of Langevin equations of motion together with a reaction rule for the study of binary reactions. Our scheme is designed to address this problem for arbitrary friction γ and temperature T. It easily accommodates the inclusion of a substrate potential, and it lends itself to straightforward numerical integration. We test this approach on diffusion-limited (γ → ∞) as well as ballistic (γ = 0) A+A → P reactions for which there are extensive exact and approximate theoretical results as well as extensive Monte Carlo results. We reproduce the known results using our integration scheme, and also present new results for the ballistic reactions

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

Science.gov (United States)

Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.

2011-09-01

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

Implementation of the Lattice Boltzmann Method on Heterogeneous Hardware and Platforms using OpenCL

Directory of Open Access Journals (Sweden)

TEKIC, P. M.

2012-02-01

Full Text Available The Lattice Boltzmann method (LBM has become an alternative method for computational fluid dynamics with a wide range of applications. Besides its numerical stability and accuracy, one of the major advantages of LBM is its relatively easy parallelization and, hence, it is especially well fitted to many-core hardware as graphics processing units (GPU. The majority of work concerning LBM implementation on GPU's has used the CUDA programming model, supported exclusively by NVIDIA. Recently, the open standard for parallel programming of heterogeneous systems (OpenCL has been introduced. OpenCL standard matures and is supported on processors from most vendors. In this paper, we make use of the OpenCL framework for the lattice Boltzmann method simulation, using hardware accelerators - AMD ATI Radeon GPU, AMD Dual-Core CPU and NVIDIA GeForce GPU's. Application has been developed using a combination of Java and OpenCL programming languages. Java bindings for OpenCL have been utilized. This approach offers the benefits of hardware and operating system independence, as well as speeding up of lattice Boltzmann algorithm. It has been showed that the developed lattice Boltzmann source code can be executed without modification on all of the used hardware accelerators. Performance results have been presented and compared for the hardware accelerators that have been utilized.

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

Directory of Open Access Journals (Sweden)

Bertrand Lods

2015-06-01

Full Text Available Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives.

Electron kinetics with attachment and ionization from higher order solutions of Boltzmann's equation

International Nuclear Information System (INIS)

Winkler, R.; Wilhelm, J.; Braglia, G.L.

1989-01-01

An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF 6 . The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation. (author)

Implementing the lattice Boltzmann model on commodity graphics hardware

International Nuclear Information System (INIS)

Kaufman, Arie; Fan, Zhe; Petkov, Kaloian

2009-01-01

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

Nonaligned shocks for discrete velocity models of the Boltzmann equation

Directory of Open Access Journals (Sweden)

J. M. Greenberg

1991-05-01

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

Identifying product order with restricted Boltzmann machines

Science.gov (United States)

Rao, Wen-Jia; Li, Zhenyu; Zhu, Qiong; Luo, Mingxing; Wan, Xin

2018-03-01

Unsupervised machine learning via a restricted Boltzmann machine is a useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from nonergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo; Vella, Dominic; Yeomans, Julia M.

2014-01-01

© 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 simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo

2014-09-04

© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Directory of Open Access Journals (Sweden)

Song-Gui Chen

2016-01-01

Full Text Available This paper presents a three-dimensional (3D parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re and Bingham number (Bn. These results reveal the flow behavior of Bingham plastics.

Some properties of the Boltzmann elastic collision operator; Quelques proprietes particulieres de l'operateur de collision elastique de Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Delcroix, J. L. [Ecole Normale Superieure (France); Salmon, J. [Commissariat a l' energie atomique et aux energies alternatives - CEA (France)

1959-07-01

The authors point out some properties (an important one is a variational property) of the Boltzmann elastic collision operator, valid in a more general framework than that of the Lorentz gas. Reprint of a paper published in 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596 [French] Les auteurs mettent en evidence quelques proprietes (dont notamment une propriete variationnelle) de l'operateur de collision elastique de Boltzmann valables dans un cadre plus general que celui du gaz de Lorentz. Reproduction d'un article publie dans 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596.

The Interaction of Boltzmann with Mach, Ostwald and Planck, and his influence on Nernst and Einstein

International Nuclear Information System (INIS)

Broda, E.

1981-01-01

Boltzmann esteemed both Mach and Ostwald personally and as experimentalists, but consistently fought them in epistemology. He represented atomism and realism against energism and positivism. In the early period Boltzmann also had to struggle against Planck as a phenomenologist, but he welcomed his quantum hypothesis. As a scientist Nernst was also under Boltzmann's influence. Einstein learned atomism from (Maxwell and) Boltzmann. After Einstein had overcome Mach's positivist influence, he unknowingly approached Boltzmann's philosophical views. Some sociopolitlcal aspects of the lives of the great physicists will be discussed. It will be shown how they all, and many of Boltzmann's most eminent students, in one way or other conflicted with evil tendencies and developments in existing society. (author)

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

Description of the approach to equilibrium in the Boltzmann equation

Energy Technology Data Exchange (ETDEWEB)

Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

1985-06-01

An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition

International Nuclear Information System (INIS)

Attar, Elham; Koerner, Carolin

2011-01-01

Purpose: The main objective of this work is to develop an algorithm to use the Lattice Boltzmann method for solving free surface thermal flow problems with solid/liquid phase changes. Approach: A multi-distribution function model is applied to simulate hydrodynamic flow and the coupled thermal diffusion-convection problem. Findings: The free surface problem, i.e. the reconstruction of the missing distribution functions at the interface, can be solved by applying a physical transparent momentum and heat flux based methodology. The developed method is subsequently applied to some test cases in order to assess its computational potentials. Practical implications: Many industrial processes involve problems where non-isothermal motion and simultaneous solidification of fluids with free surface is important. Examples are all castings processes and especially foaming processes which are characterized by a huge and strongly changing surface. Value: A reconstruction algorithm to treat a thermal hydrodynamic problem with free surfaces is presented which is physically transparent and easy to implement.

Deriving Langevin equations in curved spacetime

International Nuclear Information System (INIS)

Ramos, Rudnei O.; Tavares, Romulo F.

2013-01-01

Full text: Warm inflation is an inflationary scenario where the interactions between the inflaton and other degrees of freedom are considered. The effective equation of motion for the inflaton is in general of the form of a Langevin equation, that includes both quantum and thermal effects and where these effects manifest in the form of dissipation and stochastic noise terms, which are related by a generalized fluctuation-dissipation relation. The dissipation term is related to the interactions of the inflaton with other degrees of freedom of the thermal bath that can be obtained from the appropriate Feynman propagators. As the inflaton evolves into an expanding metric, these effects have to be taken into account when calculating the Green functions and consequently the Feynman propagators. In this work we present the considerations that must be made to calculate the Green functions in curved space (expanding metric) and in the presence of radiation in order to proper derive the effective evolution of the inflaton in the warm-inflation scenario. (author)

Lattice-Boltzmann Simulation of Tablet Disintegration

Science.gov (United States)

Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

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

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

Science.gov (United States)

Badino, M.

2011-11-01

An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

Conditional High-Order Boltzmann Machines for Supervised Relation Learning.

Science.gov (United States)

Huang, Yan; Wang, Wei; Wang, Liang; Tan, Tieniu

2017-09-01

Relation learning is a fundamental problem in many vision tasks. Recently, high-order Boltzmann machine and its variants have shown their great potentials in learning various types of data relation in a range of tasks. But most of these models are learned in an unsupervised way, i.e., without using relation class labels, which are not very discriminative for some challenging tasks, e.g., face verification. In this paper, with the goal to perform supervised relation learning, we introduce relation class labels into conventional high-order multiplicative interactions with pairwise input samples, and propose a conditional high-order Boltzmann Machine (CHBM), which can learn to classify the data relation in a binary classification way. To be able to deal with more complex data relation, we develop two improved variants of CHBM: 1) latent CHBM, which jointly performs relation feature learning and classification, by using a set of latent variables to block the pathway from pairwise input samples to output relation labels and 2) gated CHBM, which untangles factors of variation in data relation, by exploiting a set of latent variables to multiplicatively gate the classification of CHBM. To reduce the large number of model parameters generated by the multiplicative interactions, we approximately factorize high-order parameter tensors into multiple matrices. Then, we develop efficient supervised learning algorithms, by first pretraining the models using joint likelihood to provide good parameter initialization, and then finetuning them using conditional likelihood to enhance the discriminant ability. We apply the proposed models to a series of tasks including invariant recognition, face verification, and action similarity labeling. Experimental results demonstrate that by exploiting supervised relation labels, our models can greatly improve the performance.

Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

International Nuclear Information System (INIS)

Niven, Robert K.

2005-01-01

The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

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

International Nuclear Information System (INIS)

Morel, J.E.

1987-01-01

The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

Langevin dynamics simulations of large frustrated Josephson junction arrays

International Nuclear Information System (INIS)

Groenbech-Jensen, N.; Bishop, A.R.; Lomdahl, P.S.

1991-01-01

Long-time Langevin dynamics simulations of large (N x N,N = 128) 2-dimensional arrays of Josephson junctions in a uniformly frustrating external magnetic field are reported. The results demonstrate: (1) Relaxation from an initially random flux configuration as a universal fit to a glassy stretched-exponential type of relaxation for the intermediate temperatures T(0.3 T c approx-lt T approx-lt 0.7 T c ), and an activated dynamic behavior for T ∼ T c ; (2) a glassy (multi-time, multi-length scale) voltage response to an applied current. Intrinsic dynamical symmetry breaking induced by boundaries as nucleation sites for flux lattice defects gives rise to transverse and noisy voltage response

Langevin dynamics simulations of large frustrated Josephson junction arrays

International Nuclear Information System (INIS)

Gronbech-Jensen, N.; Bishop, A.R.; Lomdahl, P.S.

1991-01-01

Long-time Langevin dynamics simulations of large (N x N, N = 128) 2-dimensional arrays of Josephson junctions in a uniformly frustrating external magnetic field are reported. The results demonstrate: Relaxation from an initially random flux configuration as a ''universal'' fit to a ''glassy'' stretched-exponential type of relaxation for the intermediate temperatures T (0.3 T c approx-lt T approx-lt 0.7 T c ), and an ''activated dynamic'' behavior for T ∼ T c A glassy (multi-time, multi-length scale) voltage response to an applied current. Intrinsic dynamical symmetry breaking induced by boundaries as nucleation sites for flux lattice defects gives rise to transverse and noisy voltage response

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

International Nuclear Information System (INIS)

EL Safadi, M.

2007-03-01

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

A review of spurious currents in the lattice Boltzmann method for multiphase flows

Energy Technology Data Exchange (ETDEWEB)

Conning Ton, Kevin; Lee, Tae Hun [The City College of the City Univ. of New York, New York (United States)

2012-12-15

A spurious current is a small amplitude artificial velocity field which arises from an imbalance between discretized forces in multiphase/multi component flows. If it occurs, the velocity field may persist indefinitely, preventing the achievement of a true equilibrium state. Spurious velocities can sometimes be as large as the characteristic velocities of the problem, causing severe instability and ambiguity between physical and spurious velocities. They are typically exacerbated by large values of numerical surface tension or when the two fluids being simulated have large density ratios. The resulting instability can restrict what parameters may be simulated. To varying degrees, spurious currents are found in all multiphase flow models of the lattice Boltzmann method (LBM). There have been many studies of the occurrence of the phenomenon, and many suggestions on how to eliminate it. This paper reviews the three main models of simulating multiphase/multi component flow in the lattice Boltzmann method, as well as the subsequent modifications made in order to reduce or eliminate spurious currents.

A study of the Boltzmann and Gibbs entropies in the context of a stochastic toy model

Science.gov (United States)

Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna

2018-05-01

In this article we reconsider a stochastic toy model of thermal contact, first introduced in Onorato et al (2017 Eur. J. Phys. 38 045102), showing its educational potential for clarifying some current issues in the foundations of thermodynamics. The toy model can be realized in practice using dice and coins, and can be seen as representing thermal coupling of two subsystems with energy bounded from above. The system is used as a playground for studying the different behaviours of the Boltzmann and Gibbs temperatures and entropies in the approach to steady state. The process that models thermal contact between the two subsystems can be proved to be an ergodic, reversible Markov chain; thus the dynamics produces an equilibrium distribution in which the weight of each state is proportional to its multiplicity in terms of microstates. Each one of the two subsystems, taken separately, is formally equivalent to an Ising spin system in the non-interacting limit. The model is intended for educational purposes, and the level of readership of the article is aimed at advanced undergraduates.

Non-Boltzmann Ensembles and Monte Carlo Simulations

International Nuclear Information System (INIS)

Murthy, K. P. N.

2016-01-01

Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble and for calculating macroscopic properties of a closed system at desired temperatures. An estimate of a mechanical property, like energy, of an equilibrium system, is made by averaging over a large number microstates generated by Boltzmann Monte Carlo methods. This is possible because we can assign a numerical value for energy to each microstate. However, a thermal property like entropy, is not easily accessible to these methods. The reason is simple. We can not assign a numerical value for entropy, to a microstate. Entropy is not a property associated with any single microstate. It is a collective property of all the microstates. Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo technique called Umbrella sampling was proposed some forty years ago. Umbrella sampling has since undergone several metamorphoses and we have now, multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc . This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated as follows. First un-weight a microstates of the entropic ensemble; then re-weight it to the desired physical ensemble. Carry out weighted average over the entropic ensemble to estimate physical quantities. In this talk I shall tell you of the most recent non- Boltzmann Monte Carlo method and show how to calculate free energy for a few systems. We first consider estimation of free energy as a function of energy at different temperatures to characterize phase transition in an hairpin DNA in the presence of an unzipping force. Next we consider free energy as a function of order parameter and to this end we estimate density of states g ( E , M ), as a function of both energy E , and order parameter M . This is carried out in two stages. We estimate g ( E ) in the first stage

Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems

Directory of Open Access Journals (Sweden)

Josh Fass

2018-04-01

Full Text Available While Langevin integrators are popular in the study of equilibrium properties of complex systems, it is challenging to estimate the timestep-induced discretization error: the degree to which the sampled phase-space or configuration-space probability density departs from the desired target density due to the use of a finite integration timestep. Sivak et al., introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the Kullback-Leibler (KL divergence, in phase space, but did not specifically address the issue of configuration-space properties, which are much more commonly of interest in molecular simulations. Here, we introduce a variant of this near-equilibrium estimator capable of measuring the error in the configuration-space marginal density, validating it against a complex but exact nested Monte Carlo estimator to show that it reproduces the KL divergence with high fidelity. To illustrate its utility, we employ this new near-equilibrium estimator to assess a claim that a recently proposed Langevin integrator introduces extremely small configuration-space density errors up to the stability limit at no extra computational expense. Finally, we show how this approach to quantifying sampling bias can be applied to a wide variety of stochastic integrators by following a straightforward procedure to compute the appropriate shadow work, and describe how it can be extended to quantify the error in arbitrary marginal or conditional distributions of interest.

Conditioning and Robustness of RNA Boltzmann Sampling under Thermodynamic Parameter Perturbations.

Science.gov (United States)

Rogers, Emily; Murrugarra, David; Heitsch, Christine

2017-07-25

Understanding how RNA secondary structure prediction methods depend on the underlying nearest-neighbor thermodynamic model remains a fundamental challenge in the field. Minimum free energy (MFE) predictions are known to be "ill conditioned" in that small changes to the thermodynamic model can result in significantly different optimal structures. Hence, the best practice is now to sample from the Boltzmann distribution, which generates a set of suboptimal structures. Although the structural signal of this Boltzmann sample is known to be robust to stochastic noise, the conditioning and robustness under thermodynamic perturbations have yet to be addressed. We present here a mathematically rigorous model for conditioning inspired by numerical analysis, and also a biologically inspired definition for robustness under thermodynamic perturbation. We demonstrate the strong correlation between conditioning and robustness and use its tight relationship to define quantitative thresholds for well versus ill conditioning. These resulting thresholds demonstrate that the majority of the sequences are at least sample robust, which verifies the assumption of sampling's improved conditioning over the MFE prediction. Furthermore, because we find no correlation between conditioning and MFE accuracy, the presence of both well- and ill-conditioned sequences indicates the continued need for both thermodynamic model refinements and alternate RNA structure prediction methods beyond the physics-based ones. Copyright © 2017. Published by Elsevier Inc.

Stabilization of the Lattice Boltzmann Method Using Information Theory

OpenAIRE

Wilson, Tyler L; Pugh, Mary; Dawson, Francis

2018-01-01

A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time...

A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules

Directory of Open Access Journals (Sweden)

Germán Rojas-Lorenzo

2016-09-01

Full Text Available A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.

Boltzmann brains and the scale-factor cutoff measure of the multiverse

International Nuclear Information System (INIS)

De Simone, Andrea; Guth, Alan H.; Linde, Andrei; Noorbala, Mahdiyar; Salem, Michael P.; Vilenkin, Alexander

2010-01-01

To make predictions for an eternally inflating 'multiverse', one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by 'Boltzmann brains' - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.

An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

International Nuclear Information System (INIS)

Hui-Lin, Lai; Chang-Feng, Ma

2008-01-01

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective. (fundamental areas of phenomenology (including applications))

Revisiting Boltzmann learning: parameter estimation in Markov random fields

DEFF Research Database (Denmark)

Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik

1996-01-01

This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...

Boltzmann Oracle for Combinatorial Systems

OpenAIRE

Pivoteau , Carine; Salvy , Bruno; Soria , Michèle

2008-01-01

International audience; Boltzmann random generation applies to well-defined systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.

Solving the generalized Langevin equation with the algebraically correlated noise

International Nuclear Information System (INIS)

Srokowski, T.; Ploszajczak, M.

1997-01-01

The Langevin equation with the memory kernel is solved. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated at the assumption that the system is in the thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Levy walks with divergent moments of the velocity distribution. The motion of a Brownian particle is considered both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle. (author)

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.)

Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

International Nuclear Information System (INIS)

Salazar, Domingos S P; Lira, Sérgio A

2016-01-01

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions. (paper)

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.

Boltzmann machines for travelling salesman problems

NARCIS (Netherlands)

Aarts, E.H.L.; Korst, J.H.M.

1989-01-01

Boltzmann machines are proposed as a massively parallel alternative to the (sequential) simulated annealing algorithm. Our approach is tailored to the travelling salesman problem, but it can also be applied to a more general class of combinatorial optimization problems. For two distinct 0–1

Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Science.gov (United States)

Chen, SongGui; Sun, QiCheng; Jin, Feng; Liu, JianGuo

2014-03-01

Fresh cement mortar is a type of workable paste, which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering. In this paper, Papanastasiou's model for Bingham fluids is solved by using the multiplerelaxation-time lattice Boltzmann model (MRT-LB). Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou's model provides a good approximation of realistic Bingham plastics for values of m > 108. For lower values of m, Papanastasiou's model is valid for fluids between Bingham and Newtonian fluids. The MRT-LB model is validated by two benchmark problems: 2D steady Poiseuille flows and lid-driven cavity flows. Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability. We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle. Besides the rich flow structures obtained in this work, the dynamics fluid force on the round particle is calculated. Results show that both the Reynolds number Re and the Bingham number Bn affect the drag coefficients C D , and a drag coefficient with Re and Bn being taken into account is proposed. The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed. Finally, the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields. These results help simulation of fresh concrete flowing in porous media.

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

International Nuclear Information System (INIS)

Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

2014-01-01

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

Energy Technology Data Exchange (ETDEWEB)

Harko, Tiberiu [University College London, Department of Mathematics, London (United Kingdom); Leung, Chun Sing [Polytechnic University, Department of Applied Mathematics, Hong Kong (China); Mocanu, Gabriela [Babes-Bolyai University, Faculty of Physics, Cluj-Napoca (Romania)

2014-05-15

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

Science.gov (United States)

Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

2014-05-01

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

Entropic multiple-relaxation-time multirange pseudopotential lattice Boltzmann model for two-phase flow

Science.gov (United States)

Qin, Feifei; Mazloomi Moqaddam, Ali; Kang, Qinjun; Derome, Dominique; Carmeliet, Jan

2018-03-01

An entropic multiple-relaxation-time lattice Boltzmann approach is coupled to a multirange Shan-Chen pseudopotential model to study the two-phase flow. Compared with previous multiple-relaxation-time multiphase models, this model is stable and accurate for the simulation of a two-phase flow in a much wider range of viscosity and surface tension at a high liquid-vapor density ratio. A stationary droplet surrounded by equilibrium vapor is first simulated to validate this model using the coexistence curve and Laplace's law. Then, two series of droplet impact behavior, on a liquid film and a flat surface, are simulated in comparison with theoretical or experimental results. Droplet impact on a liquid film is simulated for different Reynolds numbers at high Weber numbers. With the increase of the Sommerfeld parameter, onset of splashing is observed and multiple secondary droplets occur. The droplet spreading ratio agrees well with the square root of time law and is found to be independent of Reynolds number. Moreover, shapes of simulated droplets impacting hydrophilic and superhydrophobic flat surfaces show good agreement with experimental observations through the entire dynamic process. The maximum spreading ratio of a droplet impacting the superhydrophobic flat surface is studied for a large range of Weber numbers. Results show that the rescaled maximum spreading ratios are in good agreement with a universal scaling law. This series of simulations demonstrates that the proposed model accurately captures the complex fluid-fluid and fluid-solid interfacial physical processes for a wide range of Reynolds and Weber numbers at high density ratios.

Multi-relaxation-time lattice Boltzmann modeling of the acoustic field generated by focused transducer

Science.gov (United States)

Shan, Feng; Guo, Xiasheng; Tu, Juan; Cheng, Jianchun; Zhang, Dong

The high-intensity focused ultrasound (HIFU) has become an attractive therapeutic tool for the noninvasive tumor treatment. The ultrasonic transducer is the key component in HIFU treatment to generate the HIFU energy. The dimension of focal region generated by the transducer is closely relevant to the safety of HIFU treatment. Therefore, it is essential to numerically investigate the focal region of the transducer. Although the conventional acoustic wave equations have been used successfully to describe the acoustic field, there still exist some inherent drawbacks. In this work, we presented an axisymmetric isothermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) model with the Bouzidi-Firdaouss-Lallemand (BFL) boundary condition in cylindrical coordinate system. With this model, some preliminary simulations were firstly conducted to determine a reasonable value of the relaxation parameter. Then, the validity of the model was examined by comparing the results obtained with the LBM results with the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Spheroidal beam equation (SBE) for the focused transducers with different aperture angles, respectively. In addition, the influences of the aperture angle on the focal region were investigated. The proposed model in this work will provide significant references for the parameter optimization of the focused transducer for applications in the HIFU treatment or other fields, and provide new insights into the conventional acoustic numerical simulations.

A fast iterative scheme for the linearized Boltzmann equation

Science.gov (United States)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

Predicting drug-target interactions using restricted Boltzmann machines.

Science.gov (United States)

Wang, Yuhao; Zeng, Jianyang

2013-07-01

In silico prediction of drug-target interactions plays an important role toward identifying and developing new uses of existing or abandoned drugs. Network-based approaches have recently become a popular tool for discovering new drug-target interactions (DTIs). Unfortunately, most of these network-based approaches can only predict binary interactions between drugs and targets, and information about different types of interactions has not been well exploited for DTI prediction in previous studies. On the other hand, incorporating additional information about drug-target relationships or drug modes of action can improve prediction of DTIs. Furthermore, the predicted types of DTIs can broaden our understanding about the molecular basis of drug action. We propose a first machine learning approach to integrate multiple types of DTIs and predict unknown drug-target relationships or drug modes of action. We cast the new DTI prediction problem into a two-layer graphical model, called restricted Boltzmann machine, and apply a practical learning algorithm to train our model and make predictions. Tests on two public databases show that our restricted Boltzmann machine model can effectively capture the latent features of a DTI network and achieve excellent performance on predicting different types of DTIs, with the area under precision-recall curve up to 89.6. In addition, we demonstrate that integrating multiple types of DTIs can significantly outperform other predictions either by simply mixing multiple types of interactions without distinction or using only a single interaction type. Further tests show that our approach can infer a high fraction of novel DTIs that has been validated by known experiments in the literature or other databases. These results indicate that our approach can have highly practical relevance to DTI prediction and drug repositioning, and hence advance the drug discovery process. Software and datasets are available on request. Supplementary data are

Numerical modeling of condensate droplet on superhydrophobic nanoarrays using the lattice Boltzmann method

International Nuclear Information System (INIS)

Zhang Qing-Yu; Zhang You-Fa; Zhu Ming-Fang; Sun Dong-Ke

2016-01-01

In the present study, the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multi-component multi-phase lattice Boltzmann model. The results indicate that three typical nucleation modes of condensate droplets are produced by changing the geometrical parameters of nanoarrays. Droplets nucleated at the top (top-nucleation mode), or in the upside interpillar space of nanoarrays (side-nucleation mode), generate the non-wetting Cassie state, whereas the ones nucleated at the bottom corners between the nanoarrays (bottom-nucleation mode) present the wetting Wenzel state. Time evolutions of droplet pressures at the upside and downside of the liquid phase are analyzed to understand the wetting behaviors of the droplets condensed from different nucleation modes. The phenomena of droplet condensation on nanoarrays patterned with different hydrophilic and hydrophobic regions are simulated, indicating that the nucleation mode of condensate droplets can also be manipulated by modifying the local intrinsic wettability of nanoarray surface. The simulation results are compared well with the experimental observations reported in the literature. (paper)

Nonequilibrium thermodynamics of restricted Boltzmann machines

Science.gov (United States)

Salazar, Domingos S. P.

2017-08-01

In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

Nonequilibrium thermodynamics of restricted Boltzmann machines.

Science.gov (United States)

Salazar, Domingos S P

2017-08-01

In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

International Nuclear Information System (INIS)

Sherrill, M.E.; Abdallah, J. Jr.; Csanak, G.; Kilcrease, D.P.; Dodd, E.S.; Fukuda, Y.; Akahane, Y.; Aoyama, M.; Inoue, N.; Ueda, H.; Yamakawa, K.; Faenov, A.Ya.; Magunov, A.I.; Pikuz, T.A.; Skobelev, I.Yu.

2006-01-01

In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He α spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model

Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

Energy Technology Data Exchange (ETDEWEB)

Sherrill, M.E. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States)]. E-mail: manolo@t4.lanl.gov; Abdallah, J. Jr. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Csanak, G. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Kilcrease, D.P. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Dodd, E.S. [Los Alamos National Laboratory, X-1, Los Alamos, NM 87545 (United States); Fukuda, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Akahane, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Aoyama, M. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Inoue, N. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Ueda, H. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Yamakawa, K. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Faenov, A.Ya. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Magunov, A.I. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Pikuz, T.A. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Skobelev, I.Yu. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation)

2006-05-15

In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He{sub {alpha}} spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model.

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

A new scheme for solving inhomogeneous Boltzmann equation for electrons in weakly ionised gases

International Nuclear Information System (INIS)

Mahmoud, M.O.M.; Yousfi, M.

1995-01-01

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)

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

Science.gov (United States)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Flow simulation of fiber reinforced self compacting concrete using Lattice Boltzmann method

DEFF Research Database (Denmark)

Svec, Oldrich; Skocek, Jan; Stang, Henrik

2011-01-01

Self compacting concrete (SCC) is a promising material in the civil engineering industry. One of the benefits of the SCC is a fast and simplified casting followed by decreased labor costs. The SCC as any other type of concrete has a significantly lower tensile and shear strength in comparison to ....... A relatively new group of models - Lattice Boltzmann Modeling (LBM) - is presented in this paper. The conventional LBM is modified to include fiber and particle suspensions and non-Newtonian rheology and is used to model the fiber reinforced self compacting concrete flow....

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials.

Science.gov (United States)

Dechant, A; Lutz, E; Kessler, D A; Barkai, E

2012-05-01

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Adaptive Non-Boltzmann Monte Carlo

International Nuclear Information System (INIS)

Fitzgerald, M.; Picard, R.R.; Silver, R.N.

1998-01-01

This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods

Adaptive Non-Boltzmann Monte Carlo

Energy Technology Data Exchange (ETDEWEB)

Fitzgerald, M.; Picard, R.R.; Silver, R.N.

1998-06-01

This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods.

First results of the EXILL and FATIMA campaign at the Institut Laue Langevin

Energy Technology Data Exchange (ETDEWEB)

Jolie, Jan; Regis, Jean-Marc; Saed-Samii, Nima; Warr, Nigel [IKP, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Wilmsen, Dennis [IKP, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); GANIL, BP 55027 (France); France, Gilles de; Clement, Emmanuel [GANIL, BP 55027 (France); Blanc, Aurelien; Jentschel, Michael; Koester, Uli; Mutti, Paolo; Soldner, Thorsten [ILL, 71 Av. des Martyrs, 38042 Grenoble (France); Simpson, Gary [University of Western Scotland, Paisley, PA1 2BE (United Kingdom); UIrban, Waldek [Faculty of Physics, University of Warsaw, 02-093 Warsaw (Poland); Bruce, Alison; Lalskovski, Stefan [SCEM, University of Brighton, Brighton BN2 4GJ (United Kingdom); Fraile, Luis [Grupo de Fisica Nuclear, Universidad Complutese, 28040 Madrid (Spain); Kroell, Thorsten [Institut fuer Kernphysik, TU Darmstadt, Darmstadt (Germany); Podolyak, Zsolt; Regan, Patrick [Dept. of Physics, University of Surrey, Guildford GU2 7XH (United Kingdom); Korten, Wolfram [CEA, Centre de Saclay, IRFU, 91191 Gif-sur-Yvette (France); Ur, Calin; Marginean, Nicu [Horia Hulubei NIPNE, 77125 Bucharest (Romania)

2015-07-01

At the PF1B cold neutron beam line at the Institut Laue Langevin the EXILL and FATIMA array consisting of 8 EXOGAM clover Ge detectors and 16 LaBr3(Ce) scintillators was used for the measurement of lifetimes using the generalised centroid difference method. The studied nuclei were formed by the (n,γ) and (n,fission) reactions. We report on the set-up and present first results on {sup 90}Zr and {sup 196}Pt.

Numerical simulation of transmission coefficient using c-number Langevin equation

Science.gov (United States)

Barik, Debashis; Bag, Bidhan Chandra; Ray, Deb Shankar

2003-12-01

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik et al., J. Chem. Phys. 119, 680 (2003); Banerjee et al., Phys. Rev. E 65, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the T2 enhancement of the rate at low temperatures and other related features of temporal behavior of the transmission coefficient over a range of temperature down to absolute zero, noise correlation, and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order.

Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis.

Science.gov (United States)

Ba, Yan; Liu, Haihu; Sun, Jinju; Zheng, Rongye

2013-10-01

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Science.gov (United States)

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions

International Nuclear Information System (INIS)

Denton, A R

2010-01-01

Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid

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

International Nuclear Information System (INIS)

Hendriks, E.M.

1983-01-01

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

Lattice Boltzmann flow simulations with applications of reduced order modeling techniques

KAUST Repository

Brown, Donald

2014-01-01

With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.

Langevin dynamics simulation on the translocation of polymer through α-hemolysin pore

International Nuclear Information System (INIS)

Sun, Li-Zhen; Luo, Meng-Bo

2014-01-01

The forced translocation of a polymer through an α-hemolysin pore under an electrical field is studied using a Langevin dynamics simulation. The α-hemolysin pore is modelled as a connection of a spherical vestibule and a cylindrical β-barrel and polymer-pore attraction is taken into account. The results show that polymer-pore attraction can help the polymer enter the vestibule and the β-barrel as well; however, a strong attraction will slow down the translocation of the polymer through the β-barrel. The mean translocation time for the polymer to thread through the β-barrel increases linearly with the polymer length. By comparing our results with that of a simple pore without a vestibule, we find that the vestibule helps the polymer enter and thread through the β-barrel. Moreover, we find that it is easier for the polymer to thread through the β-barrel if the polymer is located closer to the surface of the vestibule. Some simulation results are explained qualitatively by theoretically analyzing the free-energy landscape of polymer translocation. (paper)

Bifurcation dynamics of the tempered fractional Langevin equation

Energy Technology Data Exchange (ETDEWEB)

Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)

2016-08-15

Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method

KAUST Repository

Ibrahem, Ahmed M.

2017-05-04

In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatangar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103to105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

THE EFFECT OF CHEMICAL-STRUCTURE UPON THE THERMODYNAMICS OF MICELLIZATION OF MODEL ALKYLARENESULPHONATES - PREDICTION OF MICELLAR PROPERTIES WITH THE POISSON-BOLTZMANN MODEL

NARCIS (Netherlands)

Bijma, K; Engberts, J B F N

This paper describes how the theory of the ''dressed micelle'', which is based on the nonlinear Poisson-Boltzmann equation, can be used to calculate a number of thermodynamic quantities for micellization of sodium p-alkylbenzenesulphonates. From the Gibbs energy of micellization, the enthalpy of

Fluctuation in nuclear dynamics and multifragmentation

International Nuclear Information System (INIS)

Chomaz, P.; Di Toro, M.; Randrup, J.

1993-01-01

We first explain why any reduced descriptions, such as mean field approximation, are stochastic in nature. This concept is illustrated on the schematic example of the Hysteresis circle of two compasses. We study the dynamical behaviour of unstable systems, characterized by the occurrence of bifurcations or phase transitions. Concerning nuclear matter, we discuss the spinodal instability both in two and in three dimensions. In such a critical situation, we explore the possibility to replace the stochastic part of the collision integral in the Boltzmann-Langevin model by the numerical noise associated with the finite number of test particles in ordinary BUU treatment

Fluctuation in nuclear dynamics and multifragmentation

International Nuclear Information System (INIS)

Chomaz, P.; Colonna, M.; Burgio, G.F.; Guarnera, A.; Di Toro, M.; Randrup, J.

1993-01-01

We first explain why any reduced descriptions, such as mean field approximation, are stochastic in nature. This concept is illustrated on the schematic example of the Hysteresis circle of two compasses. We study the dynamical behaviour of unstable systems, characterized by the occurrence of bifurcations or phase transitions. Concerning nuclear matter, we discuss the spinodal instability in two dimensions. In such a critical situation, we explore the possibility to replace the stochastic part of the collision integral in the Boltzmann-Langevin model by the numerical noise associated with the finite number of test particles in ordinary BUU treatment. (author). 24 refs., 10 figs

Fluctuation in nuclear dynamics and multifragmentation

Energy Technology Data Exchange (ETDEWEB)

Chomaz, P. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); Colonna, M.; Burgio, G.F.; Guarnera, A. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)]|[Istituto Nazionale di Fisica Nucleare, Catania (Italy); Di Toro, M. [Istituto Nazionale di Fisica Nucleare, Catania (Italy); Randrup, J. [Lawrence Berkeley Lab., CA (United States)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany)

1993-12-31

We first explain why any reduced descriptions, such as mean field approximation, are stochastic in nature. This concept is illustrated on the schematic example of the Hysteresis circle of two compasses. We study the dynamical behaviour of unstable systems, characterized by the occurrence of bifurcations or phase transitions. Concerning nuclear matter, we discuss the spinodal instability in two dimensions. In such a critical situation, we explore the possibility to replace the stochastic part of the collision integral in the Boltzmann-Langevin model by the numerical noise associated with the finite number of test particles in ordinary BUU treatment. (author). 24 refs., 10 figs.

Impressions from a visit by the ASN of the Laue Langevin Institute research reactor in Grenoble

International Nuclear Information System (INIS)

Nifenecker, H.

2011-01-01

After having recalled some specific characteristics of the Laue Langevin Institute research reactor (fuel type, cooling system, power, fuel management, fuel storage pool), the author reports the examination of the emergency procedures and of the reactor maintenance. He describes two exercises which respectively simulated the occurrence of an earthquake and that of a flooding due to a dam breaching

Boltzmann, Gibbs and Darwin-Fowler approaches in parastatistics

International Nuclear Information System (INIS)

Ponczek, R.L.; Yan, C.C.

1976-01-01

Derivations of the equilibrium values of occupation numbers are made using three approaches, namely, the Boltzmann 'elementary' one, the ensemble method of Gibbs, and that of Darwin and Fowler as well [pt

Acoustic modelling in view of a determination of the Boltzmann constant within 1 ppm for the redefinition of the kelvin

International Nuclear Information System (INIS)

Gelat, Pierre; Podesta, Michael de; Sutton, Gavin; Underwood, Robin; Joly, Nicolas

2009-01-01

iMERA/Euromet Project 885 is co-ordinating European effort towards a new determination of the Boltzmann constant k B to within 1 ppm with the aim of redefining the unit of thermodynamic temperature. This project will enable the National Physical Laboratory to perform primary thermometry in the region of -40 0 C (Hg) to 156 0 C (In) with sub-millikelvin uncertainties by 2012. The chosen technique relies on determining the speed of sound in a monatomic gas. Using the radial acoustic modes of a spherical resonator, consisting of a copper shell and filled with argon or helium, the speed of sound can be measured with great precision and from this measurement the Boltzmann constant can be inferred. This project draws on expertise in dimensional, density, microwave and acoustic measurements at the state-of-the-art. In order to gain further understanding of the experimental configuration a vibro-acoustic model has been developed using the finite element method. Initial calculations were carried out to ensure that predictions of the resonant frequency could be made with the required precision by comparing against an analytical model of a spherical shell filled with a gas. A more elaborate model better representing the experimental configuration was then developed. Thermo-viscous effects close to the fluid-structure boundary were accounted for using a linear acoustic formulation, from which a normal incidence admittance boundary condition was derived and imposed on the inner surface of the resonator. Acoustic pressure, particle velocity and temperature variation as a function of position may be obtained within the gas as a function of frequency. It is therefore possible to investigate how changes in the configuration affect the frequency of radial modes. It is hoped that this approach will shed a better understanding of the underlying complex physical phenomena allowing a minimization of the overall uncertainty.

Acoustic modelling in view of a determination of the Boltzmann constant within 1 ppm for the redefinition of the kelvin

Science.gov (United States)

Gélat, Pierre; Joly, Nicolas; de Podesta, Michael; Sutton, Gavin; Underwood, Robin

2009-11-01

iMERA/Euromet Project 885 is co-ordinating European effort towards a new determination of the Boltzmann constant kB to within 1 ppm with the aim of redefining the unit of thermodynamic temperature. This project will enable the National Physical Laboratory to perform primary thermometry in the region of -40 °C (Hg) to 156 °C (In) with sub-millikelvin uncertainties by 2012. The chosen technique relies on determining the speed of sound in a monatomic gas. Using the radial acoustic modes of a spherical resonator, consisting of a copper shell and filled with argon or helium, the speed of sound can be measured with great precision and from this measurement the Boltzmann constant can be inferred. This project draws on expertise in dimensional, density, microwave and acoustic measurements at the state-of-the-art. In order to gain further understanding of the experimental configuration a vibro-acoustic model has been developed using the finite element method. Initial calculations were carried out to ensure that predictions of the resonant frequency could be made with the required precision by comparing against an analytical model of a spherical shell filled with a gas. A more elaborate model better representing the experimental configuration was then developed. Thermo-viscous effects close to the fluid-structure boundary were accounted for using a linear acoustic formulation, from which a normal incidence admittance boundary condition was derived and imposed on the inner surface of the resonator. Acoustic pressure, particle velocity and temperature variation as a function of position may be obtained within the gas as a function of frequency. It is therefore possible to investigate how changes in the configuration affect the frequency of radial modes. It is hoped that this approach will shed a better understanding of the underlying complex physical phenomena allowing a minimization of the overall uncertainty.

Application of Boltzmann equation to electron transmission and seconary electron emission

International Nuclear Information System (INIS)

Lanteri, H.; Bindi, R.; Rostaing, P.

1979-01-01

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 [fr

Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

Science.gov (United States)

Nagata, Keitro; Nishimura, Jun; Shimasaki, Shinji

2018-03-01

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and intro-duce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a 43 × 8 lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.

Modelling and investigation of partial wetting surfaces for drop dynamics using lattice Boltzmann method

Science.gov (United States)

Pravinraj, T.; Patrikar, Rajendra

2017-07-01

Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains the temporal behaviour of droplet during the spreading, recoiling and translation along with tracking of contact angle hysteresis phenomenon.

Lattice-Boltzmann Method with Dynamic Grid Refinement for Simulating Particle Deposition on a Single Fibre

Directory of Open Access Journals (Sweden)

Helmut Schomburg

2013-03-01

Full Text Available In this work a numerical approach to predict the deposition behaviour of nano-scale particles on the surface of a single fibre by resolving the resulting dendrite-like particle structures in detail is presented. The gas flow simulation is carried out by a two-dimensional Lattice-Boltzmann method, which is coupled with a Lagrangian approach for the particle motion. To decrease calculation time and system requirements the Lattice-Boltzmann model is extended to allow for local grid refinement. Because of the a priori unknown location of deposition, the simulation procedure starts on a coarse mesh which is then locally refined in a fully adaptive way in regions of accumulated particles. After each deposition the fluid flow is recalculated in order to resolve the coupling of the flow with the growing particle structures correctly. For the purpose of avoiding unphysical blocking of flow by growing particle dendrites the Lattice-Boltzmann method is extended to permeable cells in these regions using the Brinkmann equation. This extended deposition model is compared to simpler approaches, where the deposit has no retroaction on the flow or is treated as a solid structure. It is clear that the permeable model is most realistic and allows considering the particle deposition on a fibre as two-dimensional problem. Comprehensive simulations were conducted for analysing the importance of different parameters, i.e. free-stream velocity and particle diameter on the deposit structure. The results of this sensitivity analysis agree qualitatively well with former published numerical and experimental results. Finally the structure of the particle deposit was quantitatively characterised by using a modified fractal dimension.

Generalized Stefan-Boltzmann Law

Science.gov (United States)

Montambaux, Gilles

2018-03-01

We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems whose chemical potential vanishes. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.

Kinetic Boltzmann approach adapted for modeling highly ionized matter created by x-ray irradiation of a solid

Czech Academy of Sciences Publication Activity Database

Ziaja, B.; Saxena, V.; Son, S.-K.; Medvedev, N.; Barbrel, B.; Woloncewicz, B.; Stránský, Michal

2016-01-01

Roč. 93, č. 5 (2016), 1-6, č. článku 053210. ISSN 2470-0045 R&D Projects: GA MŠk(CZ) LG13029 Institutional support: RVO:68378271 Keywords : X-ray * Boltzmann equation Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.366, year: 2016

Deformation of Two-Dimensional Nonuniform-Membrane Red Blood Cells Simulated by a Lattice Boltzmann Model

International Nuclear Information System (INIS)

Hua-Bing, Li; Li, Jin; Bing, Qiu

2008-01-01

To study two-dimensional red blood cells deforming in a shear Bow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow. (fundamental areas of phenomenology(including applications))

Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

Directory of Open Access Journals (Sweden)

Kosuke Hayashi

2012-06-01

Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

Airframe Noise Prediction of a Full Aircraft in Model and Full Scale Using a Lattice Boltzmann Approach

Science.gov (United States)

Fares, Ehab; Duda, Benjamin; Khorrami, Mehdi R.

2016-01-01

Unsteady flow computations are presented for a Gulfstream aircraft model in landing configuration, i.e., flap deflected 39deg and main landing gear deployed. The simulations employ the lattice Boltzmann solver PowerFLOW(Trademark) to simultaneously capture the flow physics and acoustics in the near field. Sound propagation to the far field is obtained using a Ffowcs Williams and Hawkings acoustic analogy approach. Two geometry representations of the same aircraft are analyzed: an 18% scale, high-fidelity, semi-span model at wind tunnel Reynolds number and a full-scale, full-span model at half-flight Reynolds number. Previously published and newly generated model-scale results are presented; all full-scale data are disclosed here for the first time. Reynolds number and geometrical fidelity effects are carefully examined to discern aerodynamic and aeroacoustic trends with a special focus on the scaling of surface pressure fluctuations and farfield noise. An additional study of the effects of geometrical detail on farfield noise is also documented. The present investigation reveals that, overall, the model-scale and full-scale aeroacoustic results compare rather well. Nevertheless, the study also highlights that finer geometrical details that are typically not captured at model scales can have a non-negligible contribution to the farfield noise signature.

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

International Nuclear Information System (INIS)

Saida, Hiromi

2013-01-01

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

Entropic Lattice Boltzmann: an implicit Large-Eddy Simulation?

Science.gov (United States)

Tauzin, Guillaume; Biferale, Luca; Sbragaglia, Mauro; Gupta, Abhineet; Toschi, Federico; Ehrhardt, Matthias; Bartel, Andreas

2017-11-01

We study the modeling of turbulence implied by the unconditionally stable Entropic Lattice Boltzmann Method (ELBM). We first focus on 2D homogeneous turbulence, for which we conduct numerical simulations for a wide range of relaxation times τ. For these simulations, we analyze the effective viscosity obtained by numerically differentiating the kinetic energy and enstrophy balance equations averaged over sub-domains of the computational grid. We aim at understanding the behavior of the implied sub-grid scale model and verify a formulation previously derived using Chapman-Enskog expansion. These ELBM benchmark simulations are thus useful to understand the range of validity of ELBM as a turbulence model. Finally, we will discuss an extension of the previously obtained results to the 3D case. Supported by the European Unions Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 642069 and by the European Research Council under the ERC Grant Agreement No. 339032.

A partial entropic lattice Boltzmann MHD simulation of the Orszag-Tang vortex

Science.gov (United States)

Flint, Christopher; Vahala, George

2018-02-01

Karlin has introduced an analytically determined entropic lattice Boltzmann (LB) algorithm for Navier-Stokes turbulence. Here, this is partially extended to an LB model of magnetohydrodynamics, on using the vector distribution function approach of Dellar for the magnetic field (which is permitted to have field reversal). The partial entropic algorithm is benchmarked successfully against standard simulations of the Orszag-Tang vortex [Orszag, S.A.; Tang, C.M. J. Fluid Mech. 1979, 90 (1), 129-143].

Atoms, mechanics, and probability Ludwig Boltzmann's statistico-mechanical writings : an exegesis

CERN Document Server

Darrigol, Olivier

2018-01-01

One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844-1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given to Boltzmann's theoretical tool-box and to his patient construction of lofty formal systems even before their full conceptual import could be known. This constructive tendency largely accounts for his lengthy style, for the abundance of new constructions, for the relative vagueness of their object--and for the puzzlement of commentators. This book will help the reader cross the stylistic barrier and see how ingeniously B...

Observation of distorted Maxwell-Boltzmann distribution of epithermal ions in LHD

Science.gov (United States)

Ida, K.; Kobayashi, T.; Yoshinuma, M.; Akiyama, T.; Tokuzawa, T.; Tsuchiya, H.; Itoh, K.; LHD Experiment Group

2017-12-01

A distorted Maxwell-Boltzmann distribution of epithermal ions is observed associated with the collapse of energetic ions triggered by the tongue shaped deformation. The tongue shaped deformation is characterized by the plasma displacement localized in the toroidal, poloidal, and radial directions at the non-rational magnetic flux surface in toroidal plasma. Moment analysis of the ion velocity distribution measured with charge exchange spectroscopy is studied in order to investigate the impact of tongue event on ion distribution. A clear non-zero skewness (3rd moment) and kurtosis (4th moment -3) of ion velocity distribution in the epithermal region (within three times of thermal velocity) is observed after the tongue event. This observation indicates the clear evidence of the distortion of ion velocity distribution from Maxwell-Boltzmann distribution. This distortion from Maxwell-Boltzmann distribution is observed in one-third of plasma minor radius region near the plasma edge and disappears in the ion-ion collision time scale.

Detection of Hypertension Retinopathy Using Deep Learning and Boltzmann Machines

Science.gov (United States)

Triwijoyo, B. K.; Pradipto, Y. D.

2017-01-01

hypertensive retinopathy (HR) in the retina of the eye is disturbance caused by high blood pressure disease, where there is a systemic change of arterial in the blood vessels of the retina. Most heart attacks occur in patients caused by high blood pressure symptoms of undiagnosed. Hypertensive retinopathy Symptoms such as arteriolar narrowing, retinal haemorrhage and cotton wool spots. Based on this reasons, the early diagnosis of the symptoms of hypertensive retinopathy is very urgent to aim the prevention and treatment more accurate. This research aims to develop a system for early detection of hypertension retinopathy stage. The proposed method is to determine the combined features artery and vein diameter ratio (AVR) as well as changes position with Optic Disk (OD) in retinal images to review the classification of hypertensive retinopathy using Deep Neural Networks (DNN) and Boltzmann Machines approach. We choose this approach of because based on previous research DNN models were more accurate in the image pattern recognition, whereas Boltzmann machines selected because It requires speedy iteration in the process of learning neural network. The expected results from this research are designed a prototype system early detection of hypertensive retinopathy stage and analysed the effectiveness and accuracy of the proposed methods.

Expectation-maximization of the potential of mean force and diffusion coefficient in Langevin dynamics from single molecule FRET data photon by photon.

Science.gov (United States)

Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

2013-12-12

The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

Science.gov (United States)

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

International Nuclear Information System (INIS)

Pan, Dongqing; Chien Jen, Tien; Li, Tao; Yuan, Chris

2014-01-01

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domain with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

Energy Technology Data Exchange (ETDEWEB)

Pan, Dongqing; Chien Jen, Tien [Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201 (United States); Li, Tao [School of Mechanical Engineering, Dalian University of Technology, Dalian 116024 (China); Yuan, Chris, E-mail: cyuan@uwm.edu [Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 North Cramer Street, Milwaukee, Wisconsin 53211 (United States)

2014-01-15

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domain with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

Science.gov (United States)

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Langevin dynamics of heavy flavors in relativistic heavy-ion collisions

CERN Document Server

Alberico, W M; De Pace, A; Molinari, A; Monteno, M; Nardi, M; Prino, F

2011-01-01

We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution of soft and hard collisions. The evolution of the background medium is described by ideal/viscous hydrodynamics. Below the critical temperature the heavy quarks are converted into hadrons, whose semileptonic decays provide single-electron spectra to be compared with the current experimental data measured at RHIC. We focus on the nuclear modification factor R_AA and on the elliptic-flow coefficient v_2, getting, for sufficiently large p_T, a reasonable agreement.

Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

Science.gov (United States)

Liou, Tong-Miin; Wang, Chun-Sheng

2018-01-01

Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field

International Nuclear Information System (INIS)

Haydock, David

2005-01-01

We show that lattice Boltzmann simulations can be used to model the radiation force on an object in a standing wave acoustic field and comparisons are made to theoretical predictions. We show how viscous effects change the radiation force and predict the motion of a particle placed near a boundary where viscous effects are important

Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field

Energy Technology Data Exchange (ETDEWEB)

Haydock, David [Unilever R and D Colworth, Sharnbrook, Bedford MK44 1LQ (United Kingdom); Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom)

2005-04-15

We show that lattice Boltzmann simulations can be used to model the radiation force on an object in a standing wave acoustic field and comparisons are made to theoretical predictions. We show how viscous effects change the radiation force and predict the motion of a particle placed near a boundary where viscous effects are important.

Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

DEFF Research Database (Denmark)

Pingen, Georg; Evgrafov, Anton; Maute, Kurt

2009-01-01

We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...

Multi-component Lattice Boltzmann simulation of the hydrodynamics in drip emitters

Directory of Open Access Journals (Sweden)

Giacomo Falcucci

2017-09-01

Full Text Available In this paper, we propose a fast and efficient numerical technique based on the Lattice Boltzmann method (LBM to model the flow through a reference drip emitter geometry. The aim of the study is to demonstrate the applicability of the LBM as a reliable simulation tool for the hydraulic optimisation of irrigation systems. Results for the water flow through a rectangular drip emitter are in good agreement with literature numerical and experimental data. Furthermore, we demonstrate the feasibility of the proposed model to simulate a multi-component flow that could be used to simulate the presence of additives, contaminants, and suspended particles.

Phase transitions in restricted Boltzmann machines with generic priors

Science.gov (United States)

Barra, Adriano; Genovese, Giuseppe; Sollich, Peter; Tantari, Daniele

2017-10-01

We study generalized restricted Boltzmann machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as generalized Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore, we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalization in a teacher-student scenario of unsupervised learning.

Nonlocal Boltzmann theory of plasma channels

International Nuclear Information System (INIS)

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

1983-01-01

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

Lattice Boltzmann Approach to Resistive MHD

Czech Academy of Sciences Publication Activity Database

Macnab, A.; Vahala, G.; Vahala, L.; Pavlo, Pavol; Soe, M.

2002-01-01

Roč. 47, č. 9 (2002), s. 51 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/44th./. Orlando , Florida, 11.11.2001-15.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann, magnetic fields Subject RIV: BL - Plasma and Gas Discharge Physics

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 complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant

Energy Technology Data Exchange (ETDEWEB)

Ito, Yuta [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Graduate University for Advanced Studies (SOKENDAI),1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

2016-12-05

In many interesting physical systems, the determinant which appears from integrating out fermions becomes complex, and its phase plays a crucial role in the determination of the vacuum. An example of this is QCD at low temperature and high density, where various exotic fermion condensates are conjectured to form. Another example is the Euclidean version of the type IIB matrix model for 10d superstring theory, where spontaneous breaking of the SO(10) rotational symmetry down to SO(4) is expected to occur. When one applies the complex Langevin method to these systems, one encounters the singular-drift problem associated with the appearance of nearly zero eigenvalues of the Dirac operator. Here we propose to avoid this problem by deforming the action with a fermion bilinear term. The results for the original system are obtained by extrapolations with respect to the deformation parameter. We demonstrate the power of this approach by applying it to a simple matrix model, in which spontaneous symmetry breaking from SO(4) to SO(2) is expected to occur due to the phase of the complex fermion determinant. Unlike previous work based on a reweighting-type method, we are able to determine the true vacuum by calculating the order parameters, which agree with the prediction by the Gaussian expansion method.

Langevin equation in systems with also negative temperatures

Science.gov (United States)

Baldovin, Marco; Puglisi, Andrea; Vulpiani, Angelo

2018-04-01

We discuss how to derive a Langevin equation (LE) in non standard systems, i.e. when the kinetic part of the Hamiltonian is not the usual quadratic function. This generalization allows to consider also cases with negative absolute temperature. We first give some phenomenological arguments suggesting the shape of the viscous drift, replacing the usual linear viscous damping, and its relation with the diffusion coefficient modulating the white noise term. As a second step, we implement a procedure to reconstruct the drift and the diffusion term of the LE from the time-series of the momentum of a heavy particle embedded in a large Hamiltonian system. The results of our reconstruction are in good agreement with the phenomenological arguments. Applying the method to systems with negative temperature, we can observe that also in this case there is a suitable LE, obtained with a precise protocol, able to reproduce in a proper way the statistical features of the slow variables. In other words, even in this context, systems with negative temperature do not show any pathology.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

International Nuclear Information System (INIS)

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

2016-01-01

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

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

Science.gov (United States)

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

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

Energy Technology Data Exchange (ETDEWEB)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

International Nuclear Information System (INIS)

Gamba, Irene M.; Haack, Jeffrey R.

2014-01-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

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

DEFF Research Database (Denmark)

Svec, Oldrich; Skoček, Jan

2013-01-01

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

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

International Nuclear Information System (INIS)

Hammond, L A; Halliday, I; Care, C M; Stevens, A

2002-01-01

We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow

Experimental investigation of the Boltzmann relation for a bi-Maxwellian distribution in inductively coupled plasmas

International Nuclear Information System (INIS)

Bang, Jin Young; Chung, Chin Wook

2009-01-01

In plasma, the Boltzmann relation is often used to connect the electron density to the plasma potential because it is not easy to calculate electric potentials on the basis of the Poisson equation due to the quasineutrality. From the Boltzmann relation, the electric potential can be simply obtained from the electron density or vice versa. However, the Boltzmann relation assumes that electrons are in thermal equilibrium and have a Maxwellian distribution, so it cannot be applied to non-Maxwellian distributions. In this paper, the Boltzmann relation for bi-Maxwellian distributions was newly derived from fluid equations and the comparison with the experimental results was given by measuring electron energy probability functions in an inductively coupled plasma. It was found that the spatial distribution of the electron density in bulk plasma is governed by the effective electron temperature, while that of the cold and hot electrons are governed by each electron temperature.

Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

Science.gov (United States)

Molavi Tabrizi, Amirhossein; Goossens, Spencer; Mehdizadeh Rahimi, Ali; Cooper, Christopher D; Knepley, Matthew G; Bardhan, Jaydeep P

2017-06-13

We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

A numeric investigation of co-flowing liquid streams using the Lattice Boltzmann Method

Science.gov (United States)

Somogyi, Andy; Tagg, Randall

2007-11-01

We present a numerical investigation of co-flowing immiscible liquid streams using the Lattice Boltzmann Method (LBM) for multi component, dissimilar viscosity, immiscible fluid flow. When a liquid is injected into another immiscible liquid, the flow will eventually transition from jetting to dripping due to interfacial tension. Our implementation of LBM models the interfacial tension through a variety of techniques. Parallelization is also straightforward for both single and multi component models as only near local interaction is required. We compare the results of our numerical investigation using LBM to several recent physical experiments.

Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

Science.gov (United States)

Agarwal, Ramesh; Chen, Rui; Cheremisin, Felix G.

2006-11-01

Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.

Boltzmann factor and Hawking radiation

International Nuclear Information System (INIS)

Ryskin, Gregory

2014-01-01

Hawking radiation has thermal spectrum corresponding to the temperature T H =(8πM) −1 , where M is the mass (energy) of the black hole. Corrections to the Hawking radiation spectrum were discovered by Kraus and Wilczek (1995) and Parikh and Wilczek (2000). Here I show that these corrections follow directly from the basic principles of thermodynamics and statistical mechanics. In essence, it is the Boltzmann factor that ought to be corrected; corrections to the Hawking (or any other) radiation spectrum then follow necessarily

Stochastic sensitivity analysis and Langevin simulation for neural network learning

International Nuclear Information System (INIS)

Koda, Masato

1997-01-01

A comprehensive theoretical framework is proposed for the learning of a class of gradient-type neural networks with an additive Gaussian white noise process. The study is based on stochastic sensitivity analysis techniques, and formal expressions are obtained for stochastic learning laws in terms of functional derivative sensitivity coefficients. The present method, based on Langevin simulation techniques, uses only the internal states of the network and ubiquitous noise to compute the learning information inherent in the stochastic correlation between noise signals and the performance functional. In particular, the method does not require the solution of adjoint equations of the back-propagation type. Thus, the present algorithm has the potential for efficiently learning network weights with significantly fewer computations. Application to an unfolded multi-layered network is described, and the results are compared with those obtained by using a back-propagation method

First results of the (n,gamma) EXILL campaigns at the Institut Laue Langevin

Energy Technology Data Exchange (ETDEWEB)

Jolie, Jan; Regis, Jean-Marc; Wilmsen, Dennis; Ahmed, Samer; Pfeiffer, Michael; Saed Samii, Nima; Warr, Nigel [Institut fuer Kernphysik, Universitaet zu Koeln, Zuelpicher Str 77, 50937 Koeln (Germany); Thirolf, Peter; Habs, Dieter [Fakultaet fuer Physik, Ludwig Maximilian Universitaet, 85748 Garching (Germany); Collaboration: EXILL Collaboration; FATIMA Collaboration

2014-07-01

At the PF1B cold neutron beam line at the Institut Laue Langevin the EXILL array consisting of EXOGAM, GASP and LOHENGRIN detectors was used to perform (n,γ) measurements under very high coincidence rates. About ten different reactions were then measured in autumn 2012. In spring 2013 the EXOGAM array was combined with 16 LaBr{sub 3}(Ce) scintillators in the FATIMA rate at EXILL campaign for the measurement of lifetimes using the generalised centroid difference method. We report on the properties of both set-ups and present first results on Pt isotopes from both campaigns.

MRT Lattice Boltzmann schemes for confined suspension flows

NARCIS (Netherlands)

Sman, van der R.G.M.

2010-01-01

We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been

Convection-diffusion lattice Boltzmann scheme for irregular lattices

NARCIS (Netherlands)

Sman, van der R.G.M.; Ernst, M.H.

2000-01-01

In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the

Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry

Science.gov (United States)

Szucki, Michal; Suchy, J. S.; Lelito, J.; Malinowski, P.; Sobczyk, J.

2017-12-01

The aim of this work is the development of the lattice Boltzmann model for simulation of the mold filling process. The authors present a simplified approach to the modeling of liquid metal-gas flows with particular emphasis on the interactions between these phases. The boundary condition for momentum transfer of the moving free surface to the gaseous phase is shown. Simultaneously, the method for modeling influence of gas back pressure on a position and shape of the interfacial boundary is explained in details. The problem of the lattice Boltzmann method (LBM) stability is also analyzed. Since large differences in viscosity of both fluids are a source of the model instability, the so-called fractional step (FS) method allowing to improve the computation stability is applied. The presented solution is verified on the bases of the available reference data and the results of experiments. It is shown that the model describes properly such effects as: gas bubbles formation and air back pressure, accompanying liquid-gas flows in the casting mold. At the same time the proposed approach is easy to be implemented and characterized by a lower demand of operating memory as compared to typical LBM models of two-phase flows.

Numerical analysis of interfacial growth and deformation in horizontal stratified two-phase flow by lattice Boltzmann method

International Nuclear Information System (INIS)

Ebihara, Ken-ichi

2005-03-01

Two-phase flow is one of the important phenomena in nuclear reactors and heat exchangers at nuclear plants. It is desired for the optimum design and safe operation of such equipment to understand and predict the two-phase flow phenomenon by numerical analysis. In the present, the two-fluid model is widely used for the numerical analysis of two-phase flow. The numerical analysis method using the two-fluid model solves macroscopic hydrodynamic equations, in which fluid is regarded as continuum, with the boundary conditions at the wall, the inlet and outlet, and the interface between two phases. Since the interfacial and the wall boundary conditions utilized by this method are given as the model, such as the flow regime map and correlation, which is usually constructed on the basis of experimental results, the accuracy of the two-phase flow analysis using the two-fluid model depends on that of the utilized model or the experiment result for modeling. Tremendous progress of the computer performance and the development of new computational methods make the numerical simulation of two-phase flow with the interfacial motion possible in resent years. In such circumstances, the lattice-gas method and the lattice Boltzmann method, which represent fluid by many particles or the particle distribution function on the spatial lattice, was proposed in 1990s and these methods are applied to the numerical simulation of two-phase flow. The main feature of the two-phase fluid model of those methods is the capability of the simulation of two-phase flow without the procedure for tracking the interfacial position and shape owing to the inlet-particle potential generating the interface. Therefore it is expected that the lattice-gas method and the lattice Boltzmann method possess the predictability of the experiment by the numerical analysis of two-phase flow as well as the possibility of giving the substitute of the flow regime map and the correlation used by the two-fluid model. In this

Dissipation of the tilting degree of freedom in heavy-ion-induced fission from four-dimensional Langevin dynamics

Energy Technology Data Exchange (ETDEWEB)

Nadtochy, P.N. [Omsk State Technical University, Omsk (Russian Federation); Ryabov, E.G.; Cheredov, A.V.; Adeev, G.D. [Omsk State University, Omsk (Russian Federation)

2016-10-15

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to the calculation of a wide set of experimental observables of excited compound nuclei from {sup 199}Pb to {sup 248}Cf formed in reactions induced by heavy ions. In the model under investigation, the tilting degree of freedom (K coordinate) representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of {c,h,α} parametrization. The evolution of the K coordinate is described by means of the Langevin equation in the overdamped regime. The friction tensor for the shape collective coordinates is calculated under the assumption of the modified version of the one-body dissipation mechanism, where the reduction coefficient k{sub s} of the contribution from the ''wall'' formula is introduced. The calculations are performed both for the constant values of the coefficient k{sub s} and for the coordinate-dependent reduction coefficient k{sub s}(q) which is found on the basis of the ''chaos-weighted wall formula''. Different possibilities of the deformation-dependent dissipation coefficient (γ{sub K}) for the K coordinate are investigated. The presented results demonstrate that an impact of the k{sub s} and γ{sub K} parameters on the calculated observable fission characteristics can be selectively probed. It was found that it is possible to describe the experimental data consistently with the deformation-dependent γ{sub K}(q) coefficient for shapes featuring a neck, which predicts quite small values of γ{sub K} = 0.0077 (MeV zs){sup -1/2} and constant γ{sub K} = 0.1 -0.4 (MeV zs){sup -1/2} for compact shapes featuring no neck. (orig.)

Langevin simulations of QCD, including fermions

International Nuclear Information System (INIS)

Kronfeld, A.S.

1986-02-01

We encounter critical slow down in updating when xi/a -> infinite and in matrix inversion (needed to include fermions) when msub(q)a -> 0. A simulation that purports to solve QCD numerically will encounter these limits, so to face the challenge in the title of this workshop, we must cure the disease of critical slow down. Physically, this critical slow down is due to the reluctance of changes at short distances to propagate to large distances. Numerically, the stability of an algorithm at short wavelengths requires a (moderately) small step size; critical slow down occurs when the effective long wavelength step size becomes tiny. The remedy for this disease is an algorithm that propagates signals quickly throughout the system; i.e. one whose effective step size is not reduced for the long wavelength conponents of the fields. (Here the effective ''step size'' is essentially an inverse decorrelation time.) To do so one must resolve various wavelengths of the system and modify the dynamics (in CPU time) of the simulation so that all modes evolve at roughly the same rate. This can be achieved by introducing Fourier transforms. I show how to implement Fourier acceleration for Langevin updating and for conjugate gradient matrix inversion. The crucial feature of these algorithms that lends them to Fourier acceleration is that they update the lattice globally; hence the Fourier transforms are computed once per sweep rather than once per hit. (orig./HSI)

Coupled lattice Boltzmann method for numerical simulations of fully coupled heart and torso bidomain system in electrocardiology

OpenAIRE

Corre , Samuel; Belmiloudi , Aziz

2016-01-01

International audience; In this work, a modified coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro- to micro-scale transport processes. The propagation of electrical activity in the human heart through torso is mathematically modeled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity...

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

Science.gov (United States)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.