In this paper, the lattice Boltzmann method for convectiondiffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations o...

Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions for situations in which a "joiner particle" k pays some form of price to enter a community of size , where costs are subject to economies of scale. Maximizing the Boltzmann-Gibbs-Shann...

In this paper, a new econophysics model based on a lattice Boltzmann automata is presented. This model represents economic agents (people, countries...) as particles of a gas moving on a 2D lattice and interacting with each other. Economic transactions are modeled by particle-to-particle interactions in which money is conserved. If only particular transactions are considered (free market), the ...

Abstract The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete v...

Estimation of Distribution Algorithms (EDA) have been proposed as an extension of genetic algorithms. In this paper the major design issues of EDA’s are discussed using an interdisciplinary framework, the minimum relative entropy (MinRel) approximation. We assume that the function to be optimized is additively decomposed (ADF). The interaction graph GADF of the ADF is used to create exact or ap...

Sampling from a Boltzmann distribution is NP-hard and so requires heuristic approaches. Quantum annealing is one promising candidate. The failure of annealing dynamics to equilibrate on practical time scales is a well understood limitation, but does not always prevent a heuristically useful distribution from being generated. In this paper, we evaluate several methods for determining a useful op...

In this paper, we present the latest results on the measurement of the Boltzmann constant B k , by laser spectroscopy of ammonia at 10 μm. The Doppler absorption profile of a ro-vibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1m thermostat filled with an ice-water mixture, which sets th...

In two earlier papers, (1'2) referred to here as I and II, respectively, we showed how to calculate the drag force on a macroscopic sphere or cylinder moving through a dilute gas by using an extended Boltzmann equation. This equation differs from the usual Boltzmann equation in that it treats the effect of collisions between.gas molecules and the macroscopic object as a term in the Boltzmann eq...

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 ...

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique t...