Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. A well-known numerical method for the initialization of Boltzmann models is the Constrained Runs algorithm. This algorithm is used in literature for the initializ...

This note describes a selection procedure for genetic algorithms called Boltzmann tournament selection. As simulated annealing evolves a Boltzmann distribution in time using the Metropolis algorithm or a logistic acceptance mechanism, Boltzmann tournament selection evolves a Boltzmann distribution across a population and time using pairwise probabilistic acceptance and anti-acceptance mechanism...

In this paper, the lattice vehicular model, which is in the form the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. A 3-bit approximation, which describe uncongested traffic flow, for the discretization of the Boltzmann equation in both time and phase space is di...

We show that the Boltzmann factor has a geometrical origin. Its derivation follows from the microcanonical picture. The Maxwell-Boltzmann distribution or the wealth distribution in human society are some direct applications of this new interpretation.

Abstract The Boltzmann distribution family describes a single parameter (temperature) class of probability distributions over state space; at any given temperature, the ratio probabilities two states depends exponentially on their difference in energy. Beyond physics, this is very popular many important disciplines, under different names with interpretations. Such widespread use diverse fields ...

Generalized evolutionary algorithm based on Tsallis canonical distribution is proposed. The algorithm uses Tsallis generalized canonical distribution to weigh the configurations for ‘selection’ instead of Gibbs-Boltzmann distribution. Our simulation results show that for an appropriate choice of non-extensive index that is offered by Tsallis statistics, evolutionary algorithms based on this gen...

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suita...

The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its conceptual support: the continuous Boltzmann equation (BE). Most collision models are based on the BGK, single parameter, relaxation-term leading to constan...

This paper presents a new distribution, the product of mixture between Maxwell-Boltzmann and particular case generalized gamma distributions. The resulting called Scale Mixture Maxwell-Boltzmann, greater kurtosis than recently introduced slash distribution. We obtained closed-form expressions for its probability density cumulative distribution functions. studied some properties moments, as well...

The original publication of the article Catanzaro et al. (2017) contained following minor errors which we take this opportunity to correct.