We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the ‘cavity’ prediction for the limiting free energy per spin is correct for any temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) ...

We describe a method for numerically incorporating electron–electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature T and density n, a symmetric matrix needs to be evaluated only once, and henceforth it can be used to describe electron–electron scattering in any Boltzmann equ...

We study the Wouthuysen-Field coupling at early universe with numerical solutions of the integrodifferential equation describing the kinetics of photons undergoing resonant scattering. The numerical solver is developed based on the weighted essentially non-oscillatory (WENO) scheme for the Boltzmann-like integrodifferential equation. This method has perfectly passed the tests of analytic soluti...

In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic models. Then we consider ...

In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method,...

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative Boltzmann Distribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is mad...

Spectroscopic diagnostic technique are applied for the determination of excitation temperature Texc and electron density in Air Acetylene premixed laminar flame. A group of FeI spectral lines has been used to estimate Texc using Boltzmann plot. Electron number density was determined from atom ion line pairs for Cd and Zn using Saha Boltzmann equation after substitution the obtained value of exc...

We use Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasistationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the central limit theorem implies the Boltzmann expression in Gibbs' Gamma space. We identify the nonequilibrium submanifold of Gamma space charac...