Semiclassical Boltzmann transport has been the principal theory in the field of modeling and simulation of semiconductor technology since its early development. To date, most commer‐ cial device simulations including the full-band Monte Carlo (FBMC) method are based on the solution of the Boltzmann transport equation (BTE) and its simplified derivatives such as the hydrodynamic (HD) equations a...

IV Far-From-Equilibrium Transport 15 1 Mixed States and Distribution Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Irreversible Processes and Master Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1 The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Numerical Evaluation Methods . . . . . . . . . . . . ....

The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking c → ∞. In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic form and the Dulong-Petit law is recovered.

in this paper, two dimensional natural convection heat transfer in non-square cavities such as triangle, trapezoid, quadrant-circle and semi-circular are investigated via lattice boltzmann method. the prandtl number is taken as 0.71 that corresponds to that of air. the results show that, when the flow pattern consists of two rotating cell, there is a extremum point in the variations of the loca...

Stochastic neural networks for global optimization are usually built by introducing random uctuations into the network. A natural method is to use stochastic weights rather than stochastic activation functions. We propose a new model in which each neuron has very simple functionality but all the weights are stochastic. It is shown that the stationary distribution of the network uniquely exists ...

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where the force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition but might have instead a divergence-fre...

In this paper, we propose a population-based optimization algorithm, Sequential Monte Carlo Simulated Annealing (SMC-SA), for continuous global optimization. SMC-SA incorporates the sequential Monte Carlo method to track the converging sequence of Boltzmann distributions in simulated annealing. We prove an upper bound on the difference between the empirical distribution yielded by SMC-SA and th...

On contrary to the customary thought, the well-known " lemma " that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One of its consequences states that the velocity distribution at any point is a condensed " image " of all, complex and even dis-continuous, structures of the en...