We simulate scalar mixing and chemical reactions using the lattice Boltzmann method. Simulations of initially non-premixed binary mixtures yield scalar probability distribution functions that are in good agreement with direct numerical simulation (of NavierStokes equation) data. One-dimensional chemically-reacting ow simulation of a premixed mixture yields a ame speed that is consistent with ex...

We develop an integrated model for consumption and purchase decisions in the Rental-by-Mail (RBM) business model, which features closed loop delivery and quota-based subscription pricing. The model captures two distinct types of consumer dynamics: short-term dynamics in consumption decisions, and long-term dynamics in purchase decisions. Applying this model to a unique panel data provided by an...

The classical theory of transport processes is based on the Boltzmann transport equation. The equation can be derived simply by defining a distribution function and inspecting its time derivative. From this equation, many important results can be derived. In addition to some of the textbook results from the Boltzmann transport equation, it is still being used in many contemporary research proje...

Boltzmann machines are able to represent some probability distribution but the exact learning algorithm needs a time that is exponential in the number of neurons. The approximation method called Linear Response is not only applicable to machines with only second order interactions, but can be extended to Boltzmann machine with third and higher order interactions. It is shown that this can be us...

Abstract Damping on an object generally depends on its conformation (shape size etc.). We consider the Langevin dynamics of a model system with a conformation dependent damping and generalize the fluctuation dissipation relation to fit in such a situation. We derive equilibrium distribution function for such a case which converges to the standard Boltzmann form at the limit of uniform damping. ...

Understanding the Monte Carlo method as a versatile tool to solve integral equations enables its application to a class of problems which are not accessible by purely physically-based, imitative Monte Carlo methods. One such class is the linearized small signal analysis of nonlinear systems. In this work the small signal response of charge carriers in semiconductors is investigated, assuming se...

<p style='text-indent:20px;'>In this note, we propose a slightly different proof of Gallavotti's theorem ["Statistical Mechanics: A Short Treatise", Springer, 1999, pp. 48-55] on the derivation linear Boltzmann equation for Lorentz gas with Poisson distribution obstacles in Boltzmann-Grad limit.</p>

In the present study, commonly used weakly compressible lattice Boltzmann method and Guo incompressible lattice Boltzmann method have been used to simulate fluid flow in a stirred tank. For this purpose a 3D Parallel code has been developed in the framework of the lattice Boltzmann method. This program has been used for simulation of flow at different geometries such as 2D channel fluid flow an...