Recently, a minimal kinetic model for fluid flow, known as entropic lattice Boltzmann method, has been proposed for the simulation of isothermal hydrodynamic flows. At variance with previous Lattice Boltzmann methods, the entropic version permits to describe the non-linear dynamics of short scales in a controlled and stable way. In this paper, we provide the first numerical evidence that the en...

We introduce a method for the efficient design of a Boltzmann machine (or a Hopfield net) that computes an arbitrary given Boolean function f . This method is based on an efficient simulation of acyclic circuits with threshold gates by Boltzmann machines. As a consequence we can show that various concrete Boolean functions f that are relevant for classification problems can be computed by scala...

We introduce a method for the efficient design of a Boltzmann machine (or a Hopfield net) that computes an arbitrary given Boolean function f . This method is based on an efficient simulation of acyclic circuits with threshold gates by Boltzmann machines. As a consequence we can show that various concrete Boolean functions f that are relevant for classification problems can be computed by scala...

Xiaoyi He1,2,* and Li-Shi Luo Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Complex Systems Group T-13, MS-B213, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ICASE, MS 403, NASA Langley Research Center, 6 North Dryden Street, Building 1298, Hampton, Virginia 23681-0001 ~Received 29 April 1997; revised ma...

We introduce a method for the efficient design of a Boltzmann machine (or a Hopfield net) that computes an arbitrary given Boolean function / . TÈis method is based on an efficient simulation of acyclic circuits with threshold gates by Boltzmann machines. As a consequence u¡e can show that various concrete Boolean functions f tha| are relevant for classification problems can be computed by scal...

in English An introduction is given to the lattice Boltzmann method and its background, with a view towards acoustic applications of the method. To make a larger range of acoustic applications possible, a point source method is proposed. This point source is applied to simulate cylindrical waves and plane waves, and is shown to give a very good numerical result compared with analytic solutions ...

– The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lat...