相关论文: The Computational Complexity of the Lorentz Lattic…
We show that predicting the HPP or FHP III lattice gas for finite time is equivalent to calculating the output of an arbitrary Boolean circuit, and is therefore P-complete: that is, it is just as hard as any other problem solvable by a…
Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we…
We introduce a lattice Boltzmann computational scheme capable of modeling thermohydrodynamic flows of monatomic gases. The parallel nature of this approach provides a numerically efficient alternative to traditional methods of computational…
Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite…
We define a lattice model for rock, absorbers, and gas that makes it possible to examine the flow of gas to a complicated absorbing boundary over long periods of time. The motivation is to deduce the geometry of the boundary from the time…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a…
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…
We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions; these become increasingly…
The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
During the last two years the RealityGrid project has allowed us to be one of the few scientific groups involved in the development of computational grids. Since smoothly working production grids are not yet available, we have been able to…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
We consider Monte Carlo algorithms for the simulation of charged lattice gases with purely local dynamics. We study the mobility of particles as a function of temperature and show that the poor mobility of particles at low temperatures is…
A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of…
Lattice gauge theory's discretization of spacetime suffers from a drawback in that Lorentz covariance is lost because the axes of the lattice create preferred directions in spacetime. Smaller and smaller lattice spacings decrease the effect…
The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…