For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis...

We present an exact method for speeding up random walk in two-dimensional complicated lattice environments. To this end, we derive the discrete two-dimensional probability distribution function for a diffusing particle starting at the center of a square of linear size s. This is used to propagate random walkers from the center of the square to sites which are nearest neighbors to its perimeter ...

The variable ordering of constraint satisfaction problems affect the performance of search algorithms in CSPs. Dynamic Variable Ordering (DVO) has more advantage in improving the performance of search algorithms than static variable ordering. It is a newly developed method recent years that using particle swarm algorithm to solve binary constraint satisfaction problems, which is a global stocha...

The expansion behavior and structural phenomena of fluid-particle systems was simulated using a method analogous to the Monte Carlo method for molecular systems. Individual particles are moved, and the resulting moves are accepted or declined based on the change in the system’s potential energy and the average kinetic energy of the system. Several fluid particle systems have been successfully p...

A number of random processes in various fields of science is described by phenomenological equations of motion containing stochastic forces, the best known example being the Langevin equation (LE) for the Brownian motion (BM) of particles. Long ago Vladimirsky (1942) in a little known paper proposed a simple method for solving such equations. The method, based on the classical Gibbs statistics,...

A Monte Carlo technique is described for simulating the high-speed flow of a rarefied gas around a cylindrical body. The method uses a hard-sphere model, or, alternatively, the "Maxwellian" model to compute collisions between particles. A representative "test particle" is scattered in such a way that its statistical behavior approximates that of a random particle chosen from the actual gas. Thi...

The moment method is an image analysis technique for subpixel estimation of particle positions. The total error in the calculated particle position includes effects of pixel locking and random noise in each pixel. Pixel locking, also known as peak locking, is an artifact where calculated particle positions are concentrated at certain locations relative to pixel edges. We report simulations to g...

Many of the computer vision algorithms have been posed in various forms of differential equations, derived from minimization of specific energy functionals, and the finite element representation and computation have become the de facto numerical strategies for solving these problems. However, for cases where domain mappings between numerical iterations or image frames involve large geometrical ...