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Boundary behavior of a constrained brownian motion between reflecting-repellent walls

Lépingle D.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 2

273--287

Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and/or singular repellent drift. When the domain is a convex polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for nonhitting a face of the polyhedron is derived from the one-dimensional situation. A full answer to the question of attainability of the walls of the Weyl chamber may be given for a radial Dunkl process.

Model of Particle-Particle Interaction for Saltating Grains in Water

Czernuszenko W.

Archives of Hydro-Engineering and Environmental Mechanics

2009

Vol. 56, nr 3-4

101-120

A model of particle-particle interaction for bed sediment-laden flows, based on impulse equations, is presented. The model is applicable to dense flows in which particle motion is dominated by collisions. The model takes into account the possibility of sliding during the collision process. However, particle rotation is not considered in this model. The governing equations do not incorporate dimension of angular momentum. To verify this model, calculation of post-collision velocities was performed for several different collision simulations. The term of particle-particle interaction is implemented into a general Lagrangian model of trajectory of a sediment grain in a fluid flow. This general Lagrangian model is written according to Newton's second law; the rate of change of momentum of a particle is balanced against the surface and body forces.