A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...

Let Ñt be a standard compensated Poisson process on [0, 1]. We prove a new characterization of anticipating integrals of the Skorohod type with respect to Ñ , and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show that, if the integrand is sufficiently regular, anticipating Skorohod integral processes with respect t...

Enforcing fluid incompressibility is one of the time-consuming aspects in SPH. In this paper, we present a local Poisson SPH (LPSPH) method to solve incompressibility for particle based fluid simulation. Considering the pressure Poisson equation, we first convert it into an integral form, and then apply a discretization to convert the continuous integral equation to a discretized summation over...

We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tail...

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...

We use the functional integral technique of Edwards and Lenard [1] to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a soap film. Finite size effects and the phenomenon of charge regulation are studied. We also discuss the pressure of disjunction for such a film. Even in ...

In this paper, we establish new Poisson type inequalities with respect to a cone. As applications, the integral representations of harmonic functions are also obtained.

Since particle such as molecule, atom and nucleus are composite particle, it is important to recognize that physics must be invariant for both the composite particle and its constituent particles, this requirement is called particle invariance. But difficulties arise immediately because for fermion we use the Dirac equation, for boson we use the Klein-Gordon equation. Therefore, the particle in...

A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinitedimensional analogue of the Berezin inte...

This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...