Abstract. In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently the exact solution for the Helmholtz equation can be computed numerically. The most important features of the new schemes are that while the resulting linear system has the same simple structure as tho...

A collision model, modified from the Smoluchowski model, is developed for simulating coagulation and growth of a large number of aerosol particles with significantly different sizes. In this collision model, the particle-size distribution is discretized in volume bins, and the total mass among all the bins is conserved. In situations with significantly different particle sizes, the present mode...

Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be ...

We present a detailed analysis of the fluctuation-dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium...

Abstract The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, dynamics is ubiquitous because thermal fluctuations. Fokker–Plank–Smoluchowski equation models time evolution probability density selected degrees freedom in diffusive regime it is, therefore, a workhorse chemistry. In this paper we report on development implementation variational quan...

We calculate the escape rates of different dynamical processes for the case of a one-dimensional symmetric double-well potential. In particular, we compare the escape rates of a Smoluchowski process, i.e., a corresponding overdamped Brownian motion dynamics in a metastable potential landscape, with the escape rates obtained for a biologically motivated model known as the Fisher-Eigen process. T...