Claude Greengard

On Vortex Methods

We give error estimates for fully discretized two- and three-dimensional vortex methods and introduce a new wy of evaluating the stretching of vorticity in three-dimensional vortex methods. The convergence theory of Beale and Majda is discussed and a simple proof of Cottet’s consistency result is presented. We also describe how to obtain accurate two-dimensional vortex methods in which the initial computational points are distributed on the nodes of nonrectangular grids, and compare several three-dimensional vortex methods.

The diffusion limit of free molecular flow in thin plane channels

The subject of this paper is free molecular flow in thin channels bounded by parallel plane surfaces on which Maxwell’s boundary condition applies. With tools from probability theory, it is proved that in the limit as the domain width h tends to zero, the evolution of the density is described by a diffusion equation, on a timescale of

On the accurate calculation of vortex shedding

1/(h\log h^{-1} )

Conservation of expected momentum and energy in Monte Carlo particle simulation

, and with a diffusion coefficient of

Singular vortex systems and weak solutions of the Euler equations

(2 - \alpha )\sqrt T /(2\alpha \sqrt \pi )

Operator Splitting for Navier-Stokes and Chorin-Marsden Product Formula

(

Slow convergence in generalized central limit theorems

\alpha

System for protection of goods against counterfeiting

is the accommodation coefficient and T is the surface temperature). The logarithmic factor in the timescale is geometry dependent; in thin cylinders of diameter h, the timescale is

Event-recorder for transmitting and storing electronic signature data

1/h

Method and apparatus for securely determining aspects of the history of a good

, as Babovsky has proved in [Journal of Statistical Physics, 44 (1986), pp. 865–878]. Numerical calculations indicate that the diffusion limit is closely approximated even at fairly large values of h.