Exact solution for single-scale Gaussian random transport

Exact solution for single-scale Gaussian random transport.

A quadrature expression is derived for the probability density function of passive tracers advected from a point by a one-dimensional, single-scale, Gaussian velocity field. The effect of trapping on the tracer moments and the Lagrangian velocity variance is explicitly demonstrated.

Computing an Exact Gaussian Scale-Space

Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a di...

Autoregressive Gaussian Random Vectors of First Order

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes.

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell eq...