We investigate the effects mode truncation and dissipation characteristics have on predictions of wave shape statistics such as skewness and asymmetry. We demonstrate the effect of mode truncation by calculating wave shape statistics for data from a laboratory experiment using an increasing number of frequency components each calculation. We find that the values of skewness and asymmetry conver...

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal d...

A multiple linear process with random coefficients is investigated in the paper. Conditions for existence of such process are derived and its covariance function as well as the matrix of spectral densities are calculated. The results are applied to multiple AR(1) process with random coefficients, where the matrices of coefficients can be described by a stationary process. In this case condition...

Intermediate-depth, Boussinesq-type modelling is used to generalize previously known results for surface water waves propagating over arbitrarily shaped topographies. The improved reduced wave model is obtained after studying how small changes in the linear dispersion relation (over a flat bottom) can become dramatically important in the presence of a highly fluctuating topography. Numerical va...

We ask several questions on the structure of the polytope of doubly stochastic n n matrices Pn, known as a Birkhoo polytope. We discuss the volume of Pn, the work of the simplex method, and the mixing of random walks Pn.

Mathematics Subject Classification (2000): 53C25, 53C40, 53C42.

A class of discrete-time M=G=1 queues, including both round robin and last come rst served service, in which customers are subject to permutations is considered. These time slotted queues, analogous to the symmetric queues of Kelly, are analyzed by examination of the time reversed process. Product form stationary distributions are found for a type of doubly stochastic server of Schassberger [5]...

We claim that both of these walks have the same mixing time. This fact is in fact true for any Markov chain on groups. In this case note that we are considering a Markov chain on the symmetric group Sn. In general consider any group G and suppose we have a set of generators {g1, . . . , gk}. In each time step we choose a generator from this set according to a probability distribution μ and we a...