On the Generalized Kinetic Equation for Surface Gravity Waves, Blow-Up and Its Restraint

This article is concerned with the non-linear interaction of homogeneous random ocean surface waves. Under this umbrella, numerous kinetic equations have been derived to study the evolution of the spectral action density, each employing slightly different assumptions. Using analytical and numerical tools, and providing exact formulas, we demonstrate that the recently derived generalized kinetic equation exhibits blow up in finite time for certain degenerate quartets of waves. This is discussed in light of the assumptions made in the derivation, and this equation is contrasted with other kinetic equations for the spectral action density.

Modelling the Impact of Squall on Wind Waves with the Generalized Kinetic Equation

This is a first study of short-lived transient sea states, arising from fast variations of wind fields. This study considers the response of a wind-wave field to a sharp increase of wind over a short time interval (a squall). Conventional wind-wave models based on the Hasselmann equation assume quasi stationarity of a random wave field and are a priori inapplicable for such transient states. To describe fast spectral changes, the authors use the generalized kinetic equation (GKE) derived without the quasi-stationarity assumption. A novel efficient highly parallelized algorithm for the numerical simulation of the GKE is presented. Simulations with the GKE and the Hasselmann equation are examined and compared. While under steady wind, the spectral evolution in both cases is shown to be practically identical, but after the squall the qualitative difference emerges: the GKE predicts formation of a transient sea state with a considerably narrower peak.

QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.

Solution of Generalized Jaynes-Cummings Model for many Particle Systems

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrodinger equation, respectively.

The generalized kinetic equation for symmetric particle systems

The generalized kinetic equation is obtained for symmetric system of many particles interacting via a pair potential. A representation of a solution of the Cauchy problem for the BBGKY hierarchy is used in the form of an expansion over particle groups whose evolution is governed by the cumulants (semi-invariants).