Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres

We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions.

Iterative solution of a nonlinear static beam equation

UDC 519.6 The paper deals with a boundary-value problem for the nonlinear integro-differential equation modeling the static state of the Kirchhoff beam. The problem is reduced to a nonlinear integral equation, which is solved using the Picard iteration method. The convergence of the iteration process is established and the error estimate is obtained.

Delay-Differential-Equation Modeling of Mode-Locked Vertical-External-Cavity Surface-Emitting Lasers in Different Cavity Configurations.

A simple, versatile model for the dynamics of electrically and optically pumped vertical-external-cavity surface-emitting lasers, which are mode locked by a semiconductor saturable-absorber mirror, is presented. The difference between the laser operation in the linear and folded cavity, as well as the potential for a colliding pulse operation, are studied.