7 citations · 19 across the 7 of their papers we have counts for
7 papers
Coupling of paraxial and white-noise approximations of the Helmholtz equation in randomly layered media
Austin McDaniel, Alex Mahalov
We study the simultaneous paraxial and white-noise limit of the Helmholtz equation in randomly layered media where the refractive index fluctuations are in the direction of propaga…
Stochastic differential equation model for spontaneous emission and carrier noise in semiconductor lasers
Austin McDaniel, Alex Mahalov
We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of no…
Time-averages of Fast Oscillatory Systems in Three-dimensional Geophysical Fluid Dynamics and Electromagnetic Effects
Bin Cheng, Alex Mahalov
Time-averages are common observables in analysis of experimental data and numerical simulations of physical systems. We will investigate, from the angle of partial differential equ…
On the Problem of Electromagnetic-Field Quantization
Christian Krattenthaler, Sergey I. Kryuchkov, Alex Mahalov +1
We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional…
Wave Packets and Coherent Structures for Nonlinear Schroedinger equations in Variable Nonuniform Media
Alex Mahalov, Sergei K. Suslov
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum ca…
Euler equations on a fast rotating sphere --- time-averages and zonal flows
Bin Cheng, Alex Mahalov
Motivated by recent studies in geophysical and planetary sciences, we investigate the PDE-analytical aspects of time-averages for barotropic, inviscid flows on a fast rotating sphe…
Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains
François Golse, Alex Mahalov, Basil Nicolaenko
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating l…