We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations a...

In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the attracting equilibrium (or of another attrac...

The localization of electromagnetic waves in lossless inhomogeneous dielectric media is studied. We consider a three-dimensional lossless periodic medium (photonic crystal) having a gap in the frequency spectrum (photonic bandgap). If such a medium is perturbed by either a single defect or a random array of defects, exponentially localized electromagnetic waves arise with frequencies in the gap...

Erbium-doped fiber is a gain medium exhibiting homogeneous line broadening at room temperature, while a semiconductor optical amplifier has a dominant feature of inhomogeneous line broadening. In this work, a semiconductor optical amplifier is incorporated into the cavity of an erbium-doped fiber ring laser to form a hybrid gain medium. Theoretical analysis shows that such a gain medium support...

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diff...

We characterize the spatiotemporal evolution of a photosensitive Belousov-Zhabotinsky medium that is made up of coupled oscillatory cells with randomly distributed frequencies. The medium evolves from an initial state of multiple wave sources to a synchronized state governed by a single wave source. The synchronization occurs via a competition between the sources, which arises when the oscillat...

in this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. the timoshenko beam theory is applied instead of the classical euler-bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. t...

A three-dimensional (3-D) finite-difference timedomain (FDTD) algorithm is developed to study the transformation of an electromagnetic wave by a dynamic (time-varying) inhomogeneous magnetized plasma medium. The current density vector is positioned at the center of the Yee cube to accommodate the anisotropy of the plasma medium due to the presence of a static magnetic field. An appropriate time...

We investigate electromagnetic wave propagation in an inhomogeneous anisotropic medium. For the case of an orthotropic medium we derive the Lippmann-Schwinger equation, which is equivalent to a system of strongly singular integral equations. Uniqueness and existence of a solution is shown and we examine the regularity of the solution by means of integral equations. We prove the innnite Fr echet...

A regularized continuation method is developed for a two-dimensional inverse medium scattering problem in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy (PSTM) experiments. In addition to the ill-posedness of inverse scattering problems, two difficulties arise b...