Related papers: A mode parabolic equations method with the resonan…
Coherent resonance is the effect of resonant excitation of nonlinear coherent modes in trapped Bose condensates. This novel effect is shown to be feasible for Bose-condensed trapped gases. Conditions for realizing this effect are derived. A…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realm. As a result, a new dynamical constant for the electromagnetic field is identified and linked to the…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…
We report on experimental investigations of longitudinal collective oscillations in a highly elongated, harmonically trapped two-component Fermi gas with resonantly tuned s-wave interactions ('unitary Fermi gas'). We focus on higher-nodal…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest…
We investigate the asymptotic behavior of solutions for quasilinear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit e metastable…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
Absorption spectroscopy studies the absorption of electromagnetic wave in a material sample under test. The interacting electromagnetic wave can be propagating in free space or in a waveguide. The waveguide-based absorption spectroscopy…
In this work, we propose a coupled mode theory for resonant response from quasi-guided modes in periodic dielectric metasurfaces. First, we derived a generic set of constraints imposed onto the parameters of the temporal coupled mode theory…
We show how complex resonance poles and threshold energies for systems in hadron physics can be accurately obtained by using a method based on the Pad\'{e}-approximant which was recently developed for the calculation of resonance poles for…
In this work we examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…