Related papers: A mode parabolic equations method with the resonan…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
We present a bi-orthogonal approach for modeling the response of localized electromagnetic resonators using quasinormal modes, which represent the natural, dissipative eigenmodes of the system with complex frequencies. For many problems of…
We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise…
Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation…
The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
Reactive, semi-permeable interfaces play important roles in key biological processes such as targeted drug delivery, lipid metabolism, and signal transduction. These systems involve coupled surface reactions, transmembrane transport, and…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches its steady state in an asymptotically exponentially long…
Using a recently obtained (general) formula for the interaction energy between an excited and a ground-state atom (Sherkunov Y 2007 Phys. Rev. A 75 012705), we consider the interaction energy between two such atoms near the interface…
Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a…
The resonant formation of nonlinear coherent modes in trapped Bose-Einstein condensates is studied. These modes represent nonground-state Bose condensates. The methods of describing the spectrum of the nonlinear modes are discussed. The…
In this paper, we investigate a system of parabolic partial differential equations with unknown-dependent coefficients that integrates two models: an anisotropic orientation-adaptive denoising process in image processing and a phase-field…
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…
Many photonic devices, such as photonic crystal slabs, cross gratings, and periodic metasurfaces, are biperiodic structures with two independent periodic directions, and are sandwiched between two homogeneous media. Many applications of…
The effect on parametric instability growth of pump wave incoherence is treated by deriving a set of equations governing the space-time evolution of the ensemble-average coupled-mode amplitudes and intensities. Particular attention is paid…
We consider the asymptotic solutions to the Bethe ansatz equations of the integrable model of interacting bosons in the weakly interacting limit. In this limit we establish that the ground state maps to the highest energy state of a…
Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We place a special focus on interactions between slow wave…
We compute ionic free energy adsorption profiles at aqueous graphene interface by developing a self-consistent approach. To do so, we design a microscopic model for water and put the liquid on an equal footing with the graphene described by…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We…