相关论文: Rayleigh-type Surface Quasimodes in General Linear…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
We present a three-dimensional model describing the propagation of elastic waves in a soil substrate supporting an array of cylindrical beams experiencing flexural and compressional resonances. The resulting surface waves are of two types.…
Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-B\'enard…
In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume…
We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the…
We extend the semilinear framework developed by the two authors and the non-trapping quasilinear theory developed by the first author to solve quasilinear wave equations with normally hyperbolic trapping. The most well-known example that…
Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of the magnetic moments. The quasiclassical framework is useful because it…
Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated solitary-wave solutions to the steady gravity-capillary Whitham…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for…
Additional electromagnetic waves and additional boundary conditions (ABCs) in non-local materials attracted a lot of attention in the past. Here we report the possibility of additional propagating and evanescent waves in local anisotropic…
Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow,…
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…
Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
We construct a local matched-asymptotic description of time-harmonic elastic fields generated by Rayleigh waves near cuspidal elements of a traction-free surface. The free surface is represented locally by a cusp graph with exponent…
The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply the nonlinear generalized Rayleigh quotient method.
Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale…