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Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in powers of the small parameter characterizing the thinness of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder. The solutions obtained describe trapped modes corresponding to discrete eigenvalues of the problem (lying close to the cut-off frequency of the continuous spectrum) and resonances lying close to the embedded cut-off. We present certain conditions for the submergence of the cylinder in the upper layer when these resonances convert into previously unobserved embedded trapped modes.
The properties of the natural modes in a dispersive stratified N-layer medium are investigated. The focus is on the (over)completeness properties of these modes. Also the distribution of the natural frequencies is considered. Both the degree of (over
In a particle physics dynamics, we assume a uniform distribution as the physical measure and a measure-theoretic definition of entropy on the velocity configuration space. This distribution is labeled as the physical solution in the remainder of the
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting from the di
We use a logarithmic Lieb-Thirring inequality for two-dimensional Schroedinger operators and establish estimates on trapped modes in geometrically deformed quantum layers.
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering problem is uni