Related papers: Determining modes for the surface Quasi-Geostrophi…
To accurately predict the consequences of nearshore waves, coastal engineers often employ numerical models. A variety of these models, broadly classified as either phase-resolving or phase-averaged, exist; each with strengths and…
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the wave speed and that the free surface lies everywhere above…
In this paper, we consider the Kakutani-Matsuuchi model which describes the surface elevation of the water-waves under the effect of viscosity. We show wave breaking for the Kakutani-Matsuuchi model, namely, the solution remains bounded but…
The quality factor (Q) links seismic wave energy dissipation to physical properties of the Earth's interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common…
Theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger…
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by…
Point vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the streamfunction. Special focus is given to the case of the surface…
The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding…
A supersymmetric gradient flow for four-dimensional N=1 supersymmetric QCD (SQCD) is proposed. The flow equation is given in both the superfield and component fields of the Wess-Zumino gauge. The superfield flow equation is defined for each…
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
We derive a simple algebraic form of the nonlinear wavenumber correction of surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an…
This paper presents a conforming finite element semi-discretization of the streamfunction form of the one-layer unsteady quasi-geostrophic equations, which are a commonly used model for large-scale wind-driven ocean circulation. We derive…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
The resolvent formulation of the Navier$\text{--}$Stokes equations gives a means for the characterization and prediction of features of turbulent flows$\text{---}$such as statistics, structures and their nonlinear…
The momentum formulation of the surface quasi-geostrophic equations consists of two nonlinear terms, besides the pressure term, one of which cannot be written in a divergence form. When the anti-divergence operator is applied to such…
We prove that solutions to the quintic semilinear wave equation with variable coefficients in $\mathbb R^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to\infty$, but are…