Related papers: Wave Computation on the Hyperbolic Double Doughnut
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
We use the time real analyticity of Ricci flow proved by Kotschwar to extend a result in ~\cite{B}, namely, we prove that the Laplace spectra of negatively curved compact surfaces having same genus $\gamma \geq 2$, same area and same…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
- In this article, we prove some universal bounds on the speed of concentration on small (frequency-dependent) neighborhoods of submanifolds of L 2-norms of quasi modes for Laplace operators on compact manifolds. We deduce new results on…
We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…
In this article we study the differences of two consecutive eigenvalues $\lambda_{i}-\lambda_{i-1}$ up to $i=2g-2$ for the Laplacian on hyperbolic surfaces of genus $g$, and show that the supremum of such spectral gaps over the moduli space…
We present two methods for computing dimensionally-regulated NRQCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless…
In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green…
We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use…
We consider Laplacians on $\Z^2$-periodic discrete graphs. The following results are obtained: 1) The Floquet-Bloch decomposition is constructed and basic properties are derived. 2) The estimates of the Lebesgue measure of the spectrum in…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
We calculate frequencies of collective oscillations of two-component Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in-, and…
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements…
A method to find optimal 2nd-order perturbations is presented, and applied to find the optimal spanwise-wavy surface for suppression of cylinder wake instability. Second-order perturbations are required to capture the stabilizing effect of…