相关论文: Laminated Wave Turbulence: Generic Algorithms II
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
We propose an end-to-end quantum algorithm to simulate rapidly distorted turbulence via linear combination of Hamiltonian (LCHS). The algorithm comprises three primary stages: the efficient preparation of an initial turbulent state with a…
We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate $x$ and time $t$) Laplace transform of self-consistent plasma electric field $E(x,t) \to…
The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in…
This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion…
Theory of laminated turbulnece includes continuous layer of turbulence (statistical description, kinetic equations, Zakharov-Kolmogorov spectra, etc) AND discrete layer of turbulence (isolated groups of interacting waves, no…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received intense attention in recent years in the context of…
This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of…
A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger time steps, and a fine scale propagator which fully resolves…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…