Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math-ph/0609020

Laminated Wave Turbulence: Generic Algorithms I

E. Kartashova·A. Kartashov
View original source ↗Read source document ↗Export metadata ↓

Also available from

Abstract

The model of laminated wave turbulence presented recently unites both types of turbulent wave systems - statistical wave turbulence (introduced by Kolmogorov and brought to the present form by numerous works of Zakharov and his scientific school since nineteen sixties) and discrete wave turbulence (developed in the works of Kartashova in nineteen nineties). The main new feature described by this model is the following: discrete effects do appear not only in the long-wave part of the spectral domain (corresponding to small wave numbers) but all through the spectra thus putting forth a novel problem - construction of fast algorithms for computations in integers of order $10^{12}$ and more. In this paper we present a generic algorithm for polynomial dispersion functions and illustrate it by application to gravity and planetary waves.

Explore related subjects

math-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E. Kartashova, A. Kartashov. 2006-09-07. Laminated Wave Turbulence: Generic Algorithms I. https://doi.org/10.1142/s0129183106010042

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Functorial Theory of Defects in Abelian Chern-Simons Theory

Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.

math-ph↗
arXiv2026

Gradient nature of Laplacian growth

For a class of growth processes of Laplacian type in the plane, we suggest an interpretation as a ``gradient descent'' in the space of smooth closed curves. More precisely, we show that boundary of a growing domain moves along a gradient of a certain functional in the space of curves. In the simplest cases this functional is $\log (1/r)$, where $r$ is the external conformal radius of the growing domain.

math-ph↗
arXiv2026

Entanglement-Inducing Quantum Markov Processes

We introduce a new model for a system of interacting bosons placed in an array of sites. At its core is a nonlinear, nonlocal evolution equation, which we have dubbed the Schrödinger-Dirichlet equation. The construction is closely related to the Bose-Hubbard model and to a specific type of generalized bosons. In contrast to conventional mean-field closures, the resulting nonlinear dynamics need not preserve product structure and can generate entanglement from initially separable states. The relevant methods of analysis are based on harmonic analysis for the multiplicative group of positive rationals.

math-ph↗