Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · patt-sol/9805007

Phase instabilities in hexagonal patterns

B. Echebarria·C. Perez-Garcia
View original source ↗Read source document ↗Export metadata ↓

Abstract

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and the contributions of the new spatial terms are analysed in this paper. From these coefficients the phase stability regions in a hexagonal pattern are determined. In the case of Benard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.

Explore related subjects

patt-solnlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

B. Echebarria, C. Perez-Garcia. 1998-05-26. Phase instabilities in hexagonal patterns. https://doi.org/10.1209/epl%2Fi1998-00315-2

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

KEEP EXPLORING

Related papers

arXiv2014

Laplacian Growth I: Finger Competition and Formation of a Single Saffman-Taylor Finger without Surface Tension: An Exact Result

We study the exact non-singular zero-surface tension solutions of the Saffman-Taylor problem for all times. We show that all moving logarithmic singularities a_k(t) in the complex plane ω= e^{iϕ}, where ϕis the stream function, are repelled from the origin, attracted to the unit circle and eventually coalesce. This pole evolution describes essentially all the dynamical features of viscous fingering in the Hele-Shaw cell observed by Saffman and Taylor [Proc. R. Soc. A 245, 312 (1958)], namely tip-splitting, multi-finger competition, inverse cascade, and subsequent formation of a single Saffman-Taylor finger.

patt-sol↗
arXiv2004

Spatio-temporal dynamics of coupled array of Murali-Lakshmanan-Chua circuits

The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one of the simplest non-autonomous nonlinear electronic circuits which shows a variety of dynamical phenomena including various bifurcations, chaos and so on. In this paper we study the spatio-temporal dynamics in one and two dimensional arrays of coupled MLC circuits both in the absence as well as in the presence of external periodic force. In the absence of any external force, the propagation phenomena of travelling wave front and its failure have been observed from numerical simulations....

patt-sol↗
arXiv2000

Pulse Shepherding and Multi-Channel Soliton Transmission in Bit-Parallel-Wavelength Optical Fiber Links

We study bit-parallel-wavelength (BPW) pulse transmission in multi-channel single-mode optical fiber links for high-performance computer networks. We develop a theory of the pulse shepherding effect earlier discovered in numerical simulations, and also describe the families of the BPW solitons and bifurcation cascades in a system of N coupled nonlinear Schrödinger equations.

patt-sol↗