Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · patt-sol/9603003

Convective Fingering of an Autocatalytic Reaction Front

Michael R. Carey·Stephen W. Morris·Paul Kolodner
View original source ↗Read source document ↗Export metadata ↓

Abstract

We report experimental observations of the convection-driven fingering instability of an iodate-arsenous acid chemical reaction front. The front propagated upward in a vertical slab; the thickness of the slab was varied to control the degree of instability. We observed the onset and subsequent nonlinear evolution of the fingers, which were made visible by a {\it p}H indicator. We measured the spacing of the fingers during their initial stages and compared this to the wavelength of the fastest growing linear mode predicted by the stability analysis of Huang {\it et. al.} [{\it Phys. Rev. E}, {\bf 48}, 4378 (1993), and unpublished]. We find agreement with the thickness dependence predicted by the theory.

Explore related subjects

patt-solnlin.PS

Keep this discovery

BibTeXRIS

Michael R. Carey, Stephen W. Morris, Paul Kolodner. 1996-03-09. Convective Fingering of an Autocatalytic Reaction Front. https://doi.org/10.1103/physreve.53.6012

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

KEEP EXPLORING

Related papers

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↗
arXiv2000

Stability of Compacton Solutions of Fifth-Order Nonlinear Dispersive Equations

We consider fifth-order nonlinear dispersive $K(m,n,p)$ type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons - the compact solitary waves free of exponential tails. This interaction also generates many other solitary wave structures like cuspons, peakons, tipons etc. which are otherwise unattainable with linear dispersion. Various self similar solutions of these higher order nonlinear dispersive equations are also obtained using similarity transformations. Further, it is shown that, like the third-order nonlinear $K(m,n)$ equations, the fifth-order nonlinear dispersive equations also have the same four conserved quantities and further even any arbitrary odd order nonlinear dispersive $K(m,n,p...)$ type equations also have the same three (and most likely the four) conserved quantities. Finally, the stability of the compacton solutions for the fifth-order nonlinear dispersive equations are studied using linear stability analysis. From the results of the linear stability analysis it follows that, unlike solitons, all the allowed compacton solutions are stable, since the stability conditions are satisfied for arbitrary values of the nonlinear parameters.

patt-sol↗