Scaling laws and the prediction of bifurcations in systems modeling pattern formation

Clint Scovel; Ioannis G. Kevrekids; Basil Nicolaenko

doi:10.1016/0375-9601(88)90242-3

Scaling laws and the prediction of bifurcations in systems modeling pattern formation

Clint Scovel
, Ioannis G. Kevrekids
, Basil Nicolaenko

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.

Original language	English (US)
Pages (from-to)	73-80
Number of pages	8
Journal	Physics Letters A
Volume	130
Issue number	2
DOIs	https://doi.org/10.1016/0375-9601(88)90242-3
State	Published - Jun 27 1988

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1016/0375-9601(88)90242-3

Cite this

@article{133085d5d01446dd87b439564e78b679,

title = "Scaling laws and the prediction of bifurcations in systems modeling pattern formation",

abstract = "When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.",

author = "Clint Scovel and Kevrekids, \{Ioannis G.\} and Basil Nicolaenko",

note = "Funding Information: We are happy to acknowledget hat this-work was prompted by Professor Chris Eilbeck{\textquoteright}s comment during a CNLS seminar that “there has to be some way of predicting when the unimodal branch hits the bimodal branch”. A discussion of Michael Weinstein with one of us (IGK) was also helpful in clearing up some of the proofs. We also thank Mr. Harry S. Brown for his computational assistancei n the preparation of fig. 1. This work was supported in part by NSF Grants no. CBT-8707090 and EET-87 17787t o I.G. Kevrekidis. We acknowledget he support of the U.S. Department of Energy through the hospitality of the Center for Nonlinear Studies at Los Alamos. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",

year = "1988",

month = jun,

day = "27",

doi = "10.1016/0375-9601(88)90242-3",

language = "English (US)",

volume = "130",

pages = "73--80",

journal = "Physics Letters A",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Scaling laws and the prediction of bifurcations in systems modeling pattern formation

AU - Scovel, Clint

AU - Kevrekids, Ioannis G.

AU - Nicolaenko, Basil

N1 - Funding Information: We are happy to acknowledget hat this-work was prompted by Professor Chris Eilbeck’s comment during a CNLS seminar that “there has to be some way of predicting when the unimodal branch hits the bimodal branch”. A discussion of Michael Weinstein with one of us (IGK) was also helpful in clearing up some of the proofs. We also thank Mr. Harry S. Brown for his computational assistancei n the preparation of fig. 1. This work was supported in part by NSF Grants no. CBT-8707090 and EET-87 17787t o I.G. Kevrekidis. We acknowledget he support of the U.S. Department of Energy through the hospitality of the Center for Nonlinear Studies at Los Alamos. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1988/6/27

Y1 - 1988/6/27

N2 - When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.

AB - When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.

UR - https://www.scopus.com/pages/publications/0007430071

UR - https://www.scopus.com/pages/publications/0007430071#tab=citedBy

U2 - 10.1016/0375-9601(88)90242-3

DO - 10.1016/0375-9601(88)90242-3

M3 - Article

AN - SCOPUS:0007430071

SN - 0375-9601

VL - 130

SP - 73

EP - 80

JO - Physics Letters A

JF - Physics Letters A

IS - 2

ER -

Scaling laws and the prediction of bifurcations in systems modeling pattern formation

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this