Dependence of Turing pattern wavelength on diffusion rate

The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The di...

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Veröffentlicht in:	The Journal of chemical physics 1995-02, Vol.102 (6), p.2551-2555
Hauptverfasser:	Ouyang, Qi, Li, Rusheng, Li, Ge, Swinney, Harry L.
Format:	Artikel
Sprache:	eng
Schlagworte:	360606 > Other Materials-- Physical Properties-- (1992-) ALKALI METAL COMPOUNDS CARBOXYLIC ACIDS CHALCOGENIDES CHEMICAL REACTIONS CHLORIDES CHLORINE COMPOUNDS CHLORINE OXIDES COLLOIDS DENSITY DICARBOXYLIC ACIDS DIFFUSION DISPERSIONS GELS HALIDES HALOGEN COMPOUNDS INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY IODIDES IODINE COMPOUNDS MALONIC ACID MATERIALS SCIENCE ORGANIC ACIDS ORGANIC COMPOUNDS OXIDES OXYGEN COMPOUNDS PATTERN RECOGNITION PHYSICAL PROPERTIES SODIUM CHLORIDES SODIUM COMPOUNDS 400201 > Chemical & Physicochemical Properties STIRRING STOCHASTIC PROCESSES VARIATIONS WAVELENGTHS
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creator	Ouyang, Qi Li, Rusheng Li, Ge Swinney, Harry L.
description	The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The diffusion coefficient D of NaCl is found to vary from 0.5×10−5 to 1.8×10−5 cm2/s for the gel conditions considered. The CIMA reactants are assumed to have diffusion coefficients that are directly proportional to that of NaCl. The wavelength λ of the observed hexagonal patterns (0.13–0.28 mm) varies in accord with the predicted relation for Turing patterns, λ∼D1/2. Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.
doi_str_mv	10.1063/1.468684
format	Article
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The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The diffusion coefficient D of NaCl is found to vary from 0.5×10−5 to 1.8×10−5 cm2/s for the gel conditions considered. The CIMA reactants are assumed to have diffusion coefficients that are directly proportional to that of NaCl. The wavelength λ of the observed hexagonal patterns (0.13–0.28 mm) varies in accord with the predicted relation for Turing patterns, λ∼D1/2. Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.468684</identifier><language>eng</language><publisher>United States</publisher><subject>360606 -- Other Materials-- Physical Properties-- (1992-) ; ALKALI METAL COMPOUNDS ; CARBOXYLIC ACIDS ; CHALCOGENIDES ; CHEMICAL REACTIONS ; CHLORIDES ; CHLORINE COMPOUNDS ; CHLORINE OXIDES ; COLLOIDS ; DENSITY ; DICARBOXYLIC ACIDS ; DIFFUSION ; DISPERSIONS ; GELS ; HALIDES ; HALOGEN COMPOUNDS ; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ; IODIDES ; IODINE COMPOUNDS ; MALONIC ACID ; MATERIALS SCIENCE ; ORGANIC ACIDS ; ORGANIC COMPOUNDS ; OXIDES ; OXYGEN COMPOUNDS ; PATTERN RECOGNITION ; PHYSICAL PROPERTIES ; SODIUM CHLORIDES ; SODIUM COMPOUNDS 400201 -- Chemical & Physicochemical Properties ; STIRRING ; STOCHASTIC PROCESSES ; VARIATIONS ; WAVELENGTHS</subject><ispartof>The Journal of chemical physics, 1995-02, Vol.102 (6), p.2551-2555</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c320t-ada7378a608838dddb55ceebbdaf311d168ddb15f1dc2d996b3fecafb2956c083</citedby><cites>FETCH-LOGICAL-c320t-ada7378a608838dddb55ceebbdaf311d168ddb15f1dc2d996b3fecafb2956c083</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,778,782,883,27911,27912</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/6651011$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Ouyang, Qi</creatorcontrib><creatorcontrib>Li, Rusheng</creatorcontrib><creatorcontrib>Li, Ge</creatorcontrib><creatorcontrib>Swinney, Harry L.</creatorcontrib><title>Dependence of Turing pattern wavelength on diffusion rate</title><title>The Journal of chemical physics</title><description>The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. 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Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.</description><subject>360606 -- Other Materials-- Physical Properties-- (1992-)</subject><subject>ALKALI METAL COMPOUNDS</subject><subject>CARBOXYLIC ACIDS</subject><subject>CHALCOGENIDES</subject><subject>CHEMICAL REACTIONS</subject><subject>CHLORIDES</subject><subject>CHLORINE COMPOUNDS</subject><subject>CHLORINE OXIDES</subject><subject>COLLOIDS</subject><subject>DENSITY</subject><subject>DICARBOXYLIC ACIDS</subject><subject>DIFFUSION</subject><subject>DISPERSIONS</subject><subject>GELS</subject><subject>HALIDES</subject><subject>HALOGEN COMPOUNDS</subject><subject>INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY</subject><subject>IODIDES</subject><subject>IODINE COMPOUNDS</subject><subject>MALONIC ACID</subject><subject>MATERIALS SCIENCE</subject><subject>ORGANIC ACIDS</subject><subject>ORGANIC COMPOUNDS</subject><subject>OXIDES</subject><subject>OXYGEN COMPOUNDS</subject><subject>PATTERN RECOGNITION</subject><subject>PHYSICAL PROPERTIES</subject><subject>SODIUM CHLORIDES</subject><subject>SODIUM COMPOUNDS 400201 -- Chemical & Physicochemical Properties</subject><subject>STIRRING</subject><subject>STOCHASTIC PROCESSES</subject><subject>VARIATIONS</subject><subject>WAVELENGTHS</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNotkE1LxDAURYMoWEfBn1Bcuen4XtOmyVLGTxhwM65DmrzMVMa0JBnFf-9IXd3L5XAXh7FrhCWC4He4bIQUsjlhBYJUVScUnLICoMZKCRDn7CKlDwDArm4Kph5oouAoWCpHX24OcQjbcjI5Uwzlt_miPYVt3pVjKN3g_SENxxZNpkt25s0-0dV_Ltj70-Nm9VKt355fV_fryvIacmWc6XgnjQApuXTO9W1rifreGc8RHYrj2GPr0dnaKSV67ska39eqFRYkX7Cb-XdMedDJDpnszo4hkM1aiBYB8QjdzpCNY0qRvJ7i8Gnij0bQf1406tkL_wVCKFU-</recordid><startdate>19950208</startdate><enddate>19950208</enddate><creator>Ouyang, Qi</creator><creator>Li, Rusheng</creator><creator>Li, Ge</creator><creator>Swinney, Harry L.</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>19950208</creationdate><title>Dependence of Turing pattern wavelength on diffusion rate</title><author>Ouyang, Qi ; Li, Rusheng ; Li, Ge ; Swinney, Harry L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c320t-ada7378a608838dddb55ceebbdaf311d168ddb15f1dc2d996b3fecafb2956c083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>360606 -- Other Materials-- Physical Properties-- (1992-)</topic><topic>ALKALI METAL COMPOUNDS</topic><topic>CARBOXYLIC ACIDS</topic><topic>CHALCOGENIDES</topic><topic>CHEMICAL REACTIONS</topic><topic>CHLORIDES</topic><topic>CHLORINE COMPOUNDS</topic><topic>CHLORINE OXIDES</topic><topic>COLLOIDS</topic><topic>DENSITY</topic><topic>DICARBOXYLIC ACIDS</topic><topic>DIFFUSION</topic><topic>DISPERSIONS</topic><topic>GELS</topic><topic>HALIDES</topic><topic>HALOGEN COMPOUNDS</topic><topic>INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY</topic><topic>IODIDES</topic><topic>IODINE COMPOUNDS</topic><topic>MALONIC ACID</topic><topic>MATERIALS SCIENCE</topic><topic>ORGANIC ACIDS</topic><topic>ORGANIC COMPOUNDS</topic><topic>OXIDES</topic><topic>OXYGEN COMPOUNDS</topic><topic>PATTERN RECOGNITION</topic><topic>PHYSICAL PROPERTIES</topic><topic>SODIUM CHLORIDES</topic><topic>SODIUM COMPOUNDS 400201 -- Chemical & Physicochemical Properties</topic><topic>STIRRING</topic><topic>STOCHASTIC PROCESSES</topic><topic>VARIATIONS</topic><topic>WAVELENGTHS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ouyang, Qi</creatorcontrib><creatorcontrib>Li, Rusheng</creatorcontrib><creatorcontrib>Li, Ge</creatorcontrib><creatorcontrib>Swinney, Harry L.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ouyang, Qi</au><au>Li, Rusheng</au><au>Li, Ge</au><au>Swinney, Harry L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dependence of Turing pattern wavelength on diffusion rate</atitle><jtitle>The Journal of chemical physics</jtitle><date>1995-02-08</date><risdate>1995</risdate><volume>102</volume><issue>6</issue><spage>2551</spage><epage>2555</epage><pages>2551-2555</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><abstract>The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The diffusion coefficient D of NaCl is found to vary from 0.5×10−5 to 1.8×10−5 cm2/s for the gel conditions considered. The CIMA reactants are assumed to have diffusion coefficients that are directly proportional to that of NaCl. The wavelength λ of the observed hexagonal patterns (0.13–0.28 mm) varies in accord with the predicted relation for Turing patterns, λ∼D1/2. Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.</abstract><cop>United States</cop><doi>10.1063/1.468684</doi><tpages>5</tpages></addata></record>
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subjects	360606 -- Other Materials-- Physical Properties-- (1992-) ALKALI METAL COMPOUNDS CARBOXYLIC ACIDS CHALCOGENIDES CHEMICAL REACTIONS CHLORIDES CHLORINE COMPOUNDS CHLORINE OXIDES COLLOIDS DENSITY DICARBOXYLIC ACIDS DIFFUSION DISPERSIONS GELS HALIDES HALOGEN COMPOUNDS INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY IODIDES IODINE COMPOUNDS MALONIC ACID MATERIALS SCIENCE ORGANIC ACIDS ORGANIC COMPOUNDS OXIDES OXYGEN COMPOUNDS PATTERN RECOGNITION PHYSICAL PROPERTIES SODIUM CHLORIDES SODIUM COMPOUNDS 400201 -- Chemical & Physicochemical Properties STIRRING STOCHASTIC PROCESSES VARIATIONS WAVELENGTHS
title	Dependence of Turing pattern wavelength on diffusion rate
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