<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1794-1237</journal-id>
<journal-title><![CDATA[Revista EIA]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.EIA.Esc.Ing.Antioq]]></abbrev-journal-title>
<issn>1794-1237</issn>
<publisher>
<publisher-name><![CDATA[Escuela de ingenieria de Antioquia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-12372012000100004</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[PATRONES DE TURING SOBRE ESFERAS CON CRECIMIENTO CONTINUO]]></article-title>
<article-title xml:lang="en"><![CDATA[TURING PATTERNS ON SPHERES WITH CONTINUOUS GROWTH]]></article-title>
<article-title xml:lang="pt"><![CDATA[PADRÕES DE TURING SOBRE ESFERAS COM CRESCIMENTO CONTÍNUO]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Garzón]]></surname>
<given-names><![CDATA[Diego A.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ramírez]]></surname>
<given-names><![CDATA[Angélica M.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Duque]]></surname>
<given-names><![CDATA[Carlos A.]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Ingeniería Mecánica y Mecatrónica Grupo de Modelado y Métodos Numéricos en Ingeniería (GNUM)]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Central de Colombia Departamento de Ingeniería Mecánica ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Ingeniería Mecánica y Mecatrónica Grupo de Modelado y Métodos Numéricos en Ingeniería (GNUM)]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2012</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2012</year>
</pub-date>
<numero>17</numero>
<fpage>39</fpage>
<lpage>46</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-12372012000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-12372012000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-12372012000100004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo se desarrollan varios ejemplos numéricos sobre ecuaciones de reacción-difusión con dominio creciente, empleando el modelo de reacción de Schnakenberg, con parámetros en el espacio de Turing. Por tanto, se realizan ensayos numéricos sobre la aparición de los patrones de Turing en superficies esféricas. Para la solución de las ecuaciones de reacción-difusión se presenta un método de solución en superficies en tres dimensiones mediante el método de los elementos finitos con el uso de la formulación lagrangiana total. Los resultados muestran que la formación de los patrones de Turing depende de la velocidad de crecimiento de la superficie, el tipo de número de onda predicho en la teoría de dominios cuadrados y su tiempo de estabilización. Estos resultados pueden esclarecer algunos fenómenos de cambio de patrón en la superficie de la piel de los animales que exhiben manchas características.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[We have developed several numerical examples of reaction-diffusion equations with growth surface domain. In this research we use the Schnakenberg reaction model, with parameters in the Turing space. Therefore, numerical tests are performed on the appearence of Turing patterns in spherical surfaces. For the solution of reaction diffusion equations provides a method of settling on surfaces in three dimensions using the finite element method under the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the growth rate of the surface, the type of wave number predicted in the theory of square domains and their stabilization time. These results may explain some phenomena of pattern change on the surface of the skin of animals that exhibit characteristic spots.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Neste artigo desenvolvem-se vários exemplos numéricos sobre equações de reação-difusão com domínio crescente, empregando o modelo de reação de Schnakenberg, com parâmetros no espaço de Turing. Por tanto, realizam-se ensaios numéricos sobre o aparecimento dos padrões de Turing em superfícies esféricas. Para a solução das equações de reação-difusão apresenta-se um método de solução em superfícies em três dimensões mediante o método dos elementos finitos baixo o uso da formulação lagrangiana total. Os resultados mostram que a formação dos padrões de Turing depende da velocidade de crescimento da superfície, o tipo de número de onda predito na teoria de domínios quadrados e seu tempo de estabilização. Estes resultados podem esclarecer alguns fenômenos de mudança de padrão na superfície da pele dos animais que exibem manchas características.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[reacción-difusión]]></kwd>
<kwd lng="es"><![CDATA[Turing]]></kwd>
<kwd lng="es"><![CDATA[lagrangiano total]]></kwd>
<kwd lng="es"><![CDATA[elementos finitos]]></kwd>
<kwd lng="es"><![CDATA[deformación de superficies]]></kwd>
<kwd lng="en"><![CDATA[reaction-diffusion]]></kwd>
<kwd lng="en"><![CDATA[Turing]]></kwd>
<kwd lng="en"><![CDATA[total Lagrangian]]></kwd>
<kwd lng="en"><![CDATA[finite elements]]></kwd>
<kwd lng="en"><![CDATA[deformation of surfaces]]></kwd>
<kwd lng="pt"><![CDATA[reação-difusão]]></kwd>
<kwd lng="pt"><![CDATA[Turing]]></kwd>
<kwd lng="pt"><![CDATA[lagrangiano total]]></kwd>
<kwd lng="pt"><![CDATA[elementos finitos]]></kwd>
<kwd lng="pt"><![CDATA[deformação de superfícies]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  ]]></body><back>
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