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Diego Garzón-Alvarado

Angélica Ramírez Martínez

Carlos Duque Daza

Abstract

In this paper we present severalnumerical tests on reaction-diffusionequations in the space of Turing,under the Schnakenberg reactionmechanism. The objectivge is toobtain the patterns of each coefficientof expansion in chaos polynomials.The tests were performed on 2D unitsquare, to which random initial conditionsand Neumann zero conditionson the boundary were imposed.Theparameters that define the behaviorof the equations, more specificallythe diffusion and reactive parameters,are modeled as stochastic fields.Thus,the standard method of finite elementwith Newton-Raphson was combinedwith the spectral stochastic finiteelement method. The parametersof each equation are described byKarhunen-Loève expansion, whilethe unknown is represented by theexpansion of the polynomials of chaos.The results show the versatility of themethod to solve different physicalproblems. Furthermore, it achievesstatistical description of the solution.The results for the unknown stochasticcoefficients, show complex patternsthat mix bands and points which cannot be predicted from the dynamicsof the system.

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Keywords

Stochastic finite elements, reactiondiffusion Turing patterns, Schnakenberg reaction mechanism

References
How to Cite
Garzón-Alvarado, D., Ramírez Martínez, A., & Duque Daza, C. (2012). On Turing Pattern Formation under Stochastic Considerations. Ingenieria Y Universidad, 16(2), 471. Retrieved from https://revistas.javeriana.edu.co/index.php/iyu/article/view/1295
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