Information denoising and quantization by diffusion reaction model.
Belahmidi, Abdelmounim (2006)
APPS. Applied Sciences
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Belahmidi, Abdelmounim (2006)
APPS. Applied Sciences
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Stefan Gerhold, Johannes F. Morgenbesser, Axel Zrunek (2015)
Banach Center Publications
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Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features an interesting "almost power law" tail.
M. Malik-Garbi, O. Agam (2012)
Mathematical Modelling of Natural Phenomena
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We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a discrete analog of the continuous dynamics of evaporation of thin liquid films. Within mean field approximation the dynamics of this model, averaged over many realizations of the growing cluster, reduces to that of the idealized evaporation model in which surface tension is neglected. However fluctuations beyond the mean field level play an important ...
Piotr Paweł Szopa, Monika Joanna Piotrowska (2011)
Applicationes Mathematicae
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We consider the model, proposed by Dawidowicz and Zalasiński, describing the interactions between the heterotrophic and autotrophic organisms coexisting in a terrestrial environment with available oxygen. We modify this model by assuming intraspecific competition between heterotrophic organisms. Moreover, we introduce a diffusion of both types of organisms and oxygen. The basic properties of the extended model are examined and illustrated by numerical simulations.
Rybář, Vojtěch, Vejchodský, Tomáš
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In this contribution we add a unilateral term to the Thomas model and investigate the resulting Turing patterns. We show that the unilateral term yields nonsymmetric and irregular patterns. This contrasts with the approximately symmetric and regular patterns of the classical Thomas model. In addition, the unilateral term yields Turing patterns even for smaller ratio of diffusion constants. These conclusions accord with the recent findings about the influence of the unilateral term in...
Diewald, U., Preusser, T., Rumpf, M., Strzodka, R. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Tomán, Henrietta, Tornai, Róbert, Zichar, Marianna (2007)
Annales Mathematicae et Informaticae
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Y. Schmitz, M. Baurmann, B. Engelen, U. Feudel (2010)
Mathematical Modelling of Natural Phenomena
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We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature....
J. Zhu, Y.-T. Zhang, S. A. Newman, M. S. Alber (2009)
Mathematical Modelling of Natural Phenomena
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Skeletal patterning in the vertebrate limb, i.e., the spatiotemporal regulation of cartilage differentiation (chondrogenesis) during embryogenesis and regeneration, is one of the best studied examples of a multicellular developmental process. Recently [Alber et al., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation reaction-diffusion system was developed to describe...