Displaying similar documents to “Growth of heterotrophe and autotrophe populations in an isolated terrestrial environment”

The Effect of Bacteria on Epidermal Wound Healing

E. Agyingi, S. Maggelakis, D. Ross (2010)

Mathematical Modelling of Natural Phenomena

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Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our...

Refined wing asymptotics for the Merton and Kou jump diffusion models

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.

A Discrete Model For Pattern Formation In Volatile Thin Films

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 ...

Tumour angiogenesis model with variable vessels' effectiveness

Jan Poleszczuk, Iwona Skrzypczak (2011)

Applicationes Mathematicae

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We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical...

Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation

R. Rudnicki, R. Wieczorek (2010)

Mathematical Modelling of Natural Phenomena

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We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and...