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Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

R. Kerner (2011)

Mathematical Modelling of Natural Phenomena

An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the...

Self-similarity in chemotaxis systems

Yūki Naito, Takashi Suzuki (2008)

Colloquium Mathematicae

We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.

Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill, K. M. Shaw, B. L. Rountree, C. E. Kehl, H. J. Chiel (2011)

Mathematical Modelling of Natural Phenomena

We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...

Simulation of electrophysiological waves with an unstructured finite element method

Yves Bourgault, Marc Ethier, Victor G. LeBlanc (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.

Simulation of Electrophysiological Waves with an Unstructured Finite Element Method

Yves Bourgault, Marc Ethier, Victor G. LeBlanc (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.

Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology

J. B. Burie, A. Calonnec, A. Ducrot (2010)

Mathematical Modelling of Natural Phenomena

We investigate the structure of travelling waves for a model of a fungal disease propagating over a vineyard. This model is based on a set of ODEs of the SIR-type coupled with two reaction-diffusion equations describing the dispersal of the spores produced by the fungus inside and over the vineyard. An estimate of the biological parameters in the model suggests to use a singular perturbation analysis. It allows us to compute the speed and the profile of the travelling waves. The analytical results...

Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin (2009)

Mathematical Modelling of Natural Phenomena

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

Skupinový screening

Christian Genest, Christiane Rousseau (2021)

Pokroky matematiky, fyziky a astronomie

Skupinový screening je nezbytnou součástí boje proti šíření koronaviru. Jak ale čelit možnému nedostatku činidel a materiálu? Tím, že budeme provádět testy na bázi promíchání vzorků a využijeme přitom matematiku.

Small amplitude homogenization applied to models of non-periodic fibrous materials

David Manceau (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.

Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks

Yang Liu, Jianquan Lu, Bo Wu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability via two kinds of inputs are obtained by providing...

Some Parameter Estimation Issues in Functional-Structural Plant Modelling

P.-H. Cournède, V. Letort, A. Mathieu, M. Z. Kang, S. Lemaire, S. Trevezas, F. Houllier, P. de Reffye (2011)

Mathematical Modelling of Natural Phenomena

The development of functional-structural plant models has opened interesting perspectives for a better understanding of plant growth as well as for potential applications in breeding or decision aid in farm management. Parameterization of such models is however a difficult issue due to the complexity of the involved biological processes and the interactions between these processes. The estimation of parameters from experimental data by inverse methods...

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