All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 107

Showing per page

Microscale Complexity in the Ocean: Turbulence, Intermittency and Plankton Life

L. Seuront (2008)

Mathematical Modelling of Natural Phenomena

This contribution reviews the nonlinear stochastic properties of turbulent velocity and passive scalar intermittent fluctuations in Eulerian and Lagrangian turbulence. These properties are illustrated with original data sets of (i) velocity fluctuations collected in the field and in the laboratory, and (ii) temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass, i.e. unicelled vegetals passively advected by turbulence) sampled from highly turbulent coastal waters. The strength...

Microscopic Modelling of Active Bacterial Suspensions

A. Decoene, S. Martin, B. Maury (2011)

Mathematical Modelling of Natural Phenomena

We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly...

Modelling Circadian Rhythms in Drosophila and Investigation of VRI and PDP1 Feedback Loops Using a New Mathematical Model

D. Kulasiri, Z. Xie (2008)

Mathematical Modelling of Natural Phenomena

We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new model that incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are probabilistically...

Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

J. Clairambault (2009)

Mathematical Modelling of Natural Phenomena

This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the...

Multiphase and Multiscale Trends in Cancer Modelling

L. Preziosi, A. Tosin (2009)

Mathematical Modelling of Natural Phenomena

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.

Multi-scale Modelling for Threshold Dependent Differentiation

A. Q. Cai, Y. Peng, J. Wells, X. Dai, Q. Nie (2009)

Mathematical Modelling of Natural Phenomena

The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc,...

Necessary Optimality Conditions for a Lotka-Volterra Three Species System

N. C. Apreutesei (2010)

Mathematical Modelling of Natural Phenomena

An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.

Observers for Canonic Models of Neural Oscillators

D. Fairhurst, I. Tyukin, H. Nijmeijer, C. van Leeuwen (2010)

Mathematical Modelling of Natural Phenomena

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar...

On the Dynamics of a Two-Strain Influenza Model with Isolation

F. Chamchod, N.F. Britton (2012)

Mathematical Modelling of Natural Phenomena

Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...

On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion

J.A. Sherratt (2010)

Mathematical Modelling of Natural Phenomena

Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...

On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles

R. Dilão, A. Lakmeche (2010)

Mathematical Modelling of Natural Phenomena

We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...

Optimal Poiseuille flow in a finite elastic dyadic tree

Benjamin Mauroy, Nicolas Meunier (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we construct a model to describe some aspects of the deformation of the central region of the human lung considered as a continuous elastically deformable medium. To achieve this purpose, we study the interaction between the pipes composing the tree and the fluid that goes through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...

Optimal Proliferation Rate in a Cell Division Model

P. Michel (2010)

Mathematical Modelling of Natural Phenomena

We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...

Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2005)

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

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...

Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control...

Currently displaying 61 – 80 of 107