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Displaying 61 –
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107
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...
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...
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...
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...
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.
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,...
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.
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...
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...
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...
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,...
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...
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...
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...
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...
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107