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Modelling and control in pseudoplate problem with discontinuous thickness

Ján Lovíšek (2009)

Applications of Mathematics

This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control...

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium∗

Gloria Faccanoni, Samuel Kokh, Grégoire Allaire (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS...

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium∗

Gloria Faccanoni, Samuel Kokh, Grégoire Allaire (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS...

Modelling of Dynamic Problems in Biomechanics

I. Petrov, Y. Bolotskikh, A. Vasyukov (2011)

Mathematical Modelling of Natural Phenomena

This paper is devoted to solving of dynamic problems in biomechanics that require detailed study of fast processes. Numerical method of characteristics is used to model the temporal development of the processes with high accuracy.

Modelling of multicomponent diffusive phase transformation in solids

Vala, Jiří (2008)

Programs and Algorithms of Numerical Mathematics

Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases ( α , γ ) and in moving interface of finite thickness ( β ), in whose center the ideal liquid material behaviour can be detected....

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions

Patrick Le Quéré, Catherine Weisman, Henri Paillère, Jan Vierendeels, Erik Dick, Roland Becker, Malte Braack, James Locke (2005)

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

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of...

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 2. Contributions to the June 2004 conference

Henri Paillère, Patrick Le Quéré, Catherine Weisman, Jan Vierendeels, Erik Dick, Malte Braack, Frédéric Dabbene, Alberto Beccantini, Etienne Studer, Thibaud Kloczko, Christophe Corre, Vincent Heuveline, Masoud Darbandi, Seyed Farid Hosseinizadeh (2005)

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

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

Patrick Le Quéré, Catherine Weisman, Henri Paillère, Jan Vierendeels, Erik Dick, Roland Becker, Malte Braack, James Locke (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference...

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

Henri Paillère, Patrick Le Quéré, Catherine Weisman, Jan Vierendeels, Erik Dick, Malte Braack, Frédéric Dabbene, Alberto Beccantini, Etienne Studer, Thibaud Kloczko, Christophe Corre, Vincent Heuveline, Masoud Darbandi, Seyed Farid Hosseinizadeh (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

Modelling of Plant Growth with Apical or Basal Meristem

N. Bessonov, F. Crauste, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...

Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents

S. R. McDougall, M. A.J. Chaplain, A. Stéphanou, A. R.A. Anderson (2010)

Mathematical Modelling of Natural Phenomena

Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...

Modelling the spiders ballooning effect on the vineyard ecology

E. Venturino, M. Isaia, F. Bona, E. Issoglio, V. Triolo, G. Badino (2010)

Mathematical Modelling of Natural Phenomena

We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.

Modelling the Spread of Infectious Diseases in Complex Metapopulations

J. Saldaña (2010)

Mathematical Modelling of Natural Phenomena

Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially,...

Modelling Tuberculosis and Hepatitis B Co-infections

S. Bowong, J. Kurths (2010)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

A. Marrocco, H. Henry, I. B. Holland, M. Plapp, S. J. Séror, B. Perthame (2010)

Mathematical Modelling of Natural Phenomena

Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare...

Currently displaying 221 – 240 of 362