Displaying similar documents to “Reduced resistive MHD in Tokamaks with general density”

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Fragmentation-Coagulation Models of Phytoplankton

Ryszard Rudnicki, Radosław Wieczorek (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present two new models of the dynamics of phytoplankton aggregates. The first one is an individual-based model. Passing to infinity with the number of individuals, we obtain an Eulerian model. This model describes the evolution of the density of the spatial-mass distribution of aggregates. We show the existence and uniqueness of solutions of the evolution equation.

Global Asymptotic Stability of a Functional Differential Model with Time Delay of an Anaerobic Biodegradation Process

Borisov, Milen, Dimitrova, Neli, Krastanov, Mikhail (2017)

Serdica Journal of Computing

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We study a nonlinear functional differential model of an anaerobic digestion process of wastewater treatment with biogas production. The model equations of biomass include two different discrete time delays. A mathematical analysis of the model is completed including existence and local stability of nontrivial equilibrium points, existence and boundedness of the model solutions as well as global stabilizability towards an admissible equilibrium point. We propose and apply a numerical...

Models of interactions between heterotrophic and autotrophic organisms

Urszula Foryś, Zuzanna Szymańska (2009)

Applicationes Mathematicae

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We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.

Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating

M. Khenner, S. Yadavali, R. Kalyanaraman (2012)

Mathematical Modelling of Natural Phenomena

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The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective...

Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Anne-Claire Bennis, Tomas Chacón Rebollo, Macarena Gómez Mármol, Roger Lewandowski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness...

Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon, H. R. Thieme (2010)

Mathematical Modelling of Natural Phenomena

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For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively...

Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system

Helmut Abels (2009)

Banach Center Publications

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We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some...

Strong initial segments of models of IΔ₀

Paola D&amp;#039;Aquino, Julia F. Knight (2007)

Fundamenta Mathematicae

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McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that...

A Mathematical Model for a Contracting Interstellar Cloud

Meri Lisi, Silvia Totaro (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper, we study a one-dimensional mathematical model for a contracting interstellar cloud, with a star inside. Existence and uniqueness of a positive solution are proved by means of the fixed point theorem. A time discretization procedure is given and the case of an expanding interstellar cloud is also considered.

Thermodynamics of DNA microarrays

Enrico Carlon (2008)

Banach Center Publications

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DNA microarrays have been widely used in molecular biology laboratories. The main current application of these devices is the determination of the gene expression level for thousands of genes simultaneously. Here we review a recently introduced physical model for hybridization (i.e. the binding of complementary DNA strands) in Affymetrix arrays and compare it to experimental results. The experimental data follow rather well the microscopic model and the approach offers several advantages...