The aim of this paper is to investigate, as precisely as possible, a boundary value problem involving a third order ordinary differential equation. Its solutions are the similarity solutions of a problem arising in the study of the phenomenon of high frequency excitation of liquid metal systems in an antisymmetric magnetic field within the framework of boundary layer approximation.
We revisit a hydrodynamical model, derived by Wong from Time-Dependent-Hartree-Fock approximation, to obtain a simplified version of nuclear matter. We obtain well-posed problems of Navier-Stokes-Poisson-Yukawa type, with some unusual features due to quantum aspects, for which one can prove local existence. In the case of a one-dimensional nuclear slab, we can prove a result of global existence, by using a formal analogy with some model of nonlinear "viscoelastic" rods.
We prescrit a method to simulate the motion of self-propelled rigid particles in a twodimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion is modelled as a point force associated to each particle, placed at a certain distance from its gravity centre. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation on the whole domain, including fluid and particles: rigid...
This paper is concerned with the numerical simulation of a thermodynamically compatible viscoelastic shear-thinning fluid model, particularly well suited to describe the rheological response of blood, under physiological conditions. Numerical simulations are performed in two idealized three-dimensional geometries, a stenosis and a curved vessel, to investigate the combined effects of flow inertia, viscosity and viscoelasticity in these geometries....
This paper presents the modelling of tracing tests in column experiments. Program Transport was used for the simulation. Its main function is not to predict results of experiments but to compare influence of individual physical and chemical processes to the experiment results. The one-dimensional advection-diffusion model is based on Finite Volume Method; it includes the triple porosity concept, sorption, retardation, and chemical reactions simulated using connected program React from The Geochemist's...
A 3D nonhydrostatic, Navier-Stokes solver has been employed to simulate gravity wave induced turbulence at mesopause altitudes. This paper extends our earlier 2D study reported in the literature to three spatial dimensions while maintaining fine resolution required to capture essential physics of the wave breaking. The calculations were performed on the 512 processor Cray T3E machine at the National Energy Research Scientific Computing Center (NERSC) in Berkeley. The physical results of this study...
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.
We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and -shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...
The singularities occurring in any sort of ordering are known in physics as defects. In an organized fluid defects may occur both at microscopic (molecular) and at macroscopic scales when hydrodynamic ordered structures are developed. Such a fluid system serves as a model for the study of the evolution towards a strong disorder (chaos) and it is found that the singularities play an important role in the nature of the chaos. Moreover both types of defects become coupled at the onset of turbulence....
This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell’s equations, is not neglected. It is proved that for a small periodic force and small positive there exists a locally unique periodic solution of the investigated system. For , these solutions are shown to convergeto a solution of the simplified (and...