Magnetohydrodynamic flow due to noncoaxial rotations of a porous disk and a fourth-grade fluid at infinity.
Mathematical derivation of the power law describing polymer flow through a thin slab
Mathematical foundation of flow of glaciers and large ice masses
Maximal regularity of the spatially periodic Stokes operator and application to nematic liquid crystal flows
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal -regularity of the periodic Laplace and Stokes operators and a local-in-time existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group to obtain an -bound for the...
Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer
Mechanisms of Cell Motion in Confined Geometries
We present a simple mechanism of cell motility in a confined geometry, inspired by recent motility assays in microfabricated channels. This mechanism relies mainly on the coupling of actin polymerisation at the cell membrane to geometric confinement. We first show analytically using a minimal model of polymerising viscoelastic gel confined in a narrow channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this mechanism...
Method of straight lines for a Bingham problem.
Method of straight lines for a Bingham problem as a model for the flow of waxy crude oils.
MHD flow of an elastico-viscous fluid under periodic body acceleration.
Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results
Mixed methods for the approximation of liquid crystal flows
The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
Mixed Methods for the Approximation of Liquid Crystal Flows
The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H2(Ω) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
Modeling, mathematical and numerical analysis of electrorheological fluids
Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.
Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects
A numerical model to compute the dynamics of glaciers is presented. Ice damage due to cracks or crevasses can be taken into account whenever needed. This model allows simulations of the past and future retreat of glaciers, the calving process or the break-off of hanging glaciers. All these phenomena are strongly affected by climate change.Ice is assumed to behave as an incompressible fluid with nonlinear viscosity, so that the velocity and pressure...
Modelling fluid flow and heat transfer in a saturated porous medium.
Mori's memory function formalism in nonlinear statistical hydrodynamics
Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity
The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions...
Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
Nonequilibrium reaction-diffusion structures in rigid and visco-elastic media : knots and unstable noninertial flows