Mathematical model for diamond-type crystals with impurities or defects.
Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation
Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version...
Mathematical models for laser-plasma interaction
We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the...
Mathematical models for laser-plasma interaction
We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the...
Mathematically Modelling The Dissolution Of Solid Dispersions
A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design....
Mean Green's function of the Anderson model at weak disorder with an infra-red cut-off
Mean-field evolution of fermionic systems
We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...
Mesures semi-classiques et croisement de modes
Metric rigidity of crystallographic groups.
Microtheoretical and numerical calculation of phonon spectra in superlattices.
Minimizers of the Lawrence–Doniach energy in the small-coupling limit : finite width samples in a parallel field
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 a quantum Hall system via elliptic equations.
Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling
Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in...
Modelli di Spin deterministici con comportamento vetroso
Modelling the electromagnetic behaviour of SiFe alloys using the Preisach theory and the principle of loss seperation.
Monotonicity of a key function arised in studies of nematic liquid crystal polymers.
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...
Moving domain walls in magnetic nanowires