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I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.
The study of small magnetic particles has become a very important topic, in
particular for the development of technological devices such as those
used for magnetic recording. In this field, switching the magnetization inside
the magnetic sample is of particular relevance. We here investigate mathematically
this problem by considering the full partial differential model of Landau-Lifschitz
equations triggered by a uniform (in space) external magnetic field.
In this paper we are interested in the numerical modeling
of absorbing ferromagnetic materials
obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the
propagation and scattering of electromagnetic waves.
In this work
we consider the 1D problem.
We first show that the corresponding Cauchy problem
has a unique global solution.
We then derive a numerical scheme based on an appropriate modification
of Yee's scheme, that we show to preserve some important
properties of the continuous...
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...
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...
We will describe recent some of the recent theoretical progress on making objects invisible to electromagnetic waves based on singular transformations.
We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg. 191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...
We present and analyze an interior penalty
method for the numerical discretization of the indefinite
time-harmonic Maxwell equations in mixed form.
The method is based on the mixed
discretization of the curl-curl operator developed
in [Houston et al.,
J. Sci. Comp.22 (2005) 325–356]
and can be understood as a non-stabilized variant
of the approach proposed in [Perugia et al.,
Comput. Methods Appl. Mech. Engrg.191 (2002) 4675–4697].
We show the well-posedness of this approach and
derive optimal...
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.
In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) > 0 such that, for 0 < ε < ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions.
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