- Meals
and lodging expenses will be paid by the summer school for all
participants
- Travel expenses are not covered by the
summer school
- For
CNRS employees, travel expenses can be covered by The "Formation
Permanente" of the "Délégation CNRS" of their
institute,
that they should contact
- The
organizers will set a
bus shuttle from Toulouse to Seix depending on Sunday june 11 afternoon
and from Seix to Toulouse on Friday June 16 after lunch (Please, see
Application form below).
Program
| Monday the 12th |
| 10h00-10h30 | Welcome |
| 10h30-12h00 | Lenya Ryzhik | Nonlinear
propagation in random media and time reversal |
| Lunch |
| 14h00-15h30 | Simone
Santandrea | Transport
calculations for Reactor Physics. The challenge of Generation IV |
| 15h30-16h30 | Hedia Chaker | High
Field Asymptotics for the Boltzmann equation
|
| Coffee
break |
| 17h30-19h00 | Josselin
Garnier | Wave
propagation in random media |
| Tuesday the 13th |
| 08h30-10h00 | Lenya Ryzhik | Nonlinear
propagation in random media and time reversal |
| 10h30-12h00 | Josselin
Garnier | Wave
propagation in random media |
| Lunch |
| 16h00-17h00 | Olivier
Vanbésien | Multiscale
aspects of parameter extraction in left-handed metamaterials |
| Coffee
break |
| 17h30-19h00 | Yalchin
Efendiev | Multiscale
analysis and simulations for the transport of porous media flows |
| Wednesday the 14th |
| 08h30-10h00 | Yalchin
Efendiev | Multiscale
analysis and simulations for the transport of porous media flows |
| 10h30-12h00 | Andrey
Piatnitski | Periodic
Homogeneisation |
| Lunch |
| 14h00-19h00 |
Free
Aternoon
|
|
|
| Thursday the 15th |
| 08h30-10h00 | Josselin
Garnier | Wave
propagation in random media |
| 10h30-12h00 | Yalchin
Efendiev | Multiscale
analysis and simulations for the transport of porous media flows |
| Lunch |
| 14h00-15h00 | Jean-François
Clouet | Effective
behaviour for transport of photons and supra-thermal particles in
binary mixtures |
| 15h00-15h30 | Mihai Bostan | The
relativistic Vlasov-Maxwell system for laser-plasma interaction
|
| 15h30-16h00 | Catherine
Choquet | Asymptotics
in porous media |
| Coffee
break |
| 17h30-18h00 | Xianto Li | Boundary
conditions for molecular dynamics |
| 18h00-19h30 | Andrey
Piatnitski | Periodic
Homogeneisation |
| Friday the 16th |
| 08h30-10h00 | Andrey
Piatnitski | Periodic
Homogeneisation |
| 10h30-12h00 | Lenya Ryzhik | Nonlinear
propagation in random media and time reversal |
| Lunch |
Abstracts
Mihai Bostan
(Univ. Franche-Comté)
The relativistic
Vlasov-Maxwell system for laser-plasma interaction
[Slides] We
consider a population of relativistic electrons interacting through the
action of their self-consistent electro-magnetic ¯eld. We
investigate here a reduced 1D Vlasov-Maxwell system introduced recently
in the physical literature for studying laser-plasma interactions. The
assumptions of this model are the following : all unknowns depend on
only one space variable and the electrons are monokinetic in the
transversal directions. The above model describes the interaction of
the electro-magnetic field created by a laser wave (called pump wave)
with a population of charged particles. The strong nonlinear coupling
through the Lorentz factor makes this system difficult to study
theoretically but also numerically. Other reduced models have been
considered by physicists. 1) The nonrelativistic model NR ; it is
physically justified when the temperature is low enough, so that the
proportion of relativistic electrons is negligible and the intensity of
the pump is small. 2) The quasi-relativistic model (also called
semi-relativistic by some authors) denoted QR ; it is acceptable when
the proportion of ultra-relativistic electrons (v ~ c) is negligible
and the pump intensity is moderate. 3) The original model will be
referred to as fully relativistic FR. The NR and QR models were studied
recently by Carrillo and Labrunie. They proved the existence of weak
and mild solutions for the space periodic and free-space problems.
computations involving L1 test functions. This method has been already
In this work one focus on the FR case. Actually the same method applies
to the QR case and some arguments can be also used for analyzing the NR
case. Nevertheless, we are able to construct global solutions by
characteristics in the QR and FR cases, whereas only local solutions by
characteristics are available in the NR case. The arguments relie on
iterative procedure. The main idea consists in using the formulation by
characteristics to obtain L1 estimates for the electro-magnetic field
and the spacial derivatives by duality used to prove the existence and
uniqueness of the solution by characteristics for the 1D Vlasov-Poisson
initial-boundary value problem. To our knowledge this is the first
theoretical work on the FR reduced Vlasov-Maxwell model. It has common
features with the Nordström-Vlasov system, studied recently by
Calogero and Rein.
Hedia
Chaker (Univ. Tunis)High Field Asymptotics
for the Boltzmann equation
[Slides]The
high field approximation of a fermionic Boltzmann equation of
semiconductors is performed after the formation of shocks.
By employing a new entropy,
whose dissipation measures the departure from the high field
equilibrium, convergence towards the entropic solution of the limiting
conservation law is proven. The entropy is also used in the
construction of kinetic shock profiles for entropic shocks and to prove
non-existence of non-entropic shock profiles.
Jean-François
Clouet (CEA Saclay)Effective behaviour for
transport of photons and supra-thermal particles in binary mixtures
[Slides]Numerical simulations of fusion
targets require solving both hydrodynamic motion and particle
transport. Due to hydrodynamic instabilities, small hydrodynamic scales
appear and interact with the computation of transport coefficients for
particles. The talk will describe various subgrid models which can be
used for finding effective behavior for particle transport in
non-homogeneous media.
Yalchin
Efendiev (Texas A&M University)
Multiscale analysis and
simulations for the transport of porous media flows
[Slides 1]
[Slides 2][Slides 3]I
will talk about numerical homogenization methods based on multiscale
finite element methods for computation of problems with multiple
scales. First, I will give a background on multiscale finite element
methods and various ways of computing multiscale basis functions. Both
linear and nonlinear elliptic/parabolic equations will be considered. I
will discuss the main error sources in these numerical approximations
and possible improvements. Both spatial and temporal scales will be
considered. I will present explicit convergence rates for
nonlinear equations and general convergence results for problems with
random homogeneous space-time heterogeneities. In the latter case, I
will also present some new homogenization results. Further, I will
discuss multiscale methods using a limited global information. The
limited global information is important for the cases without scale
separation where homogenization theory is not applicable. I will show
the convergence of the multiscale numerical methods without using
homogenization techniques. Purely hyperbolic equations and multiscale
numerical methods for them will be also considered. I will also present
upscaling methods for hyperbolic equations with and without limited
global information. Finally, I will present the results for two-phase
immiscible porous media flow dynamics as a coupled system of elliptic
and hyperbolic equations.
Numerical results will be presented.
The
methods presented in the talk can be used on unstructured grids (both
coarse and fine) for highly heterogeneous porous media. I will also
mention applications of multiscale finite element methods to inverse
problems. This is a joint work with J. Aarnes, T. Hou and V. Ginting.
Josselin
Garnier (Univ. Paris 7)
Wave propagation in random media
[Slides 1]
[Slides 2]
[Slides 3]
[Slides 4]Our
motivation to give this lecture is twofold. On one hand the
theory of waves propagating in randomly layered media has been
intensively studied during the last thirty years and the results are
scattered among numerous papers. It is now in a stable state, in
particular in the extremely interesting regime of separation of scales
as introduced by G. Papanicolaou and his co-authors. On the other
hand the time reversal experiments conducted since
the
nineties, with ultrasonic waves by M. Fink
and his group in
Paris,
or in the context of ocean acoustics by W. Kuperman and his
collaborators, has attracted a lot of attention due to the surprising
effects of refocusing and enhanced resolution by multiple scattering of
the waves. These experiments, have opened the door to numerous
potential applications, in particular in the
domains of
imaging and communications. A quantitative mathematical
analysis is crucial in the understanding of these phenomena
and
for the development of their applications.
Wave
propagation in random media is a vast field where a lot of work in
various regimes have been done. This lecture focuses mainly on wave
propagation in randomly layered media, where strong medium fluctuations
can be rigorously analyzed. We shall also give an analysis of wave
propagation in a random waveguide, where transverse effects are
important. This final part can be seen as an opening to the full
three-dimensional world, that will also be discussed by the other
lecturers (see the lecture by L. Ryzhik).
- Homogenization
theory, diffusion approximation, and asymptotic theory for random
differential equations
- Wave propagation in randomly
layered media: the coherent front wave and the incoherent wave
fluctuations
- Time reversal in randomly layered media
- Statistical
stability of time reversal in randomly layered media
- Wave
propagation and time reversal in a random waveguide
Xiantao LI (Penn
State Univ.)
Boundary conditions for molecular
dynamics
Andrey
Piatnitski (Univ. Narvik)Homogenization of
singular structures and measures
[Slides]
[Notes]We will focus on homogenization
of differential equations and variuational problems in variable spaces
involving integration with respect to periodic or random stationary
measures. As particular cases we consider the homogenization of
networks, junctions and thin structures. We will discuss the following
topics
- Singular
structures. Variable Sobolev spaces. Convergence in variable spaces.
- Potential
and solenoidal vectors. Connectedness of periodic measures.
- Two-scale
convergence and homogenization in variable periodic spaces. Examples of
singular structures.
- Random ergodic stationary
measures.
- Stochastic two-scale convergence in
variable spaces. Connectedness of random measures.
- Homogenization
of random variable spaces. Random singular structure
Lenya Ryzhik
(Univ. Chicago)
Propagation of waves in highly
heterogeneous media is often described in terms of various kinetic
equations posed in phase space, that is, wave energy density is
described in terms of the spatial position and wave vector. The
validity of a particular kinetic model depends on the regime of various
physical parameters: wave length, correlation length and the
fluctuation strength. The simplest kinetic model is the spatial
diffusion equation, where all directional information is lost because
of the multiple scattering. Other commonly used models include the
radiative transport equation and the Fokker-Planck equation. Despite a
large amount of work in this area, the rigorous passage from the
microscopic description in terms of the wave equation to the kinetic
models remains a challenging mathematical problem. In my lectures I
will mostly concentrate on two regimes. First is the regime of random
geometric
optics where the passage from the wave equation to
the energy diffusion equation can be rigorously obtained. Another is
the paraxial approximation of the wave equation. I will also describe
some applications to the theory of the time-reversal experiments in a
three-dimensional medium. These lectures will be complimentary to those
of Josselin Garnier.
Simone
Santandrea (CEA)
Transport calculations for
Reactor Physics. The challenge of Generation IV
[Slides]Olivier
Vanbésien (IEMN, USTLille)
Institut d'Electronique, de
Microélectronique et de Nanotechnologie
(IEMN - UMR
CNRS 8520)
Cité Scientifique - Avenue
Poincaré - BP 60069
59652 Villeneuve d'Ascq Cedex
"Multiscale
aspects of parameter extraction in left-handed metamaterials"
[Slides]Abnormal
properties of wave propagation in artificial media have received great
attention recently since it permits to go beyond the classical
properties of homogeneous materials. More specially, left-handed
metamaterials which support negative refraction or backward waves,
appear promising in terms of applications. It is believed that, under
strong operating conditions, a perfect flat lens, overcoming Rayleigh's
diffraction limit, can be built. Two main ways can be followed to
conceive such a "perfect" material, perfect in the sens of a refraction
index (n) equal to -1 and a surface impedance (z) of 1. In other words,
using equivalent parameters as the permittivity (epsilon) or the
permeability (mju), this means that these two parameters must be equal
to -1, simultaneously.
On
the practical side, to reach these objectives, mainly two routes are
explored : (i) dielectric photonic crystals and (ii) metallic lattices
of "quasi-particles" able to impact both electric and
magnetic
fields behaviours. In général, the characteristic
dimensions (d) of these periodic strucutres are fixed as a function of
the operating wavelength. For photonic crystals, such regimes of phase
velocity reversal can be found for d close to lambda/4, whereas large
subwavelength regimes (d < lambda/10) can be exploited in
metallic
structures.
If full wave calculations at the structuration
level
are possible to extract dispersion properties of the metamaterials, the
situation appear more complex when real applications are studied. In
général, the strucutre is of finite dimension,
injection
and collection process have to be taken into account during the
prototype design. This means that equivalent parameters as n, z ,
epsilon and mju are of great help to understand the complete system
behaviour. However, recovering these parameters from ab-initio
simulations is not an easy task since the geometry of the
quasi-particles at very small scales (especially for magnetic
behaviour) can be quite complex.
In this lecture, we will
present
a variety of potentially promising metamaterials based devices build
for operation at terahertz frequencies or in the optical domain .
Attention will be paid to the efforts made to describe at large scale
the consequences of their micro- or nano-structuration by ad-hoc
parameters.
Useful
Informations
Adress
of the summer school
Centre International de
Séjours
La Maison du Haut Salat.
WEB adress http://www.maisonduhautsalat.com
For
any problems or questions
regarding this page, please contact me
