20/01/2012
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| 11 heures
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Salle de conférences
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Christian Bracco (Labo Fizeau et IUFM)
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Poincaré et la relativité en 1905 : un pionnier de la physique théorique du XXe siècle
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À
la suite du travail d’Arthur Miller, historien de la physique, sur
le Mémoire de Palerme de
Poincaré concernant la dynamique de l’électron, il a été
souvent considéré que l’approche de la relativité par Poincaré
était prisonnière d’une vision électromagnétique du monde et
dépendait de modèles obsolètes de l’électron. « Son mode
de pensée essentiellement mathématique » aurait même été
« l’un des facteurs qui l’a empêché de tirer des
conclusions physiquement pertinentes de ses recherches dans la
théorie électromagnétique » (invariance de la vitesse c
de la lumière, remise en cause explicite du
temps). Comme on le verra, la logique du Mémoire
est au contraire extrêmement moderne car elle s’appuie sur les
concepts de groupe de symétrie et d’action invariante qui seront
au cœur de toute la physique théorique du XXe
siècle, à commencer par l’approche d’Hilbert de la relativité
générale en 1915.
Quatre
clés permettent de comprendre cette logique du Mémoire.
La première concerne, comme nous l’avons montré, l’utilisation
de transformations actives par Poincaré. Elles lui servent à
corriger le travail antérieur de Lorentz sur l’invariance de
l’électromagnétisme et le dispensent de changer de référentiel.
La seconde est la nécessité pour la mécanique d’exclure de ce
groupe de transformations les dilatations (par la condition qui lui
est venue à l’esprit suite à sa correspondance avec Lorentz). La
troisième concerne la place dans le Mémoire
de l’action et de son invariance, propriété que Poincaré étend
au-delà de l’électromagnétisme et qui lui permet d’obtenir
trivialement (avant Max Planck) le lagrangien relativiste.
Finalement, les modèles discutés par Poincaré font plutôt figure
d’exemple et contre-exemples, même si la « pression de
Poincaré » que l’histoire a retenue et qui assure de façon
covariante la stabilité nécessaire de l’électron, est proche de
modèles actuels de confinement des quarks.
Je
terminerai cette présentation par une confrontation du Mémoire,
seul article scientifique rédigé par Poincaré sur la relativité,
à ses textes secondaires, qui présentent un historique lorentzien
de la relativité, sans rapport avec le contenu du Mémoire,
et sur lesquels de nombreux historiens ou physiciens se sont basés
pour faire porter à Poincaré des jugements erronés sur la
relativité.
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27/01/2012
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| | 11 heures
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| Salle de conférences
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Guillaume Attuel
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| Assessing atrial fibrillation as a chaotic dynamical state of coupled oscillators.
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| Clinical Background:
Fibrillation is an electrical pathology of the heart responsible for
sudden death, when striking the ventricles. The more common atrial
fibrillation (AF), which though in itself not lethal highly increases
the risk of stroke.
It has been shown that a pathology called conduction block, between
atria and ventricle exhibits typical patterns of chaotic map (Glass
1981). However, it is generally believed that fibrillation is a
consequence of the substrate abnormalities alone, such as fibrosis, and
therefore is due to fractionated propagation, thereby inflicting a kind
of wave turbulence, the so called functional reentry (Allessie 1973).
This vision has been challenged more recently with the discovery of
foci, especially near the pulmonary veins, triggering AF in certain
occasions, after the electrical isolation of which normal sinus rhythm
is spontaneously recovered in patients suffering paroxysmal AF, i.e.
episodes of AF lesser than 24h (Haissaguerre 1998). Since then, an
intense debate holds on the identification of the zones to target in
the case of sustained AF, i.e. episodes lasting weeks. No consensus has
emerged in identifying more regular behaviors, as rotors, or apparently
random fractionation, and the means to quantify these hypothesized
areas.
The possibility that AF stems from a quasi periodic route to chaos has been first pointed out by Garfinkel (1999).
Motivations:
We are addressing the clinical and physiological concern of trigger and
perpetuation of fibrillation as being a manifestation of one single
phenomenon.
Methods:
Our aim is to assess a fibrillatory state as a state past a dynamical
phase transition of a system of many coupled oscillators. Collective
motion in these systems is known to show synchronized or desynchronized
phases (Kuramoto 1981), as well as intermediate more complex phases.
We would like to present a non exhaustive overview of this class of
systems, in particular to insist on the importance of the mean field
interaction among the oscillators, and its influence on the collective
behavior, such as the possibility to ignite a trapping instability.
We describe then a transition due to this instability, the critical
neighborhood of which is abnormally wide, the parameter window where
fluctuations are found to be relatively large. The intrinsic mean field
plays a key role in perpetuating the fluctuations far from the
transition point.
In this respect, we will also cast a bridge with the aspects of
spatio-temporal intermittency, seen in Rayleigh-Bénard turbulence.
We will point out an open question, of great relevance in our opinion,
which deals with the classification of the possible dynamical states
arising in such systems, according for instance to how much non local
the mean field is.
We will put forward during the presentation as many key experimental facts of AF as known to us which support this approach.
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3/02/2012
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| | 11 heures
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| Salle de conférences
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Bernard Raffaelli
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| TOWARDS A “REGGEIZATION” OF BLACK HOLE PHYSICS?
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Beyond
the purely mathematical definition of a black hole as a solution of
Einstein equations in vacuum, there are some observational clues, as
pointed out by Kip Thorne, from the first observation of the binary
system Cygnus X1 to recent assumptions related to the presence of
hypothetical supermassive black holes in the center of various
galaxies, concerning their existence in our Universe and,
consequently, encouraging their study. But, what is a black hole? In
physics, it is well-known that in order to obtain information on
interactions between fundamental particles, atoms, molecules, etc…,
and on the structure of composite objects, we have to make collision
experiments or, more precisely, scattering experiments. This is
exactly the aim of this talk. Indeed, after defining “roughly”
what a black hole is (and is not!), studying how it can interact with
its environment should allow us to obtain fundamental information
about those “invisible weird objects”. It should be noted that
this study is also useful to understand the kind of signals one could
detect by the future gravitational waves astronomy devices and, so to
speak, to finally have a way to observe directly the presence of a
black hole in a given region of our Universe. We will mainly focus on
resonance and absorption phenomena of a scalar field by (the “quite
simple” example of) the Schwarzschild black hole. The originality
of this study is about the use of an old semiclassical method known
as the “complex angular momentum theory”, which brings concepts
like S-matrix, Regge poles techniques, into high energy black holes
physics, as suggested implicitly by Chandrasekhar in the middle of
the seventies, in order to understand related properties as the
so-called quasinormal modes and the behavior of the absorption cross
section. This approach allows us to have simple and quite intuitive
physical interpretations of resonance and absorption phenomena,
supported by very accurately novel analytical expressions within the
framework of a field theory.
References :
- Y. Decanini, A. Folacci, B. R, « Resonance and absorption
spectra of the Schwarzschild black hole for massive scalar
perturbations: a complex angular momentum analysis »,
PhysRevD.84:084035, 2011
- Y. Decanini, A. Folacci, B. R., « Fine structure of high energy
absorption cross sections for black holes », Class. Quantum Grav.
28:175021, 2011
- Y. Decanini, A. Folacci, B. R., « Unstable circular null
geodesics of static spherically symmetric black holes, Regge poles and
quasinormal frequencies », Phys.Rev.D81:104039, 2010
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10/02/2012
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| | 11 heures
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| Salle de conférences
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17/02/2012
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| | 11 heures
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| Salle de conférences
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21/02/2012
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| | 11 heures
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| Salle de conférences
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Mario Gattobigio (UNSA - INLN)
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| Few-body physics: an Hyperspherical Harmonics approach
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| The
few-body physics is the study of quantum systems made up of only few
particles, typically from three up to six particles. Historically, this
field started in nuclear physics; the basic problem were, and is, the
ab-initio description of light nuclei starting from the knowledge of
the "true" nucleon-nucleon interaction. Nowadays, the few-body physics
has extended its domain also to (cold)-atomic physics, especially after
the experimental realization of the Efimov state, an universal
three-body state(s) predicted long time ago by the russian physicist
Vitaly Efimov [1].
In the few-body nuclear-research program there are two major problems;
first, we need to know the fundamental nucleon-nucleon interaction [2].
Second, we must be able to solve the few-body Schroedinger equation;
without an effective method of solution, we can not discriminate
between the different proposed models of nucleon-nucleon interaction.
In our group we have developed a method based on Hyperspherical
Harmonics (HH) functions that allows us to solve few-body problems up
to six particles [3]. The HH basis set has been extensively used to
describe bound and low energy scattering states in three- and four-body
systems in nuclear as well as in atomic physics. The extension of the
method to describe heavier systems has encountered difficulties mainly
due to two causes: the large degeneracy of the basis, and the
complexity required in the construction of states with well defined
symmetry.
In our approach we circumvent the two difficulties: the large
degeneracy of the HH basis has been tackled noticing that the
Hamiltonian can be expressed as a sum of products of sparse matrices;
the use of a dedicated algebra for sparse matrices produces a fast
matrix vector product that allows for an efficient eigenvalue search
algorithm. In addition, the HH basis has been implemented without a
preliminary construction of specific symmetries. However, the
eigenvectors reflect the symmetries of the Hamiltonian and, in the case
of identical particles, the eigenvectors have well defined symmetry and
can be readily identified.
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2/03/2012
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| | 11 heures
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| Salle de conférences
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Pas de séminaire (vacances)
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09/03/2012
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| | 11 heures
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| Salle de conférences
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15/03/2012
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| | 11 heures
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| Salle de conférences
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23/03/2012
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| | 11 heures
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| Salle de conférences
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| Kurusch Ebrahimi-Fard
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| The Magnus expansion, trees and Knuth's rotation
correspondence
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| | In numerical analysis the successful use of combinatorics on
trees can be traced back to the pioneering work of John Butcher on
an algebraic theory of integration methods. Since then, exploring
and unfolding algebraic structures in the context of the theory of
numerical integration methods became a useful tool. In this talk we
report on recent work on the fine structure of the so-called Magnus
expansion. The latter is a peculiar Lie series involving Bernoulli
numbers, iterated Lie brackets and integrals. It results from the
recursive solution of a particular differential equation, which was
introduced by Wilhelm Magnus in 1954, and which characterizes the
logarithm of the solution of linear initial value problems for
linear operators. Arieh Iserles and collaborators were the first to
use planar tree structures in an intriguing way to study the Magnus
expansion. Our work is based on using simple combinatorics on planar
rooted trees, which allows us to prove a closed formula for the
Magnus expansion in the context of free dendriform algebra. From
this, by using a well-known dendriform algebra structure on the
vector space generated by the disjoint union of the symmetric
groups, we derive the Mielnik-Plebanski-Strichartz formula for the
continuous Baker-Campbell-Hausdorff series.
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30/03/2012
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| | 11 heures
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| Salle de conférences
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06/04/2012
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| | 10h30 heures
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| Salle de conférences
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| François Delarue (UNSA - JAD)
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13/04/2012
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| | 11 heures
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| Salle de conférences
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20/04/2012
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| | 14 heures
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| Salle 2
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Chiu Fan Lee (Max Planck Institute for the Physics of Complex Systems, Dresden, Germany)
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Spatial organisation of the cell cytoplasm: P granule localisation by phase separation in the C. elegans embryo
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| Pattern
formation in the cell cytoplasm plays an important role in a number of
biological processes. During cell division, the cell cytoplasm
undergoes dramatic spatial reorganization. In the case of asymmetric
cell division, cytoplasmic components are segregated spatially. An
intriguing example is the spatial organization of the cytoplasm during
asymmetric cell division in the C. elegans embryo, which involves the
generation of a concentration gradient of the protein Mex-5 that in
turn drives localization of P granules to the posterior side. P
granules are liquid drops consisting of RNA and proteins that are
important for germline specification. In this talk, I will describe how
the Mex-5 concentration gradient controls the spatial profile of P
granule formation and as a result the localization of P-granules to the
posterior of the cell. Furthermore, we demonstrate that with the help
of phase separation, the P granule concentration gradient can be
drastically amplified in comparison to the Mex-5 concentration
gradient.
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27/04/2012
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| | 11 heures
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| Salle de conférences
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03/05/2012
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| | 11 heures
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| Salle de conférences
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11/05/2012
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| | 11 heures
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| Salle 2
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Martin Krupa (Donders Institute for Brain, Cognition and Behaviour)
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| Systèmes dynamiques lents-rapides et canards: aspects théoriques, numériques, applications et problèmes ouverts.
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| Dans
cet exposé, je commencerai par donner quelques éléments historiques sur
la découverte des canards au sein de l'école non-standard de
Strasbourg, et de leur présence dans de nombreuses applications
(aérodynamique, réactions chimiques, oscillateurs neuronaux). Ensuite,
je présenterai rapidement les principales techniques d'analyse
mathématique de ces objets (analyse non-standard, recollement de
développements asymptotiques, asymptotique des séries Gevrey,
éclatements à paramètres et réduction à des variétés centrales) puis
j'insisterai plus longuement sur mon travail utilisant des
éclatements à paramètres. Dans une seconde partie, je passerai aux
applications de la théorie des canards en neuroscience, dans le cadre
des systèmes à trois dimensions avec deux variables lentes, explicitant
en particulier le lien avec les oscillations complexes (mixed-mode
oscillations ou MMOs). Je mentionnerai également brièvement les
techniques numériquesqui permettent d'étudier au mieux ces systèmes. Je
terminerai mon exposé en donnant une liste de problèmes ouverts.
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