Séminaire Interfaces des mathématiques et systèmes complexes

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Séminaires à Venir


Jeudi 21 octobre  à 11 h (salle de séminaires du LJAD)

P.J. Morrison (Austin)

"GEMPIC: An exact Poisson integrator for the full
Vlasov-Maxwell System

The Vlasov-Maxwell (VM) system, which couples the evolution of the phase space probability
density with the full system of Maxwell’s equations, was shown in the 1980s to be an infinite-
dimensional noncanonical Hamiltonian system. 1 Noncanonical means the Poisson operator does
not have the standard canonical form in terms of conjugate coordinates and momenta and is de-
generate, giving rise to Casimir invariants. This talk will summarize recent work 2 on a novel frame-
work for Finite Element Particle-in-Cell computation developed by discretizing the VM Hamilto-
nian structure. A semi-discrete (finite-dimensional) Poisson bracket that retains the properties of
anti-symmetry and the Jacobi-identity, as well as conservation of discrete versions of its Casimir
invariants, implying that the semi-discrete system retains the parent Hamiltonian structure, was
obtained. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used
in conjunction with Hamiltonian splitting methods for integration in time. Techniques from Finite
Element Exterior Calculus ensure conservation of the divergence of the magnetic field and Poisson’s
equation as well as stability of the field solver. The resulting methods are gauge-invariant, feature
exact charge conservation and show excellent long-time energy and momentum behavior. Due to
the generality of the framework, these conservation properties are guaranteed independently of any
particular choice of the Finite Element basis, as long as the corresponding Finite Element spaces
satisfy compatibility. Plasma physical examples using the GEMPIC code 3 will be described.





Archives vidéos (2009-2011)


Archives séminaires (2011-2015)



Magnetic anisotropy in mono- and bi-nuclear complexes: theoretical insight and prospects

Renaud Ruamps;A R. Maurice;B C. de Graaf,C and Nathalie GuihéryA

A Université de Toulouse 3, Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France;

B SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue A. Kastler, BP 20722, 44307 Nantes Cedex 3, France;

C Universitat Rovira i Virgili, Marcel-li Domingo s:n, 43007 Tarragona, Spain

Magnetic anisotropy is the origin of the single molecule magnet (SMM) behavior
which is manifested by a slow relaxation of the magnetization and a
blocking of the magnetization for low enough temperatures. Since this
bistable behavior may lead to possible technological applications in
the domain of data storage and quantum computing, the understanding
of the microscopic origin of magnetic anisotropy has received a
considerable interest during the last two decades.

Mono-nuclear complexes having exotic coordination of the metal ion have recently
been shown to exhibit a very large magnetic anisotropy. A first study
will be devoted to the rationalization of the magnitude and nature of
single ion anisotropy from theoretical calculations. It will be shown
that the competition between relativistic effects and Jahn Teller
distortion may lead to very large magnetic anisotropy (see figure 1).

The overall magnetic anisotropy of a poly-nuclear complex comes from both
the local anisotropies of paramagnetic ions and their interactions.
The second part of this presentation will focus on the understanding
of synergistic effects between local anisotropies in bi-nuclear
species for which we have both tuned the local anisotropies by
imposing peculiar geometries and combined various types of local
anisotropies (see figure 2, values are in cm

The method used here was successfully confronted to experimental values in series of mono- and bi-nuclear complexes.[1]


[1] J. of Chem. Theo. Comp., 2009 5, 11 2977; J Chem. Theor. Chem 2010 6 1, 55; J. Chem. Theor. Chem. 2010 6 10, 3092; Phys. Rev. B, 2010 81 21, 214427;  J. Chem. Phys. 2010 133, 084307; Inorg. Chem. 2011 50 13, 6229; Phys. Rev. B 2012, 85, 014409;
Phys. Rev. B 2012, 86, 024411; Chem. Euro. J. 2013, 19, 950; R. Ruamps et al. J. Am. Chem. Soc.
2013, 135, 3017A, Phys. Chem. Chem. Phys., 2013, 15 (43), 18784.




Kurusch Ebrahimi-Fard,

"Saving a species in a Lotka-Volterra model via an Hopf algebra antipode"

Abstract: Lotka-Volterra systems can be viewed as nonlinear input-output systems when
time-varying parameters are taken as system inputs and the population
levels are the system outputs. By varying some of these inputs, an
open-loop control problem results, and one objective may be to determine
appropriate inputs to produce desired system profiles. This is known as
the left inversion problem. In this talk we outline the general left
inversion problem for multivariable input-output systems that can be
represented in terms of Fliess operators (aka Chen-Fliess series) using
concepts from combinatorial Hopf algebras. The antipode plays a central
role in this context. This is then applied to a three
species Lotka-Volterra system. The aim is to change the population
dynamics of the top-level predator species in a food chain in such a way
as to prevent extinction.

(Joint work with W. S. Gray and L. Duffaut Espinosa.)



10/05/2016 à 14h en Salle de conf., Séminaire commun avec Proba-Stat (attention jour et horaire exceptionnel)

Eric Guerci, "Why do we need “quantum-like” models for cognition"




20/05/2016 à 11h en Salle de conf., Séminaire commun avec Proba-Stat

Claire Guerrier, (ENS Ulm) "Modélisation mathématique et simulations multi-échelles pour l'étude de la relâche vésiculaire dans les synapses neuronales."

	Nous avons étudié plusieurs structures neuronales à différentes
échelles allant des  synapses aux réseaux neuronaux. Notre objectif était de développer et analyser des modèles mathématiques, afin de déterminer comment les propriétés des synapses au niveau moléculaire façonnent leur activité, et se propagent au niveau du réseau. Ce changement d’échelle peut être formulé et analysé à l’aide de plusieurs outils tels que les équations aux dérivées partielles, les processus stochastiques ou les simulations numériques. Dans un premier temps, nous avons calculé le temps moyen pour qu’une particule brownienne arrive à une petite ouverture définie comme le cylindre faisant la jonction entre deux sphères tangentes. La méthode repose sur une transformation conforme de Möbius appliquée à l’équation de Laplace. Nous avons également estimé, lorsque la particule se trouve dans un voisinage de l’ouverture, la probabilité d’atteindre l’ouverture avant de quitter le voisinage. De nouveau, cette probabilité est exprimée à l’aide d’une équation de Laplace, avec des conditions aux limites mixtes. En utilisant ces résultats, nous développons un modèle et des simulations stochastiques pour étudier la libération vésiculaire au niveau des synapses, en tenant compte de leur géométrie particulière. En nous appuyant sur ces résultats, nous avons développer un modèle pour le terminal pré-synaptique, qui couple un système d’équations d’action de masse à un ensemble d’équations de Markov, ce qui permet d’obtenir des résultats analytiques et de réaliser des simulations stochastiques rapides.





Rachel Sparks, Tomsk State University, Russia

"Nanotechnology: Small Science, Big Ideas"

Nanoscience studies the world of very small objects, it aims to shape the world
atom by atom, to create new artificial structures with improved
properties, due entirely to their size.
enables the development of new materials, devices, or other useful
structures. Applications include; electronics, automotive, sports,
textiles, construction, energy, medicine and environment, to name a
few. Nanotechnology is producing revolutions in these areas by making
devices smaller, lighter, cheaper and faster with better performance.

Electronic devices at the nano scale have now become an essential feature of
modern technology and the field of molecular electronics is
continuously striving towards ever smaller electronic devices.
Understanding what is happening on such a small scale is becoming
increasingly more important. The rapid increase in computing power
available and the advancement of the modelling tools available have
led to theory that now reflects reality. Theoretical tools such as
Density Functional Theory (DFT), enable scientists to make accurate
predictions about molecular structures in addition to providing an
explanation of experimental results.

Molecular switches are a desirable concept in molecular electronics. The aim is
to have the ability to manipulate, control and fully understand the
process that enables the molecule to switch reversibly at room
temperature, a goal that has not yet been reached.





Faith Chiu, UCL, UK

"An analysis of coupling and decoupling neural activity in speech perception"

Speech perception relies on the
accurate identification of phonemes within an auditory string. These
phonemes have been argued to be the smallest of meaningfully contrastive
units in speech ; a change in phoneme will concurrently induce a change
in meaning. Previous modelling efforts implicate that a change in word
meaning (caused by a change in phoneme) causes a change in coupling
activity in the cortical hierarchy (Schofield et al., 2009). However,
MMN has been shown to reflect language-specific phonemic representations
regardless of word meaning, even in non-words (Näätänen et al., 1997).
To disentangle this phoneme-meaning relationship, I present preliminary
results from a current study which applies Dynamic Causal Modelling
(Kiebel et al., 2006) on elicited Mismatch Negativity responses to
categorical speech sound changes. We notice condition-specific
significant changes in effective connectivity for connection strengths
involving the superior temporal gyri (STG) which are located within
higher levels of the auditory cortical hierarchy.



14h Salles des Séminaires

Paulo Amorim (Univ. fédérale de Rio)

Ant foraging dynamics: From reaction-diffusion to individual-based models


15h30 Salles des Séminaires

Fernando Peruani (LJAD)

Collective dynamics in sheeps herds


Jeudi 22 / 09 / 2016 à 14h00 en salle de séminaires

[Séminaire commun edp-an / mecaflu/ interfaces]

Ana Maria Alonso Rodriguez (univ. Trento )

Finite Element Potentials

aim of this talk is to furnish a simple and efficient way for
constructing finite elements with assigned gradient, or curl, or
divergence. Clearly in numerical computations this is important any time
one has to reduce a given problem to an associated one with vanishing
data. Some simple notions of homology theory and graph theory applied to
the finite element mesh are basic tools for devising the solution


Vendredi 23 / 09 / 2016 à 11h30 en salle de séminaires

Igor Aranson, Prof. Invité au Lab. Dieudonné

Ferromagnetic swimmers, spinners and rollers

is a colloidal system of self-propelled particles, similar to the
Quincke Rollers (but not identical).  The active particles exhibit
various collective patterns.


Vendredi 30 / 09 / 2016 à 11h30 en salle de séminaires

Igor Aranson, Prof. Invité au Lab. Dieudonné

Living nematic: linking motility and liquid crystallinity

letting bacteria swim in a suspension of liquid crystals, Igor and
collaborators managed to see how the swimming of bacteria distorted
nematic order around them, which allowed them to learn about the
swimming of bacteria.


Vendredi 14 Octobre 2016 à 14h00 en salle de conférences

 Gabriela Petrungaro (Buenos aires)

Titre:  Dynamics of mobile, delayed-coupled oscillators

 Résumé :

	The vertebrate body is provided with a repetitive structure of
segments, which originate sequentially -one by one- during embryonic
development, with a definite rhythm. This rhythm is controlled by a
biological clock, known as the vertebrate segmentation clock, which
relies on synchronization of cellular oscillators. It is thought that
each of the cells involved in the process acts as an independent
genetic oscillator. A local communication mechanism between cells
couple their dynamics giving rise to synchronization. Two key
components of this mechanism are communication delays and cell
movement. Intercellular communication involves synthesis and transport
of macromolecules which act as ligands and receptors. This aspect can
be described by incorporating delays in the coupling between
oscillators. Furthermore, cell mobility in the context of coupled
oscillators could promote synchronization by extending the effective
range of the coupling. Motivated by this mechanism we study the
dynamics of a system of coupled oscillators that includes these two
fundamental aspects of cell communication. We find that the system
exhibits complex spatio-temporal patterns on its way towards



Vendredi 14 Octobre 2016 à 10h30 en salle de conférences

André Galligo (LJAD)  [travail effectué en collaboration avec Didier Clamond (LJAD)  et Jean Rajchenbach (LPMC)].

Titre: Modélisation de la compression d'un matériau polycarbonate en nids d'abeilles.

 Résumé :

solides cellulaires (e.g. en nids d'abeilles) sont fréquemment 
rencontrés aussi bien dans la nature que dans l'industrie, où ils sont
appréciés pour leurs propriétés mécaniques et leur légerté.  Nous
étudions le cas d'un polycarbonate formé en thermocollant un amas de
cylindres circulaires. En réponse à des compressions latérales, il
montre des comportements inattendus qui dépendent de  l'orientation.
Pour les expliquer, nous présentons une modélisation avec deux échelles 
de grandeurs: celle des petits interstices et celle de la plaque
entière de polycarbonate. On peut alors, dans ce cadre, préciser les
différentes notions d'elasticité et d'inélassticité et les comparer aux
comportements de nos composants locaux (triangles elasticae) et de notre
matériau global.  L'originalité de notre approche consiste à
privilégier les déformations des interstices et à souligner l'intér\^et
(théorique et pratique) du concept de triangle elastica.  La
présentation  et l'explication seront largement illustrées avec des
images et des diagrammes.

Vendredi 18 Novembre à 11 heures en salles de séminaires

Ophelie Guinaudeau (i3s) Titre: Abstraction de la structure et de la dynamique du neurone biologique pour une étude formelle de l'intégration dendritique


neurone possède des dendrites qui sont des prolongements ramifiés au
niveau desquelles il reçoit des messages nerveux provenant de milliers
d'autres neurones. Ces messages se propagent dans l'arborescence
dendritique en direction du corps cellulaire du neurone qui permet, sous
certaines conditions, la transmission du message résultant aux neurones
adjacents. Notre apport est de modéliser le traitement et la
transmission des messages en faisant collaborer une modélisation
discrète et une modélisation continue: le neurone peut être vu comme un
système complexe qui reçoit des entrées discrètes, les convertit en un
signal continu le long de l'arborescence dendritique et le re-discrétise
à la sortie du corps cellulaire. La complexité réside notamment dans le
fait que les entrées qui sont distribuées sur l'arborescence
dendritique interagissent dans le temps et dans l'espace lors de leur
propagation. De plus, cette propagation est accompagnée d'une
atténuation du signal qui est décrite par la théorie des câbles. En se
basant sur cette théorie, nous avons développé un modèle de neurone
individuel permettant d'étudier l'influence de la topologie des
dendrites sur la fonction du neurone. Les abstractions que nous
proposons conservent la précision biophysique tout en réduisant le
nombre de paramètres impliqués. Ceci nous a permis de démontrer un
théorème qui définit des classes d'équivalence de comportements. Il
implique que la topologie des dendrites est, de manière surprenante,
assez peu déterminante dans la fonction d'entrée-sortie du neurone. Il
en résulte que la forme de l'arbre dendritique est probablement
essentiellement dictée par la géométrie du cerveau.




Vendredi 2 décembre en Salle 2 du LJAD à 11 heures

M. Krupa (Inria)

"Heteroclinic chains as a model of priming"

is the ability of the brain to more quickly activate a target concept
in response to a related stimulus (prime). Experiments point to the
existence of an overlap between the populations of the neurons coding
for di erent stimuli. Other experiments show that prime-target relations
arise in the process of long term memory formation. The classical
modelling paradigm is that long term memories correspond to stable
steady states of a Hop eld network with Hebbian connectivity.
Experiments show that short term synaptic depression plays an important
role in the processing of memories. This leads naturally to a
computational model of priming, called latching dynamics; a stable state
(prime) can become unstable and the system may converge to another
transiently stable steady state (target). We show that in the context of
Hop eld networks latching dynamics is closely approximated by (robust)
heteroclinic chains and discuss the role of sparse connectivity,
inhibition and noise in the approximation. Further, we derive necessary
conditions for the existence of heteroclinic chains in Hop eld networks
with synaptic depression and show how a Hop eld network supporting a
heteroclinic chain can be extended to a larger network in which the
weights are derived from a Hebbian learning rule.


Jeudi 9 février en Salle de Conférences du LJAD à 11 heures

Séminaire commun GAD / Interfaces

Jacques Féjoz (Dauphine)

"Théorème KAM, symétrie et dégénérescence"

La persistence de solutions quasipériodiques dans les systèmes hamiltoniens presque
intégrables dépend de conditions de non-dégénérescences. Nous analyserons comment ces
conditions et leurs conséquences sont modifiées en présence de symétries, avec le problème
des trois corps en guise d'application.

Lundi 27 février en Salle de Conférences du LJAD à 11 heures

Tarcísio M. Rocha Filho (Brasília)

"Equilibrium and Non-Equilibrium Statistical Mechanics of Systems with Long-Range Interactions"

I will presente some recent developments on equilibrium and non-equilibrium Statistical  Mechanics of systems with long-range interactions. Our results concern mainly kinetic theory, chaos, ensemble inequivalence and the classical analogue of Goldstone modes excited by thermal fluctuations


Vendredi 10 mars en Salle de Conférences du LJAD à 11 heures     Andreas Deutsch (Dresden)

Collective effects in cancer growth and invasion: insights from
mathematical models
Cancer growth and  invasion can be interpreted as  collective behaviour arising in migrating
 and interacting cell populations. Here, we demonstrate how cellular automaton models allow
for prediction and analysis of emerging properties (e.g. invasion speed) arising from particularly
 chosen cell migration and interaction scenarios (especially go or grow“ and „go and grow“
dynamics). We use our models for the interpretation of data from in vitro cancer cell invasion
assays and will also discuss implications of the „go or grow“ dichotomy for cancer growth and
A. Deutsch, S. Dormann:  Cellular Automaton Modeling of Biological Pattern Formation: Characterization,
Applications, and Analysis. Birkhäuser, Boston, 2005 (2nd ed. 2016)

Mercredi 10 mai en Salle de Conférences du LJAD à 11 heures

Antonio Celani (ICTP, Trieste)

"Learning to navigate in dynamic environments: animal behavior and artificial intelligence"

I will discuss two examples of difficult navigation tasks in highly
dynamical environments. The first one is thermal soaring in birds. Birds
 and gliders piggyback ascending currents to fly with a reduced
expenditure of energy, for example, during migration, and to extend
their flying range. Flow in the thermals is highly turbulent, which
poses the challenge of the orientation in strongly fluctuating
environments. The second one is gravitaxis by smart
microswimmers. These are self-propelled particles that can sense basic
mechanical cues from their surroundings and respond to them in order to
reach the highest altitude within some time horizon. We
 combine numerical simulations of fluid flow with reinforcement learning
 methods to identify strategies of navigation that can cope with
potentially dangerous flow configurations and exploit favorable ones.



Jeudi 11 mai en Salle de Conférences du LJAD à 11 heures

Stijn de Baerdemacker (Université de Gent)

"Richardson-Gaudin integrability for strongly correlated quantum systems"
One of the most intriguing problems in quantum many-particle physics
 is the emergence of strong quantum correlations and complexity.
Theoretical physics is tasked with explaining, understanding, and even
predicting these complex phenomena starting from fundamental premises.
Unfortunately, this is an unsurmountable task due to the size-explosion of the
Hilbert space, limiting exact computations to few-particle systems only.
 Interestingly, for the class of integrable systems, an exact solution can be
 obtained in the form of a Bethe Ansatz wavefunction, even when the
correlations are strong.  In this presentation, I will discuss and present the class
 of Richardson-Gaudin integrable systems, and show how they can be used as an
 optimal starting point for realistic quantum many-particle systems.


Vendredi 12 mai en Salle de Conférences du LJAD à 11 heures

Boris Nectoux (Cermics and INRIA)

"Metastability and the Eyring Kramer’s law"

In materials science, biology and chemistry, atomistic models are now used
in order to predict the macroscopic properties from a microscopic description of
matter. The basic ingredient is a potential energy function f : R d → R which
associates to a set of coordinates of particles the energy of the system. Using
this function f , two types of models are built:
1. continuous state space Markov models such as the Langevin dynamics or
the overdamped Langevin dynamics and,
2. discrete state space Markov models (jump Markov processes). One major issue for the sampling of the trajectories of the Langevin dynamics
is the possible metastable behaviour of this dynamics. Metastability refers to
the case when the typical time to observe transitions between some regions of
the configuration space is much longer than the typical timestep of vibrations
of the system. To deal with this issue, kinetic Monte Carlo methods are used
to design an underlying jump Markov process between metastable states. The
ingredient in kinetic Monte Carlo algorithms is the collection of transition rates
which are computed in practize with the help of the Eyring-Kramers law.
I will present recent results which aim at justifying rigorously the use of the
Eyring Kramers law in the small temperature regime. The proofs are based on
tools from semi-classical analysis.


Vendredi 19 mai en Salle de Conférences du LJAD de 11 à 15 heures

Suivi des thèses de l'équipe IMSC

  Nom Prénom Directeur Titre comité de suivi
11:00 Gomez Nava Luis Alberto F. Peruani Modelling and controlling collective behavior in animal groups F. Peruani, B. Marcos, P. Cassam-Chenaï
11:25 Perez Thomas P. Cassam-Chenaï Problèmes d’algèbre multilinéaire liés à l’intrication quantique des fonctions d’onde moléculaires F. Patras, P. Cassam-Chenaï
       11:50 Métivier David J. Barré Interactions à longue portée et physique statistique hors équilibre J. Barré, B. Marcos, P. Cassam-Chenaï
12:15 Buffet déjeunatoire        
14:15 Stephano Jonathan B. Mauroy Propriétés du transport de l'oxygène et du dioxyde de carbone chez les mammifères et sélection naturelle B. Mauroy, P. Biwole, P. Cassam-Chenaï


Mercredi 14 juin à 16h (salle de conférences du LJAD)

Roberto Benzi (Università di Roma "Tor Vergata") https://scholar.google.com/citations?user=QJeFmVEAAAAJ&hl=en

"Earthquake statistics and plastic events in soft-glassy materials"

We propose a new approach for generating synthetic earthquakes based on the physics of soft
glasses. The continuum approach produces yield-stress materials based on Lattice–Boltzmann
simulations. We show that if the material is stimulated below yield stress, plastic events occur,
which have strong similarities to seismic events. Based on a suitable definition of displacement
in the continuum, we show that the plastic events obey a Gutenberg–Richter law with exponents
similar to those for real earthquakes. We also find that the average acceleration, energy release,
stress drop and interoccurrence times scale with the same exponent. Furthermore, choosing
a suitable definition for aftershocks, we show that they follow Omori’s law. Finally, the far
field power spectra of elastic waves generated by these plastic events decay as ω −2 similar to
those observed for seismic waves. Our approach is fully self-consistent and all quantities can
be calculated at all scales without the need of ad hoc friction or statistical assumptions. We
therefore suggest that our approach may lead to new insights into the physics connecting the
micro- and macroscales of earthquakes.   



Vendredi 23 juin à 11h (salle 2 du LJAD)

Mathias Legrand (McGill)

"Equation des ondes en une dimension et contraintes unilatérales"

Ce travail concerne le calcul des modes de vibration non-linéaires d'une structure mécanique simplifiée, une barre, encastrée à une extrémité et sujette à des conditions de contact unilatéral, à l'autre. Mathématiquement, il s'agit de chercher des familles continues de trajectoires périodiques satisfaisant l'équation d'onde en une dimension d'espace sur le domaine de la barre ainsi que la condition de complémentarité traduisant le contact unilatéral. Ces familles forment alors l'extension de la notion de "modes de vibration" bien connus dans le cadre de la dynamique des structures linéaires. La méthode des éléments finis introduit des difficultés numériques qui peuvent être levées grâce à une variante d'un schéma de type "volumes finis". La résolution numérique permet de dégager des solutions exactes. Le lien entre solutions forcées périodiquement et solutions modales sera illustré à l'aide de diagrammes "Energie-Fréquence".


Vendredi 30 juin à 11h (salle de conférences du LJAD)

Séminaire commun ATG / Interfaces

Elena Magliaro (Mines - Paritech)

"Overview of Loop Quantum Gravity"

La relativité générale et la mécanique quantique sont les deux théories révolutionnaires qui ont changé la physique au siècle dernier. La recherche d’une théorie qui fonde ceux deux théories dans un cadre cohérent est la recherche d’une théorie de la gravité quantique, ou de l’espace-temps quantique.

Aujourd’hui, un programme de recherche prometteur est la gravité quantique à boucles (Loop Quantum Gravity), développée désormais depuis 30 ans. Dans ce séminaire je présenterai les bases de cette théorie, dans sa version hamiltonienne et covariante (mousse de spin) en mentionnant les résultats les plus significatifs.