Séminaire Interfaces des mathématiques et systèmes complexes

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Séminaires à Venir

 

Vendredi 15 décembre 2017

Relâche pour cause de la conférence en honneur à Pierre Coullet, les 14 et 15 décembre.

 

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Archives vidéos (2009-2011)

 

Archives séminaires (2011-2017)

 

 

Jeudi 21 septembre 2017 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.

 

 

Mardi 26 septembre 2017 à 11 h (salle de séminaires du LJAD)

Juan Pablo Di Bella ( University of Buenos aires )

"Analysis of transient properties in Dose-Response functions"

Abstract

Sensing extracellular changes initiates signal transduction and is the first
stage of cellular decision-making. Ligand binding to cell membrane
receptors is a key event in those sensing stages. It is rarely certain
whether cellular responses are related to initial changes in receptor
binding or to the level of receptor binding achieved at some later time,
but it is likely that the dynamics of receptor/ligand binding
contributes significantly to the dynamics of the response. Particularly,
certain properties of the sensing steps are usually characterized in
equilibrium, like the value of half-maximal effective concentration, the
dynamic range, and the Hill coefficient. However, if the time constant
of downstream signal transduction steps is shorter than that of
ligand-receptor binding, those properties should be evaluated in
pre-equilibrium. We explored how the main features of these properties,
are being limited when considering different signaling topologies. Two
models of receptor activation, a covalent modification cycle, and a
transcriptional model are considered here, we explored their specific
features and also the effect when we couple some of these modules.

Our results imply that pre-equilibrium sensing is possible depending on the
relation of binding and activation rates. When binding rates are slower
than activation rates, the system can sense high dose concentrations on
pre-equilibrium. Conversely, when binding is faster than activation,
pre-equilibrium sensing properties remains similar than steady state
properties. Moreover, when the time scales are similar, pre-equilibrium
sensing is possible but with certain limitations, depending on the time
constant and the ligand concentration involved on the downstream
process.

 

Vendredi 13 octobre 2017 à 11 h (salle 1 du LJAD)

M. Cencini (ISC-CNR, Rome)

"Facilitated Diffusion of Transcription Factors: role of the genetic background

assessed by stochastic simulations over real energy landscapes"

 

 

Transcription factors are proteins able to bind specific sites of DNA

such as to promote or inhibit DNA transcription.  Such proteins are

able to associate to their target sites faster than the physical limit

posed by diffusion. Such high association rates can be achieved by

alternating between three-dimensional diffusion and one- dimensional

sliding along the DNA chain, a mechanism dubbed Facilitated Diffusion

and proposed in the ’80s by  Berg and von Hippel.

 

In this talk I will discuss the role of the genetic background around the 

target sequences of transcription factors on the one dimensional diffusion

of the proteins along the DNA. In particular, I will

show that the binding energy landscape around the

target sequences of Escherichia coli  and of Bacillus subtilis  is

organized in a funnel-like structure. By means of an extensive computational study

of  a stochastic model for  the  sliding process along the energetic landscapes obtained

from the database I will show that the funnel can significantly

enhance the probability of transcription factors to find their target

sequences when sliding in their proximity. Such enhancement leads to a

speed-up of the association process.

 

Vendredi 27 octobre 2017 à 11 h (salle de séminaires du LJAD)

Jean-Baptiste Fouvry (IAS, Princeton)

"Finite-N effects and the secular evolution of self-gravitating systems"

 

The dynamics of long-range interacting systems generically comprise two phases: first a phase of (violent) collisionless relaxation, followed by a slower phase of collisional relaxation driven by the fluctuations remaining in the system. These fluctuations may either originate from external disturbances, or from the intrinsic graininess of the system. When sourced by finite-N effects, the associated long-term relaxation is captured by the inhomogeneous Balescu-Lenard equation. I will present this kinetic formalism, and emphasise the key mechanisms at play in this context. In particular, I will show how one can account for the constituents' intricate individual trajectories (inhomogeneity), as well as the system's ability to amplify perturbations (self-gravity). I will also review the different approaches that may be used to obtain this kinetic equation, which all offer different insights on these mechanisms. Finally, I will briefly present recent applications of this new framework to investigate the long-term orbital restructuration of astrophysical self-gravitating systems, such as stellar discs and galactic nuclei.

 

Vendredi 1er décembre 2017 à 11 h (salle de réunion de Fizeau)

Harold Berjamin (Aix Marseille)

		"Modélisation de la propagation d’ondes non linéaire dans
 les solides à dynamique lente"
		Le comportement mécanique de solides hétérogènes tels le  grès ou
le béton est fortement non linéaire.
En effet, la vitesse  du son mesurée dans un barreau sous sollicitation
dynamique chute au  court du temps,
puis retrouve sa valeur initiale à l’arrêt de  l’excitation.
Un modèle de milieu continu a été développé afin
de reproduire ces phénomènes. Il comporte une variable d’état scalaire supplémentaire,
qui traduit l’amollissement du matériau.  L’évolution de cette variable d’état
est régie par une  équation thermodynamiquement admissible.
Une méthode numérique de  type volumes finis a été construite pour résoudre
les équations du  mouvement. Qualitativement, les résultats numériques
sont en accord avec des résultats expérimentaux d’acousto-élasticité dynamique
et de résonance non linéaire.

Vendredi 8 décembre 2017 à 11 h (salle de réunion de Fizeau)

Simon Thalabard (Oca Nice)

"Turbulent dispersion from a point-source: Insights from Markovian models."

		Modeling how particles separate in a
turbulent environment is a long-standing problem, that can be traced
back to Richardson’s seminal description of the dispersion of particles
clusters in terms of a scale-dependent diffusivity. One example of a practical
outcome is to determine how localized injection statistics translate
into large scale inhomogeneities for the concentration field, whose
spatial patterns stem from an intricate interplay between the source
statistics and the Lagrangian statistics of the turbulent field.
In this talk, I will highlight this interplay in the idealized
``point-source’’ setting, using simple Markovian models for the
turbulent velocity field, such as the Kraichnan model and variations thereof.
While unrealistic, those models provide an insightful framework
to analyze genuine turbulent datasets, as obtained from direct
numerical simulations. If time permits, I will then discuss various
ideas that can be used to incorporate Non-Markovian effects,
in order to better capture the statistics of extreme Lagrangian events.