Publié sur *Mathématiques et Interactions à Nice* (http://math.unice.fr)

**Mardi 23 janvier 2018 à 14 heures en salle I **

**(seminaire commun avec l'équipe GAD)**

**Martin Krupa (LJAD)**

**"The blow-up method in singular perturbation theory and secondary canard solutions"**

In this talk, I will describe how the blow-up method can be applied to desingularize the dynamics near non-hyperbolic points in singular perturbation problems. Subsequently, I will briefly review the classical canard phenomenon and define canard solutions in systems with two or more slow dimensions, by generalizing canard cycles. Such generalized canards can be loosely classified into primary and secondary type and primary canard solutions are typically much easier to find. I will focus on secondary canard solutions and discuss how they can be found using the blow-up approach.

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Archives vidéos (2009-2011) [1]

Archives séminaires (2011-2017) [2]

**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.
```

**Vendredi 15 décembre 2017 **

**Relâche pour cause de la conférence en honneur à Pierre Coullet [3], les 14 et 15 décembre.**

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**Liens:**

[1] http://math.unice.fr/seminairesequipesdi/archives-vid%C3%A9os-des-s%C3%A9minaires-de-l%C3%A9quipe-interfaces

[2] http://math.unice.fr/seminairesequipesdi/archives-des-s%C3%A9minaires-de-l%C3%A9quipe-interfaces

[3] https://nonlinearities.sciencesconf.org