Séminaire Interfaces des mathématiques et systèmes complexes

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Séminaires à Venir

Mardi 17 Décembre 2019 à 14 heures en salle Fizeau du LJAD

Prof. Aziz-Aloui (Université du Havre) LMAH, ISCN, FR-CNRS-3335, France.


" Systèmes complexes et réseaux d'interaction. Application au comportement asymptotique de réseaux de systèmes de réaction-diffusion en neuroscience et en écosystèmes "

"Complex Systems and Interaction Networks: Application to the Asymptotic
Behavior of Networks of Reaction-Diffusion Systems in Neuroscience
and Ecosystems"



Neuroscience consists of the study of the nervous system and especially the brain.
The neuron is an electrically excitable cell processing and
transmitting information by electrical and chemical signaling, the
latter via synapses, specialized connections with other cells.
A. L. Hodgkin and A. Huxley proposed the first neuron
model to explain the ionic mechanisms underlying the initiation and
propagation of action potentials in the squid giant axon. Here, we
are interested in the asymptotic behavior of complex networks of
reaction-diffusion (PDE) systems of such neuron models. We show the
existence of the global attractor and the identical synchronization
for the network. We determine analytically, for a given network
topology, the onset of such a synchronization. We then present
numerical simulations and heuristic laws giving the minimum coupling
strength necessary to obtain the synchronization, with respect to the
number of nodes and the network topology.






Archives vidéos (2009-2011)


Archives séminaires (2011-2019)


Vendredi  8  Novembre 2019  à 11 h (salle de conf du LJAD)

Oleksandr Chepizhko (Innsbruck Univ.)

'Transport properties of circle microswimmers in heterogeneous media '


We simulate the dynamics of a single circle microswimmer exploring a disordered array of fixed obstacles. The microswimmer moves on circular orbits in the freely accessible space and follows the surface of an obstacle for a certain time upon collision. Two cases are considered, an ideal microswimmer[1] and a microswimmer subject to rotational diffusion[2]. Depending on the obstacle density and the radius of the circular orbits, the microswimmer displays either long-range transport or is localized in a finite region.
We show that for the ideal microswimmer there are transitions from two localized states to a diffusive state each driven by an underlying static percolation transition. We determine the non-equilibrium state diagram and calculate the mean-square displacements and diffusivities by computer simulations. Close to the transition lines transport becomes subdiffusive which is rationalized as a dynamic critical phenomenon.
The interplay of two different types of randomnesses, quenched disorder and time-dependent noise, is investigated to unravel their impact on the transport properties of the microswimmer subject to the rotational diffusion. We compute lines of isodiffusivity as a function of the rotational diffusion coefficient and the obstacle density. We find that increasing noise or disorder tends to amplify diffusion, yet for large randomness the competition leads to a strong suppression of transport. We rationalize the suppression and amplification of transport by comparing the relevant time scales of the free motion to the mean-free path time between collisions with obstacles.

1. O. Chepizhko, T. Franosch, Soft Matter, 2019, 15, 452
2. O. Chepizhko, T. Franosch, submitted