|
|
Seminari A.A. 2017-2018 |
|
I Seminari si svolgono il martedì alle 14:30 nell'aula 311
del Dipartimento di Matematica
(salvo diversa indicazione)
|
|
|
Relatore |
Titolo |
Data |
|
|
2017-18/
|
Michele Correggi
Università "La Sapienza" |
|
22 Maggio 2018 |
|
|
|
Serena Cenatiempo
GSSI L'Aquila |
|
15 Maggio 2018 |
|
|
|
Margherita Disertori
University of Bonn |
|
8 Maggio 2018 |
|
|
|
Vieri Mastropietro
Università di Milano |
|
17 Aprile 2018 |
|
|
|
Alfonso Sorrentino
Università Tor Vergata |
|
12 Aprile 2018 (giovedì) |
|
|
|
Martin Tassy
University of California |
|
06 Febbraio 2018 |
|
|
|
Monia Capanna
Università dell'Aquila |
|
31 Gennaio 2018 (mercoledì ore 11:30 Aula 211) |
|
|
|
In [1], the author introduces a reaction-diffusion system to model the
pattern formation phenomenon present in morphogenesis. Under the
assumption that the reaction part of the system is stable around an
equilibrium point, he finds condiditions over the diffusion
coefficients under which the hole system is unstable due to the
amplification of non-zero Fourier modes. This phenomenon is known as
Turing instability.
In this talk, we introduce an interacting particle system at which
the latter phenomenon is present. The system is a continuous-time
Markov process that has two coupled discrete toruses with Ising spins
as state-space. The evolution in each torus responds to macroscopic
ferromagnetic Kac's potentials, while the spins in different toruses
interact in a local attractive-repulsive way. About this model, we
prove hydrodynamic limit, and find conditions that guarantee the
occurence of Turing instability.
In the Turing instability regime, we analyze the fluctuations of the
density fields around the equilibrium point (0,0) by studying the
limiting behaviour of the discrete Fourier modes of the system. More
precisely, we prove that, at a time at which the process is
infinitesimal, and under the proper spatial scaling, the unstable
Fourier modes converge to a normal distribution while the rest of the
modes vanish. We finally give a result about pattern formation at a
time that converges to the critical one at which the process starts to
be finite.
[1] A. M. Turing, The chemical basis of morphogenesis.
|
|
|
|
Alexandre Efremov
École Polytechnique Palaiseau |
|
30 Gennaio 2018 |
|
|
|
Yinon Spinka
Tel Aviv University |
|
26 Gennaio 2018 (venerdì) |
|
|
|
Eric Ossami Endo
Universidade de São Paulo |
|
23 Gennaio 2018 |
|
|
|
N.J.B. Aza
Universidade de São Paulo |
|
22 Gennaio 2018 (lunedì ore 11:30) |
|
|
|
Clément Erignoux
IMPA |
|
9 Gennaio 2018 |
|
|
|
Domenico Monaco
Università Roma Tre |
|
21 Novembre 2017 |
|
|
|
Eris Runa
Max Planck Institut |
|
14 Novembre 2017 |
|
|
|
Hugo Duminil-Copin
IHES |
|
7 Novembre 2017 |
|
|
|
Fabio Toninelli
Université Lyon 1 |
|
17 Ottobre 2017 |
|
|
|
Suren Pogosian
Armenian Academy of Sciences |
|
04 Ottobre 2017 (mercoledì aula 211) |
|
|
---|
|
|