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| Seminari A.A. 2019-2020 |
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Relatore |
Titolo |
Data |
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Christoph Lehner
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17 dicembre 2019 |
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Chiara Boccato
IST Austria |
12 novembre 2019 |
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Maxime Hauray
Univeristé Aix-Marseille |
05 novembre 2019 |
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Nguyen Tong Xuan
GSSI L'Aquila |
28 ottobre 2019 (lunedì) |
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Sara Daneri
GSSI L'Aquila |
22 ottobre 2019 |
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Abstract ritorna |
In this talk I will review some recent results obtained in
collaboration with E. Runa and A. Kerschbaum on the one-dimensionality
of the minimizers of a family of continuous local/nonlocal interaction
functionals. Such functionals have a local term, typically the
perimeter or its Modica-Mortola approximation, which penalizes
interfaces, and a nonlocal term favouring oscillations which are high
in frequency and in amplitude. The competition between the two terms
is expected by experiments and simulations to give rise to periodic
patterns at equilibrium.
Functionals of this type are used to model pattern formation, either
in material science or in biology. The difficulty in proving the
emergence of such structures is due to the fact that the functionals
are symmetric with respect to permutation of coordinates, while
minimizers are not. We will present results showing that for two
classes of functionals (used to model generalized anti-ferromagnetic
systems, respectively colloidal suspensions), both in sharp interface
and in diffuse interface models, minimizers are one-dimensional and
periodic, in general dimension. In the discrete setting such results
had been previously obtained by Giuliani and Seiringer.
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Horst Knörrer
ETH Zürich |
15 ottobre 2019 |
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