ETD system

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Tesi etd-09142006-181514


Thesis type
Tesi di laurea specialistica
Author
Spadaro, Emanuele Nunzio
email address
e.spadaro@sns.it
URN
etd-09142006-181514
Title
Un modello variazionale per la formazione di strutture periodiche
Struttura
SCIENZE MATEMATICHE, FISICHE E NATURALI
Corso di studi
MATEMATICA
Commissione
Relatore Prof. Alberti, Giovanni
Parole chiave
  • Gamma-convergenza
  • separazione di scala
  • copolimeri a blocchi
  • perturbazione non locale
  • gizburg-landau
Data inizio appello
29/09/2006;
Consultabilità
completa
Riassunto analitico
We study a non local variational problem with both long and short range interactions. The functional in consideration comes from the modellization of diblock copolymer melts, and it is the scalar Ginzburg-Landau functional plus a negative Sobolev norm.
What we are interested in is the periodic structure of the minima of this functional: it is showed by the experiments that solutions of diblock copolymers are highly periodic, for example lamellar, bcc centred spheres, cylindrical tubes, bicontinuous gyroids etc...

We discuss briefly the statistical derivation of the functional; then the 1d case, in which we show that the minima are exactly periodic.
The last chapter is devoted to the study of the general case in higher dimension: we prove that in this case there is a periodic distribution of the energy.
To prove this risult we consider the sharp interface analogous of our functional, which is probably the simpler one with this property.
We prove also a rigorous but abstract connection between this two functional, showing the convergence of the minima.

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