[ingegneria-matematica] (no subject)

[Giuseppe Tomassetti < >]

Il prof. Paolo Biscari (Politecnico di Milano) terra' due seminari presso il
Dipartimento di Matematica dell'Universita` di Roma II


Giovedi' 19, ore 16.00 aula Dal Passo
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Order, disorder, and defects in liquid crystals

Abstract: The talk covers a variety of problems, related to
variational theories of liquid crystals.
In the first part of the seminar we examine the properties of novel
liquid crystal phases, recently synthesized and observed, for which a
satisfactory continuum theory is still missing.
In the second part, we will review some recent results which explain
some effects peculiar to nematic liquid crystals, and deeply linked
with the possibility for the molecules to locally reduce their degree
of orientation.
Finally, we describe how it is possible to drive the motion of liquid
crystal defects through suitable external magnetic fields, and present
an asymptotic theory which includes the coupling between micro- and
macroscopic dynamics.


Venerdi' 20, ore 14.00 aula Dal Passo.
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Mathematical models of lipid membranes.

Abstract: Lipid membranes are aggregates of amphiphilic molecules,
which consist of a hydrophilic head and one or more hydrophobic tails.
Living in an aqueous environment, these molecules tend to form
bilayers where the hydrophobic parts are hidden by the hydrophilic
ones, and so their contact with water is reduced. A further reduction
is obtained when the bilayer closes itself to form a vesicle, which is
modeled as a compact, two-dimensional surface. We will first survey
the classical results concerning the analysis of the elastic energy
functional which determines the equilibrium vesicle shapes when both
their area and enclosed volume are fixed.
Proteins, thought of as rigid bodies, are usually modelled as small
cones. When embedded in a lipid bilayer, they modify the membrane
configuration by fixing the direction of the surface normal at the
contact points. In the two-dimensional approximation, where the
membrane shape is modeled by a closed curve, we determine the exact
equilibrium shape of the membrane in the presence of one or more
proteins. The excess of elastic energy induced by the proteins gives
rise to a mediated interaction between them. The interaction may be
either attractive or repulsive, depending on the protein shape and
relative distance. In the three-dimensional case, however, the
panorama changes: the shape perturbations induced by the proteins are
strongly localized and decay within a characteristic length-scale of
the order of the protein diameter. Asymptotic methods allow to derive
the analytical shape of the perturbation, the effective potential
which identifies the optimal places where the protein prefers to sit,
and the effective interaction between proteins, mediated by the
membrane elasticity.

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email;internet:
 
tel;work:0672597049
tel;cell:3204223325
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