14
Novembre
ore 12.0014.00
Aula Consiglio 
Lorenzo Marrucci
Molding geometrical structures of light with
liquid crystal tools
A beam of light is
characterized by the following local properties: intensity, phase, and
polarization. In most practical cases, these optical properties are
either uniform or varying in space in a smooth, simple fashion. But it
is nowadays possible to create
strongly spacevariant light beams, in which one or more of these
properties vary in space in a prescribed way, forming nontrivial
geometrical patterns. In other words, it is possible to endow light
with a geometrical “structure”.
We will not be concerned here so much with the case of patterns of
light intensity, which may be considered just as usual optical images.
In my talk, I will mainly focus on optical patterns of phase and/or
polarization. In contrast to intensity, which is defined as a
nonnegative real number, phase and polarization can be represented as
points in closed manifolds, e.g. a circle or a sphere. A pattern of
these properties may then acquire a rich geometrical structure,
including the possible appearance of topological singularities of
different kinds, e.g. optical scalar vortices (singularities of phase)
and vectorvortices (singularities of polarization), a multiplehelix
shape of the optical wavefront, and other rather nontrivial
threedimensional structures of the light field.
While conceiving these structures in theory is often very simple,
realizing them in the lab is usually not as simple. There are today
different tools allowing the experimenter to control the spatial
structure of light. In my talk, I will mainly focus on a relatively
recent invention for generating phase and polarization vortices and
other structures exploiting a singularpatterned liquid crystal cell,
commonly named “qplate”. This name is due to the presence of a
topological singularity of given charge “q” in the medium structure,
exploiting the longrange orientational order that characterizes liquid
crystals. Interestingly, even the working principle allowing this
device to control the structure of light is somehow “geometrical” in
its nature, being related to the socalled “geometric phase”, an
ubiquitous concept crossing many boundaries of physics, ranging from
optics to classical mechanics, to quantum mechanics.

10
Ottobre
ore 12.0014.00
Aula Consiglio 
Claudio Zannoni
Modelling liquid crystals in the bulk and close
to their boundaries
Liquid Crystals (LC) are
anisotropic fluids characterized by long range orientational order and
pair correlations. Mesoscale models, based on the drastic
simplification of representing molecules as simple rigid objects such as
(LC) theories and computer simulations. While these approaches are
still very valuable in obtaining the general properties of complex LC
one of the most important current challenges is to relate a realistic
molecular structure to spherocylinders or ellipsoids or even spins on a
lattice have been the cornerstone of the first generation of liquid
crystal physical observables and predict properties such as
morphologies, order parameters, and phasetransition
temperatures.
Atomistic molecular dynamics (MD) simulations, consisting in the
numerical solution of Newton equations of motion for all the atoms in
the system now start to make this possible, also allowing the test of
classical theories for bulk LC (e.g. MaierSaupe or Onsager). However,
for most practical applications LC are not used in bulk but in thin
films where the LC is aligned with the help of surface interactions, so
it is somewhat surprising that surface effects are still described only
empirically, while little is known on their molecular origin. In the
talk we shall show that computer simulations start to shed some light
on the interfacial behavior of liquid crystals and show examples for
the prediction of the alignment and anchoring of LC at the
interface with different solid surfaces e.g. silicon or crystalline and
glassy silica with different roughness (see figure). Simulations show
in various cases that molecular organizations at the interface differ
radically from those in the bulk, showing either discontinuities or
broad distributions of orientations rather than the simple Dirichlet
type boundary conditions assumed by many continuum type theories. In
the talk an introduction to these systems and a discussion of some open
problems will be presented.

11
Aprile
ore 12.0014.00
Aula Consiglio 
Guido
Montorsi
Analog Digital Belief Propagation and its
application to channel decoders
As required by
information theory, channel codes with long code words
are necessary building blocks in a transmission system to achieve
reliable communications with minimal power and maximal throughputs over
noisy physical channels.
Nowadays capacityachieving large random binary codes are actually
adopted in most telecommunication standards. The breakthrough that
allowed their practical use has been to substitute the optimal maximum
likelihood decoding techniques at the receiver with suboptimal
iterative techniques based on “belief” propagation.
Belief propagation is a powerful inference technique working on graphs
used in many different applications. Graph nodes are associated
to factors or constraints of the model while graph edges are associated
to random variables. Belief propagation algorithm proceeds by
iteratively updating messages associated to the random variables,
according to the constraints imposed by nodes.
In the framework of channel decoding the graph nodes represent the
deterministic, usually linear, code constraints. They are either
associated to a (binary) parity check sum, or to a repetition of
the variable. Belief propagation is initialized with a set of messages
obtained from the noisy channel observations of the transmitted bits
and proceeds iteratively, updating the messages according to the code
constraints until convergence is reached.
Most practically used codes are linear and binary codes, so that
messages propagated in the graph are binary messages usually
represented with a single scalar (the LogLikelihood Ratio).
In order to increase the throughput of communication systems, the use
of non binary codes is an attractive solution as each symbol can
carry more information bits. Non binary codes can be constructed over
groups, rings, or fields and there is a vast literature on
the design of capacity achieving non binary codes.
The extension of the application of belief propagation to the non
binary codes however poses several complexity problems as both message
representation and message updating at check node grows at least
linearly with the cardinality of the non binary alphabet and
consequently exponentially with the increase of required throughput.
In this talk I will start by recalling the fundamental ideas and
terminology beyond binary channel coding constructions and
corresponding iterative decoding with belief propagation and other
iterative techniques. I will then extend the concepts to non binary
codes and summarize the main algorithms and complexity problems related
with them. I will then introduce a new algorithm, named Analog Digital
Belief
Propagation (ADBP) which solves the complexity problems of belief
propagation for non binary codes. I will discuss the main
properties of the algorithm, its possible extensions and code design
problems related to the adoption of this algorithm.
During the talk I will also try to provide some open problems related
to encoding and decoding of non binary codes that will
hopefully stimulate the discussion and the interaction with the
attendees having a mathematical background.

10
Gennaio
ore 11.3013.30
Aula Consiglio 
Vincenzo
Vitelli
Shocks and failure in fragile matter
A minimal model for
studying the mechanical properties of amorphous solids is a disordered
network of point masses connected by springs. At a critical value of
its mean connectivity, such a network becomes fragile: it undergoes a
rigidity transition signaled by a vanishing shear modulus and
transverse sound speed. We first investigate analytically and
numerically the linear and nonlinear viscoelastic response of these
fragile solids by probing how shear fronts propagate through them.
Our approach, that we tentatively label shear front rheology, provides
an alternative route to standard oscillatory rheology. In the linear
regime, we observe at late times a diffusive broadening of the fronts
controlled by an effective shear viscosity that diverges at the
critical point. No matter how small the microscopic coefficient of
dissipation, strongly disordered networks behave as if they were
overdamped because energy is irreversibly leaked into diverging
nonaffine fluctuations. Close to the transition, the regime of linear
response becomes vanishingly small: the tiniest shear strains generate
strongly nonlinear shear shock waves. The inherent nonlinearities
trigger an energy cascade from low to high frequency components that
keep the network away from attaining the quasistatic limit. This
mechanism, reminiscent of acoustic turbulence, causes a superdiffusive
broadening of the shock width.
Finally, we show that the mechanism of failure of such networks,
consists of meandering cracks whose width diverges at the transition.
Thus, upon approaching the critical point, we can effectively zoom
inside the fracture process zone.

