Notiziario Scientifico
Settimana dal 9 al 15 dicembre 2013
Lunedì 9 dicembre 2013
Martedì 10 dicembre 2013
Martedì 10 dicembre 2013
Martedì 10 dicembre 2013
Mercoledì 11 dicembre 2013
Mercoledì 11 dicembre 2013
Giovedì 12 dicembre 2013
Giovedì 12 dicembre 2013
Venerdì 13 dicembre 2013
Venerdì 13 dicembre 2013
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it,
o nella casella della posta di Luigi Orsina, entro le ore 9 del venerdì
precedente la settimana di pubblicazione.
Ore 14:30, Aula di Consiglio
Seminario di Analisi Matematica
What is the analogue of the principal eigenvalue for elliptic operators with non-compact resolvents?
Focusing on the case where the lack of compactness is due to the unboundedness of the domain, we
show that the answer depends on the property one is looking for: existence of a positive
eigenfunction, simplicity, lower bound of the spectrum, characterization of the maximum principle.
Indeed, there is not a unique notion fulfilling all such properties in general. In the last part of
the talk we present some recent results concerning degenerate elliptic operators.
Ore 10:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
Zero-sum stochastic games with finite state and action spaces, perfect information, and mean payoff
criteria arise in particular from the monotone discretization of mean-payoff pursuit-evasion
deterministic differential games. When the Markov chains associated to strategies are irreducible,
the value of the game can be computed by using Hoffman and Karp policy iteration algorithm (1966),
which is similar to the one introduced by Denardo (1967) for solving discounted games. A feature of
policy iteration is that the number of iterations is small in practice, whereas in general it can
only be bounded by the number of strategies. Recently, Ye and Hansen, Miltersen and Zwick showed
that policy iteration for one or two player zero-sum stochastic games, restricted to instances with
a fixed discount rate, is strongly polynomial. We shall show that the Hoffman and Karp algorithm is
also strongly polynomial for mean-payoff games with bounded first mean return time to a given state.
The proof is based on methods of nonlinear Perron-Frobenius theory and on a reduction of the
mean-payoff problem to a discounted problem with state dependent discount rate. When no
irreducibility assumption is satisfied (multichain games), the policy iteration algorithm needs to
be adapted to avoid cycling in degenerate iterations. Such an adaptation was proposed by
Cochet-Terrasson and Gaubert (2006), and developped in particular in the software PIGAMES of
Detournay (2012). We shall present numerical results of this algorithm on pursuit-evasion games.
Ore 14:15, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
The planar Euler equations describe the motion of a 2-D inviscid incompressible fluid, and also
arise as a model problem for the study of the barotropic mode (to put it simply, the vertical
average) of the Primitive equations of the ocean. It is a result by Yudovich that, in the
space-periodic case, there exist a unique weak solution to the Euler system whenever the initial
data has bounded vorticity. Relying on a refinement of the sharp A_p weighted bounds for singular
integrals by Buckley, we prove an L^infinity version of Grisvard's shift theorem on domains with
corners, and extend the Yudovich theory of weak solutions for the Euler equations to this class of
domains. We also discuss analogous results for the barotropic mode of the Primitive equations. This
is partly joint work with Roger Temam and Claude Bardos.
Ore 15:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
Two-point boundary value problems (TPBVPs) for conservative systems are studied in the context of
the stationary action principle. For sufficiently short time horizons, this converts dynamical
systems into optimal control problems, and for longer time horizons, into a generalization of such
control problems. One obtains a fundamental solution, whereby two-point boundary value problems are
solved via max-plus convolution of the fundamental solution with a cost function related to the
terminal data. The classical mass-spring system and one-dimensional wave equation are briefly
discussed as examples. The n-body problem under gravitation is then discussed. There, the stationary
action principle formulation is converted to a differential game, where an opposing player maximizes
over a parametrized set of quadratics associated to a type of semiconvex dual of the additive
inverse of the gravitational potential. The fundamental solution for the n-body problem takes the
form of a set in a space whose dimension is related to the number of bodies. Once one computes this
set for a specific set of masses and time-duration, solutions of a large class of TPBVPs Êare
immediately obtainable via max-plus convolution.
Ore 16:00, Aula F, Università di Roma III
I tè di matematica
La spintronica persegue l'utilizzazione dello spin dell'elettrone al fine di sviluppare nuove
funzionalità per i dispositivi elettronici. In quest'impresa si imbatte in problemi
affascinanti di natura fondamentale, che sono interessanti di per se stessi al di là delle
ricadute tecnologiche. In questo seminario presenterò alcuni temi generali della ricerca in
spintronica sia dal punto di vista teorico che da quello sperimentale. In particolare, mi
soffermerò sull'effetto GMR (giant magnetoresistance), sull'effetto Hall di spin e sugli
isolanti topologici.
Ore 16:00, Aula C
Seminario di Finanza Matematica
Phase-space methods have been long used to establish the approximation of quantum dynamics in the
semiclassical regime by classical kinetic equations. This is well understood for smooth potential
fields. Following the Di Perna-Lions-Bouchut-Ambrosio results for the well-posedness of classical
flows under potentials with conical singularities, several recent results have appeared, extending
semiclassical asymptotics for such flows. However, very little is known in the case of full
interaction with multivalued trajectories. In this talk we will present the state of the art on
semiclassical limits for potentials with conical singularities, and some recent results dealing with
multivalued classical flows, and the semiclassical selection principle that can be constructed.
(Joint work with T. Paul, Th. Katsaounis, I. Kyza and G. Makrakis). Links with nonlinear problems
will also be discussed.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
Ore 16:00, Aula 311, Università di Roma III
Seminario di Fisica Matematica
We consider the two dimensional van der Waals' free energy functional, with scaling parameter
epsilon, in the positive quadrant with inhomogeneous Dirichlet boundary conditions. We impose the
two stable phases on the horizontal boundaries and free boundary conditions on the vertical right
boundary. Finally, the datum on the left vertical side is chosen in such a way that the interface
between the pure phases is pinned at some point (0,y). We prove the existence of a critical scaling
of the pin location y where the competing effects of repulsion from the boundary and penalization of
gradients both play a role in determining the optimal shape of the interface. This result develops
the study of the boundary layer in the variational theory of phase separation, which goes back to
the 1987 paper by L. Modica. This is a joint work with L. Bertini and A. Garroni.
Ore 12:00, Aula di Consiglio
Seminari MoMa
The mechanical behaviour of granular materials depends on their grading. Crushing of particles under
compression or shear modifies the grain size distribution, with a tendency for the percentage of
fine material to increase. It follows that the frictional properties of the material and the
critical states are modified as a consequence of the changes in grain size distribution and the
available range of packing densities. The seminar will illustrate some problems connected with the
selection of appropriate descriptors of particle shape (such as e.g., roundness, angularity, and
roughness) and the results of an extended experimental investigation of the evolution of the grading
of an artificial granular material, consisting of crushed expanded clay pellets under different
loading conditions. The changes of grading of the material after isotropic, one-dimensional and
constant mean effective stress triaxial compression are described using a single parameter based on
the ratio of the areas under the current and an ultimate cumulative particle size distribution,
which are both assumed to be consistent with self-similar grading with varying fractal dimension.
Relative breakage is related to the total work input for unit of volume.
Ore 14:30, Aula dei seminari di Fisica, Dipartimento SBAI
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