Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 20 al 26 marzo 2017
Lunedì 20 marzo 2017
Ore 14:00, aula Amaldi, dipartimento di Fisica
seminario delle Meccaniche
Guido Gentile
Periodic and quasi-periodic attractors of the spin-orbit dynamics of Mercury
Mercury is entrapped in a 3:2 resonance: it rotates on its axis three times for every
two revolutions it makes around the Sun. It is generally accepted that this is due to
the large value of Mercury's eccentricity. However, the mathematical model commonly used
to study the problem -sometimes called the spin-orbit model- proved not to be entirely
convincing, because of the expression used for the tidal torque.
Only recently, a different model for the tidal torque has been proposed, with the
advantage of both being more realistic and providing a higher probability of capture
into the 3:2 resonance with respect to the previous models. On the other hand, a drawback
of the model is that the function describing the tidal torque is not smooth and appears as
a superposition of peaks, so that both analytical and numerical computations turn out to
be rather delicate. We shall present numerical and analytical results about the nature
of the librations of Mercury's spin in the 3:2 resonance, as predicted by the realistic
model. In particular we shall provide evidence that the librations are quasi-periodic in
time, so that the very concept of resonance should be revisited. The analytical results
are mainly based on perturbation theory and leave several open problems, that we shall
discuss.
Lunedì 20 marzo 2017
Ore 14:30, aula C
seminario di Equazioni Differenziali
Pierpaolo Esposito (Università di Roma Tre)
L'equazione di Liouville quasi-lineare
Discutiamo in Rn un risultato di classificazione per l'equazione
di Liouville quasi-lineare che coinvolge l'operatore n-Laplaciano ed una
non-linearità esponenziale.
Passeremo prima di tutto in rassegna il caso semi-lineare in R2
per il quale tre approcci alternativi sono disponibili, e discuteremo poi il caso
quasi-lineare n≥3.
Martedì 14 marzo 2017
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Paolo Podio-Guidugli (Università di Roma Tor Vergata &
Accademia Nazionale dei Lincei)
On the modeling of transport phenomena
Sound modeling is a necessary premise for all problems in
mathematical analysis that are meant to be of interest for applications.
Equations intended to capture the phenomenology of convection, diffusion,
and drift, are no exceptions. Firstly, I will review the deterministic
approach of Continuum Mechanics. Next, I will discuss how probabilistic
counterparts of the basic CM balance equations can be arrived at within
the framework of non-equilibrium Statistical Mechanics. Finally, on moving
from Einstein's and Langevin's probabilistic/stochastic modeling of
Brownian motion, I will briefly introduce anomalous diffusion.
Martedì 21 marzo 2017
Ore 14:30, Main Lecture Hall, GSSI, viale F. Crispi 7 L'Aquila
PDEs Day @GSSI
Thierry Gallay (Grenoble)
Viscous vortex rings with axial symmetry
A three-dimensional incompressible flow is called a vortex ring if the associated
vorticity distribution is concentrated in a solid torus, so that the fluid particles
spin around an imaginary line that forms a closed loop. Such flows are ubiquitous in
nature, and appear to be very stable. For the Euler equations with axial symmetry,
a large family of uniformly translating vortex rings can be constructed by
variational techniques. In the viscous case, we show that the Navier-Stokes
equations have a unique axisymmetric solution without swirl if the initial
vorticity is a circular vortex filament with arbitrarily large Reynolds number.
The solutions constructed in this way are archetypal examples of viscous vortex
rings, and can be thought of as axisymmetric analogues of the self-similar
Lamb-Oseen vortices in two-dimensional flows. This talk is based on a joint
work with Vladimir Sverak (Minneapolis).
Martedì 21 marzo 2017
Ore 15:45, Main Lecture Hall, GSSI, viale F. Crispi 7 L'Aquila
PDEs Day @GSSI
Matteo Novaga (Pisa)
A two phase model with cross and self attractive interactions
I consider a variational model for two interacting phases, subject to cross and
self attractive forces. I discuss existence and qualitative properties of minimizers.
Depending on the strengths of the forces, different behaviors are possible: phase
mixing or phase separation with nested or disjoint phases.
Martedì 21 marzo 2017
Ore 16:30, aula D'Antoni, Università di Roma Tor Vergata
seminario di Analisi Complessa
Chiara de Fabritiis (Università Politecnica delle Marche)
Generalizzazione dell'esponenziale per funzioni s-regolari sui quaternioni
Le funzioni s-regolari sui quaternioni sono state introdotte da Gentili e Struppa una
decina di anni fa come possibile generalizzazione del concetto di funzione olomorfa al
caso del corpo non commutativo dei quaternioni. Dopo aver dato un'introduzione alla
materia, esaminando analogie e differenze con il caso complesso, introdurremo la
*-esponenziale di una funzione regolare e studieremo le sue caratteristiche principali;
in particolare discuteremo quali proprietà dell'esponenziale in ambito complesso
siano ancora vere e quali invece valgano soltanto sotto appropriate condizioni.
(Lavoro in collaborazione con A. Altavilla, Università di Roma Tor Vergata)
Martedì 21 marzo 2017
Ore 17:00, Main Lecture Hall, GSSI, viale F. Crispi 7 L'Aquila
PDEs Day @GSSI
Andrea Corli (Ferrara)
Traveling waves for collective movements on a network
The talk is concerned with the propagation of (semi-) wavefront solutions for scalar
parabolic equations, on the real line or on a network. These equations have a possibly
degenerate diffusion term and, if they are nonhomogeneous, the process has only one
stationary state. They can be interpreted as modeling collective movements (crowd
dynamics, for instance). In the case of a single equation on the real line, the
results concern the existence, regularity, monotone properties of semi-wavefront
solutions; the convergence to wavefront solutions is also discussed. In the case
of a network and without source terms, we find necessary and sufficient conditions
for the existence of wavefronts, which are essentially of algebraic nature.
Mercoledì 22 febbraio 2017
Ore 12:00, aula B
seminario di Modellistica Differenziale Numerica
Stefan Volkwein (Kostanz)
POD-Based Multicriterial Optimal Control by the Reference Point Method
In the talk bicriterial optimal control problem governed by a parabolic partial
differential equation (PDE) and bilateral control constraints is considered.
For the numerical optimization the reference point method is utilized.
The PDE is discretized by a Galerkin approximation utilizing the method of proper
orthogonal decomposition (POD). POD is a powerful approach to derive reduced-order
approximations for evolution problems. Numerical examples illustrate the efficiency
of the proposed strategy. Joint work with S. Banholzer and D. Beermann
Mercoledì 22 marzo 2017
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
seminario di Fisica Matematica
Luca Biferale (Università di Roma Tor Vergata)
Turbulent energy cascades in hydrodynamics and magnetohydrodynamics
We review direct and inverse energy transfer properties of homogeneous turbulence
under different forcing and boundary conditions, from numerical, theoretical and
experimental view points. We review recent numerical studies based on Fourier mode
reduction of the original Navier-Stokes equations to highlight specific properties
of triadic interactions as a function of the helical content and/or of the degree
of locality among the interacting modes. In particular, we distinguish the impact
of different mode-reduction protocols on the mean fluxes, on the intermittent
small-scales fluctuations and on the global regularity of the three dimensional
Navier-Stokes equations.
Mercoledì 22 marzo 2017
Ore 15:00, aula 1B1, dipartimento SBAI
seminario
Thomas Bartsch (Giessen University)
Nonlinear time-harmonic Maxwell equations in bounded domains
Giovedì 23 marzo 2017
Ore 14:30, aula di Consiglio
seminario PDN P(n)
Sunra Mosconi (Università di Catania)
Qualche applicazione della submodularità ai problemi non locali
Descriveremo due applicazioni della submodularità a funzionali coinvolgenti
le norme frazionarie di Gagliardo. La prima &6grave; la dimostrazione della diseguaglianza
di Levy-Stampacchia in un contesto astratto per funzionali convessi submodulari su
lattici di Banach. La seconda è il decadimento delle funzioni che realizzano
la miglior costante nelle disequazioni di Sobolev o Hardy-Sobolev. Verranno inoltre
discusse alcune applicazioni ed alcuni problemi aperti in entrambi i contesti.
Giovedì 23 marzo 2017
Ore 14:30, aula 211, Università di Roma Tre,
l.go san L. Murialdo 1
seminario di Geometria
Lionel Lang (Uppsala University)
Tropical degenerations of curves and Jacobians
A family of planar curves Ct is said to converge to a tropical curve C
in R2 if the corresponding family of amoebas A(Ct) converges
in Hausdorff distance to C (after some rescaling). Our aim is to understand this
convergence abstractly, in terms of the moduli of the underling family of Riemann
surfaces. Doing so, we come to an abstract notion of tropical convergence of families
in Mg to abstract tropical curves.
This notion allows to keep track of the periods of the Riemann surfaces of the family,
unifying two already existing concepts: the Jacobians of algebraic curves and the Jacobians
of Tropical curves. This approach has potential applications in classical problems:
compactification of moduli spaces, Riemann-Schottky, Brill-Noether. We will try to
introduce every object carefully. In particular, no background in tropical geometry
should be required.
Venerdì 24 marzo 2017
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Claudio Bernardi (Sapienza Università di Roma), Antonio Veredice
(Liceo Peano di Monterotondo)
Il codice ISBN
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