Mo
MA

Modelli   Matematici per
 le Applicazioni

Dipartimento di Matematica, Sapienza, Università di Roma

Seminari 2012


4 Maggio

ore 12.00-14.00

Aula Consiglio

David Quéré

On the shapes of water


As we learnt from Young and Laplace, the cohesion of fluids makes them choose specific shapes, in particular spheres at a small scale. We discuss several ways to maintain this ideal shape on a solid, which leads to unique dynamical situations: water pearls do not stick, they run easily and they bounce - a little bit as if they were solid marbles. (But they are not. And the liquid nature of these pearls has interesting consequences on the dynamical shapes they adopt, for example.) The high mobility of liquid pearls implies that tiny forces are sufficient to move them, and we plan to present recent achievements where some asymmetric patterns at a solid surface permit the self-propulsion of the liquid. We would also like to discuss the effects of various fields to control these elusive drops.

30 Marzo

ore 12.00-14.00

Aula Consiglio

Lorenzo Giacomelli

Mathematical models of wetting phenomena

Wetting phenomena at "small" scales (a water drop on a glass, the precorneal tear-film) may be described by quite a few different mathematical models: diffuse interface ones, sharp ones such as the Navier-Stokes equations, and reduced ones such as the lubrication and the quasi-static approximations. Furthermore, they open up fundamental questions whose answer is yet debated, such as the description of the interface (if any) which separates "dry" from "wet" regions. Which model and which answer are most appropriate is likely to depend on the physics of the specific phenomena, and I will provide introductory information for most of them. However, all of these models are grounded on a basic and unifying physical mechanism: the balance of capillary and frictional (e.g. viscous) forces. Enlightening this principle will hopefully help understanding and enjoying the subsequent lectures within this series.

2 Marzo

ore 12.00-14.00

Aula Consiglio

Vittorio Loreto

Recent advances in language dynamics

Language dynamics is an emerging field that focuses on all processes related to the emergence, evolution and extinction of languages. Recently the study of the self-organization and evolution of language and meaning has recently led to the idea that a community of language users can be seen as a complex dynamical system that collectively solves the problem of developing a shared communication framework through the back-and-forth signaling between people.


In this talk I will review some of the progresses made in the last few years and highlight potential future directions for the research in this area. I will discuss in particular several examples corresponding to the early stages of the emergence of a language, namely the emergence of a common lexicon and the emergence of a shared set of linguistics categories. I will point out how synthetic modeling has nowadays reached sufficient maturity to contribute significantly to the ongoing debate in cognitive science. For instance it has been recently possible to reproduce in a numerical model the outcomes of an important experimental survey, the so-called World Color Survey (WCS).


In addition new experimental frameworks are becoming progressively available. Finally I will discuss the crucial issue in linguistics of whether structures of languages we adopt are the outcome of an individual-based process of optimization or rather the result of a complex socially-driven cultural negotiation. I will argue that a general scenario in language dynamics could be such that shared linguistic conventions would not emerge as attractors, but rather as metastable states.

3 Febbraio

ore 12.00-14.00

Aula Consiglio

Steven Strogatz

Social networks that balance themselves

Consider a fully-connected social network of people, companies, or countries, modeled as an undirected complete graph with real numbers on its edges. Positive edges link friends; negative edges link enemies. I'll discuss two simple models of how the edge weights of such networks might evolve over time, as they seek a balanced state in which "the enemy of my enemy is my friend." The mathematical techniques involve elementary ideas from linear algebra, random graphs, statistical physics, and differential equations. Some motivating examples from international relations and social psychology will also be discussed. This is joint work with Seth Marvel, Jon Kleinberg, and Bobby Kleinberg.

http://dueallamenouno.comunita.unita.it/2012/02/04/i-nemici-dei-miei-nemici/

13 gennaio

ore 12.00-14.00

Aula Consiglio

Maurizio Battaglia

Modeling volcano deformation made easy:constraining the source of the 2004-2011 volcano unrest at Mount St Helens (WA).

Precise measurements of ground deformation have become increasingly common as large networks of GPS receivers and borehole strainmeters have been established over the last decade. Complementing this continuous record are comparatively infrequent but spatially dense images of ground deformation from radar satellites, and a long historical record of leveling, Electronic Distance Meter, triangulation, and tilt data. Deformation can arise from tectonic and volcanic forces and from human activities such as aquifer withdrawal or geothermal exploitation. Mathematical models of how the crust deforms in response to different physical processes are required to characterize driving processes and constrain source location, size, orientation, and strength. This information is valuable for hazards forecasting and mitigation.






Seminari 2011


2 dicembre

ore 12.00-14.00

Aula Consiglio

Marco Cuffaro

Plate kinematic models and lithosphere/mantle interactions at mid-ocean ridges

Plate kinematics represents the first evidence of plate tectonic processes and the basics of plate dynamic models. The kinematics of plates is defined by Euler pole and angular velocity, and the main difficulty in describing plate motions is the choice of the reference frame. This problem is solved doing relative analysis, keeping one of the two plates fixed: then, plate displacements can be observed directly and computed by data coming from geology, geophysics and space geodesy. In contrast, there is not a direct way to measure motions relative to the mantle, and they need to be inferred indirectly, using results of relative plate kinematic models. Plate motions in the mantle-framework are useful to understand why plates move and what forces are involved, and also represents the initial conditions for plate dynamic numerical modeling. Tectonic evolution at the base of the oceans is generally obtained, modeling with relative plate motions and steady-state processes. A better way to understand lithosphere/mantle interactions, at mid-ocean ridges, corresponds to plate kinematic analyses with respect to the mantle, modeling time-dependent tectonic processes. Numerical solutions for viscosity flow beneath plates, that thicken with increasing age, provide useful relationships between mantle temperature and thickness of the oceanic lithosphere.

4 novembre

ore 13.00-15.00

Aula Consiglio
Carlo Doglioni

Tectonic asymmetry of the Earth: any relation with tides?

The Earth shows a systematic asimmetry of the first order tectonic features, both along subduction zones, orogens and oceanic rifts.
This signature is consistent with the "westerly" directed rotation of the lithospheric Earth's outer shell (about 100 km). We still do not know why the lithospheric plates move, and why there is such a net rotation of the lithosphere. We are testing the idea that the westward drift and tectonics at plate margins (e.g., earthquakes) are generated by a combination of thermal dissipation of the planet and the body tide. The body tide, or solid Earth tide, is westerly polarized due to the misalignment of the tidal bulge with respect to the Moon and Sun gravitational alignments. This permanent instability should generate a westerly directed moment. The transit of the associated wave should generate a slow, permanent shift in the order of 0.1 mm/half-day.


7 ottobre

ore 12.00-14.00

Aula Consiglio

Claudio Landim

Central limit theorem for Markov processes: the martingale approach

claudio landim