Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 10 al 16 luglio 2017
Martedì 11 luglio 2017
Ore 14:30, aula 311, Dipartimento di Matematica e Fisica, Università
di Roma Tre, largo san L. Murialdo 1
seminario di Fisica Matematica
Cyrill Muratov (New Jersey Institute of Technology)
A universal thin film model for Ginzburg-Landau energy with dipolar interaction
We present an analytical treatment of a three-dimensional variational model of a system that
exhibits a second-order phase transition in the presence of dipolar interactions. Within the
framework of Ginzburg-Landau theory, we concentrate on the case in which the domain
occupied by the sample has the shape of a flat thin film and obtain a reduced two-dimensional,
non-local variational model that describes the energetics of the system in terms of the order
parameter averages across the film thickness. Namely, we show that the reduced two-dimensional
model is in a certain sense asymptotically equivalent to the original three-dimensional model for
small film thicknesses.
Using this asymptotic equivalence, we analyze two different thin film limits for the full three-dimensional
model via the methods of Γ-convergence applied to the reduced two- dimensional model.
In the first regime, in which the film thickness vanishes while all other parameters remain fixed, we r
ecover the local two-dimensional Ginzburg-Landau model. On the other hand, when the film thickness
vanishes while the sample's lateral dimensions diverge at the right rate, we show that the system exhibits
a transition from homogeneous to spatially modulated global energy minimizers. We identify a sharp
threshold for this transition.
Mercoledì 12 luglio 2017
Ore 10:30, aula riunioni (primo piano), IAC-CNR, via dei Taurini 19
seminario di Matematica Applicata
Anna Melchiori (IAC-CNR )
A Matheuristic approach for the Quickest Multicommodity k-splittable
Flow Problem (Joint work with Antonino Sgalambro (University of Sheffield, IAC-CNR))
The literature on k-splittable flows [1] provides evidence on how controlling the
number of used paths enables practical applications of flows optimization in many
real-world contexts. Such a modeling feature has never been integrated so far in Quickest
Flows, a class of optimization problems suitable to cope with situations such as emergency
evacuations, transportation planning and telecommunication systems, where one aims to
minimize the makespan, i.e. the overall time needed to complete all the operations [2].
In this talk, in order to bridge this gap, we introduce a novel optimization problem, the
Quickest Multicommodity k-splittable Flow Problem (QMCkSFP). The problem seeks to
minimize the makespan of transshipment operations for given demands of multiple com-
modities, while imposing restrictions on the maximum number of paths for each single
commodity. The computational complexity of this problem is analyzed, showing its
NP-hardness in the strong sense, and an original mixed-integer programming formulation is
detailed. We propose a matheuristic algorithm based on a hybridized Very Large-Scale Neighborhood
Search [3] that, utilizing the presented mathematical formulation, explores multiple
search spaces to solve efficiently large instances of the QMCkSFP. High quality computational
results obtained on a set of benchmark instances are presented and discussed, showing how
the proposed matheuristic largely outperforms a state-of-the-art heuristic scheme
frequently adopted in path-restricted flow problems.
[1] Baier, G., Kohler, E., Skutella, M., On the k-splittable flow problem, Algorithmica 42,
231-248 (2005).
[2] Pascoal, M.M.B., Captivo, M.E.V., Climaco, J.C.N., A comprehensive survey on the
quickest path problem, Annals of Operations Research 147, 5-21 (2006).
[3] Ball, M. O., Heuristics based on mathematical programming, Surveys in Operations
Research and Management Science 16, 21-38 (2011).
Giovedì 13 luglio 2017
Ore 14:30, aula Seminari, dipartimento SBAI (pal. RM004), via A. Scarpa 14
seminario di Analisi Matematica
Fabio Punzo (Politecnico di Milano)
The Porous Medium Equation with Large Initial Data on Negatively Curved Riemannian
Manifolds
We discuss existence and uniqueness of very weak solutions of the Cauchy problem for the porous
medium equation on Cartan-Hadamard manifolds satisfying suitable lower bounds on Ricci curvature,
with initial data that can grow at infinity at a prescribed rate, that depends crucially on the curvature
bounds. Furthermore, we give a precise estimate for the maximal existence time, and we show that
in general solutions do not exist if the initial data grow at infinity too fast. Such results have been
recently obtained jointly with G. Grillo and M. Muratori
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