Prossimi notiziari settimanali

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Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma

Settimana dal 25-02-2019 al 03-03-2019

Martedì 26 febbraio 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Seminario di Modellista Differenziale Numerica
Ourania Giannopoulou (Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma)
Chorin’s approaches revisited: Particle Vortex Method vs Finite Volume Method
In this work a Vortex Particle Method is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on Chorin’s operator splitting approach, consisting of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz-Hodge Decomposition, while the no–slip condition is enforced by an indirect boundary integral equation. No mesh is used for the solution of the Poisson equation for the velocity (advection step) and the diffusion step is performed on a Regular Point Distribution with no topological connection; therefore, the resulting algorithm is completely meshless. We also revise the use of the same decomposition for the solution of the Navier–Stokes equations in primitive variables and its role in maintaining the divergence–free constraint. The results are compared with those obtained by a mesh-based Finite Volume Method, where the pseudo-compressible iteration is exploited to enforce the solenoidal constraint on the velocity field. Several benchmark tests were performed for verification and validation purposes; in particular, the unsteady flow past a circular cylinder, an ellipse with incidence and an equilateral triangle was simulated for several values of the Reynolds number.

Mercoledì 27 febbraio 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di Dipartimento
Alberto Abbondandolo (Ruhr-Universität Bochum)
On short closed geodesics, shadows of balls and polar bodies
How long is the shortest closed geodesic on a Riemannian sphere? How large is the shadow of a symplectic ball? How large is the volume of the polar of a centrally symmetric convex body? I will discuss how these seemingly different problems can be addressed within the setting of Reeb dynamics.

Mercoledì 27 febbraio 2019
Ore 16:30, aula di Consiglio, Dipartimento di Matematica
seminario di Fisica Matematica
Claudio Cacciapuoti (Università degli Studi dell'Insubria)
Scattering from local deformations of a semitransparent plane
I will discuss the scattering problem for a quantum particle in dimension three in the presence of a semitransparent unbounded obstacle, modeled by a surface. The generator of the dynamics is the operator formally defined as the Laplacian plus a delta-interaction supported by the surface. I will consider the case in which the surface is obtained through a local deformation of a plane, it can be identified by the graph of a compactly supported, Lipschitz continuous function. In this configuration, the reference dynamics is the one generated by the Laplacian plus a delta-interaction supported by the plane. I will discuss existence and asymptotic completeness of the wave operators, provide a representation formula for the scattering matrix, and show that the scattering matrix converges to the identity as the deformation goes to zero (with a quantitative estimate on the rate of convergence). The talk is based on the joint paper with Davide Fermi and Andrea Posilicano: J. Math. Anal. Appl. 473 (2019) 215–257.

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