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Geometry, Dynamics and Mechanics Seminar

A series of online seminars aiming at maintaining and reinforcing collaboration and connection among researchers working in the broad field of Geometry, Dynamics and Mechanics.
 

Previous GDMSeminars (list, abstracts, recordings)
 

Upcoming GDMSeminars

  • Tuesday, June 2, 2020, 15:00 GMT
    (08:00 Los Angeles, 10:00 Mexico City, 11:00 New York, 12:00 Rio de Janeiro, 16:00 London, 17:00 Rome, 18:00 Moscow, 23:00 Beijing, 01:00 Sydney)
    Richard Montgomery (UCSC)
    Scattering and Metric Lines
    Zoom ID: 97290551962
    Zoom Password: 411451
    Abstract: Scattering in classical mechanics concerns asymptotics of dynamics under forces decaying at infinity rapidly enough so that trajectories escaping to infinity have asymptotically constant velocities. There are many similarities between classical scattering and the study of globally minimizing geodesics, or "metric lines" in noncompact complete metric spaces as initiated largely through the work of Buseman. Solutions to Newton's equations having fixed energy are - for the most part - geodesics for the Jacobi-Maupertuis metric at that energy. This metric is a singular Riemannian metric whose geodesics are solutions to Newton's equations having that energy.
    We start off with the classical Rutherford scattering, the scattering for the Kepler problem and look at its geodesic reformulation. The Kepler problem admits no metric lines but it does admit metric rays. Does the planar 3-body problem admit metric lines? We do not know. But by Maderna-Venturelli this 3-body problem does admit metric rays connecting any given finite configuration to any asymptotic configuration at infinity. What do the metric lines look like in subRiemannian Carnot geometries? What are scattering states for the N-body problem? Is there a scattering map? What does it look like?
    We will answer some of these questions and point out open problems as we go.

    References

 

  • Tuesday, June 16, 2020, 15:00 GMT
    (10:00 Mexico City, 11:00 New York, 12:00 Rio de Janeiro, 16:00 London, 17:00 Rome, 18:00 Moscow, 23:00 Beijing, 01:00 Sydney)
    François Gay-Balmaz (CNRS-LMD, ENS)
    Geometric variational finite element discretization of compressible fluids
    Zoom ID and Password: .........
    This is a joint seminar with the Workshop Geometric Integration and Computational Mechanics.
    Abstract: We review recent progress made in the development of structure preserving finite element integrators for compressible fluids. This approach combines the geometric formulation of fluid dynamics on groups of diffeomorphisms with finite element discretization techniques. A specific feature of the discrete geometric formulation is the occurrence of a nonholonomic right-invariant distribution on the discrete group of diffeomorphisms, that is shown to be isomorphic to a Raviart-Thomas finite element space. The resulting finite element discretizations correspond to weak forms of the compressible fluid equations that don't seem to have been used in the finite element literature. It extends previous work done on incompressible flows and at the lowest order on compressible fluids. We illustrate the benefits of this geometric approach and present potential future directions. This is a joint work with E. Gawlik.

 

Info

  • Seminars are broadcasted via Zoom.
  • Zoom ID and password will be posted here, and sent to registered participants, about 24 hours before each seminar.
  • The Zoom Meeting Room will open 15 minutes before the beginning of the seminar for socialization.
  • Most seminars will be recorded.

For more information see Info
 

Registration   (Required beginning with the June 16's seminar. )

 

 


Organizers:  Paula Balseiro (UFF),  Francesco Fassò (Padova), Luis García-Naranjo (UNAM), David Iglesias-Ponte (La Laguna), Tudor Ratiu (Shanghai), Nicola Sansonetto (Verona).

For info, requests and suggestions write us at GDMSeminar@math.unipd.it