| Date: | September 20, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Johnny Guzman, Brown University |
| Title: | Discrete elasticity complexes |
| Abstract: | Mixed finite element methods for elasticity have several advantages
including being robust in the nearly incompressible limit. Since the 2002 paper by Arnold and Winther there have been several inf-sup stable elasticity finite elements (a space for the stress and displacement) developed in two and three dimensions. However, finding an entire elasticity complex remained challenging in three dimensions. In the last few years, a few discrete elasticity complexes have been constructed. I will discuss our construction that uses macro-triangulations.
This is joint work with Snorre Christiansen, Kaibo Hu, Sining Gong, Jay Gopalakrishnan, Michael Neilan. |
|
| Date: | September 27, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Dionisios Margetis, University of Maryland |
| Title: | On a non-Hermitian formalism for many-body Boson quantum dynamics |
| Abstract: | The last three decades have witnessed interesting advances in atomic physics. Notably, the first experimental observation of a single macroscopic quantum state in
trapped atomic gases, known as the phenomenon of ``Bose-Einstein condensation’’, at extremely low temperatures was reported in 1995. Since then, the efforts of physicists to harness
cold atomic gases have expanded considerably. An emergent and far-reaching advance is the highly precise manipulation of atoms by optical or magnetic means in laboratory settings.
In this talk, I will discuss mathematical implications of a physically motivated model for a dilute gas of zero-spin particles (Bosons) with repulsive pairwise interactions at zero temperature.
In particular, I will describe aspects of the excited many-body quantum states of this system by accounting for the scattering of atoms in pairs from the macroscopic state (condensate).
Key in this formulation is a non-unitary transformation of a prototypical many-body Hamiltonian. This transformation makes use of the ``pair-excitation kernel'', a function that satisfies a nonlinear
partial integro-differential equation.
For stationary tates, I will present an existence theory for solutions to this equation in a variational framework. I will also discuss how this theory is intimately connected to the physically
motivated concept of ``quasiparticles’’, or collective excitations, in the atomic gas.
This is joint work with M. Grillakis (UMD) and S. Sorokanich (NIST). |
|
| Date: | October 18, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Sangyun Lee, Florida State University |
| Title: | TBA |
| Abstract: | TBA |
|
| Date: | November 8, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Annalisa Quaini, University of Houston |
| Title: | TBA |
| Abstract: | TBA |
|
| Date: | November 15, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Yulong Xing, Ohio State University |
| Title: | TBA |
| Abstract: | TBA |
|
| Date: | November 29, 2023 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Michael Neilan, University of Pittsburg |
| Title: | TB A |
| Abstract: | TBA |
|
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