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Explicitly solvable models and their applications to current challenges in mechanics and wave propagation

Venue: CIMAT, Unidad Mérida. 

The meeting will provide an overview and a discussion forum for modelling the behaviour of highly heterogeneous media using "explicitly solvable" formulations, e.g. by replacing an operator in an infinite-dimensional space by a finite-size matrix. The analysis of the related approximation error and the implications of such effective formulations on spectral properties and wave propagation will span the range of the discussion topics.


Talk schedule

Wednesday 4 January

10:30--11:30: Kirill Cherednichenko "..."

11:30--12:00: Coffee

12:00--13:00: Mikhail Cherdantsev "..."

13:00-14:00: Lunch at CIMAT

14:00--15:00: Luis Octavio Silva "..." 

15:00--16:00: Coffee and open research discussion

Thursday 5 January

10:00--11:00: Danila Prikazchikov "Nonlocally elastic Rayleigh-type waves"

Abstract: Nonlocally elastic surface waves are studied within both integral and differential formulations, and the issue of their non-equivalence is discussed. Consistent differential constitutive relations assuming an extra boundary condition along the surface are proposed. Both antiplane shear and Rayleigh waves are considered. The asymptotic procedure is developed, incorporating the contribution of nonlocal boundary layers. It is shown that the associated nonlocal correction to the classical Rayleigh wave speed is of order of microscale parameter, which is by order of magnitude higher than that originating from the equations of motion obtained by Eringen. In addition, it appears that the nonlocal boundary layers also support nonlocal shear surface waves which are not the feature of classical elasticity. An explicit formulation for the nonlocally elastic Rayleigh wave excited by a prescribed surface loading is also derived.

11:00--11:30: Coffee

11:30--12:30: Yulia Ershova "Derivation of instantaneous frequencies of tectonic plates from gravimetric data"

Abstract: We present a mathematically rigorous procedure to obtain spectrograms of tectonic plate eigenmodes in an extremely low-frequency band, corresponding to oscillation periods of 15 min to 8 hours. The data is sourced from superconducting gravimeters (IGETS network). The motivation for this research stems from the proposal by Pavlov et al to use this spectral data in monitoring of the state of active zones located along plate boundaries.

12:30-13:30: Lunch at CIMAT

13:30--14:30: Yi Sheng Lim "..."

14:30--15:00: Coffee

15:00--16:00: Julius Kaplunov "Asymptotic analysis of thin walled transversely inhomogenenous structures"


Monday 9 January

10:30--11:30: Gerardo Martin Franco "Levinson theorem for matrix-valued Schrödinger operators on the discrete line"

Abstract: We consider matrix-valued Schrödinger operators on the discrete line with a non-compactly supported perturbation whose first moment is assumed to exist. We derive explicit formulas for the scattering matrix and extend them to the band edges. We then prove a Levinson theorem, which establishes a relation between scattering data and spectral properties (bound and half-bound states) of the corresponding Hamiltonians.

11:30--12:00: Coffee

12:00--13:00: Alexander Kiselev "An example of a phase transition in a periodic tubular structure"


13:00-14:00: Lunch at CIMAT

14:00--15:00: Josip Žubrinić "..."

15:00--16:00: Coffee and open research discussion



Kirill Cherednichenko
Alexander Kiselev
Yi Sheng Lim
Matthew Glenn Dawson
Rafael Herrera Guzmán
Adolfo Sánchez Valenzuela
Rafael del Rio
Gerardo Martin Franco
Luis Octavio Silva
Josip Žubrinić
Mikhail Cherdantsev (Cardiff)
Yulia Ershova (Texas A&M)
Julius Kaplunov (Keele)
Danila Prikazchikov (Keele)
Vladimir Ryzhov