Dear Friends,
On Friday, January 17, there will be an ITAMP topical lunch discussion.
Time: 12:00-1:30
Location: B-106 @ Center for Astrophysics (60 Garden Street)
Directions: after entering the lobby of the CfA, turn right to enter the
hallway of the B building. In the hallway, turn right again, and B-106 is
there.
As always pizza will be served.
Speaker: Prof. Bala Sundaram (Chair, Physics Department, U Mass Boston)
Title: Persistent Patterns in Fluids and Wave Mechanics
Abstract:
Persistent patterns in periodically driven dynamics have been reported in a
wide variety of contexts ranging from table-top and ocean-scale fluid
mixing systems to the weak quantum-classical transition in open Hamiltonian
systems. These refer to deviations from homogeneity which is expected under
the prevailing conditions. We illustrate a common framework for the
emergence of these patterns by considering a simple measure of structure
maintenance provided by the average radius of the scalar distribution in
transform space. Using this Dirichlet coefficient, scaling laws related to
both the formation and persistence of patterns in phase space are
presented. Further, within a model system, we directly relate the spectral
properties of the one period advection-diffusion operator to the
phase-space geometry of the Lagrangian advecting field. Parametric
variation allows for the creation of multi-scale mixed phase space
structures where stable islands of various sizes and periodicities co-exist
with extended regions of non-uniformly hyperbolic chaos. The relative
algebraic simplicity of the map and the implementation of an efficient
numerical scheme enable direct computation of a number of the most stable
spectral modes of the advection-diffusion operator for ultra low diffusion
values. Once the diffusive length scale falls below the size of any stable
island structure, a spectral branch containing the dominant eigenmode
behaves diffusively, exhibiting a strong analogy with a quantum particle in
a box. Interspersed with modes localized on the full extent of the
elliptical islands are other families of modes governed by local minima of
the potential. In contrast to the diffusive, square-well modes, the decay
rates of the super-localized, harmonic oscillator modes exhibit distinct
scaling. Simple counting arguments, based on these known scaling relations
and the purely Lagrangian geometry of the map, allows accurate prediction
of the relative importance of the different spectral contributions for any
finite value of the diffusivity. In concluding, we briefly discuss the use
of conformal transformations to analytically extract all aspects of the
spectral scaling.
Looking forward to seeing you there,
Misha Lemeshko
--
Dr. Mikhail Lemeshko
Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP)
Harvard-Smithsonian Center for Astrophysics MS-14
60 Garden St.
Cambridge, MA 02138
U.S.A.
mlemeshko(a)cfa.harvard.edu
http://sites.google.com/site/mishalemeshko/
Tel. +1 (617) 496-7610
Fax +1 (617) 496-7668