Stat.Physics seminar

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR



Wednesday, 4 June    -    11:00 a.m.


Seminar Room - first floor ICTP Leonardo Building


S. SASTRY ( Jawaharlal Nehru Centre for Advanced Scientific Research, 
Bangalore )


" Growing length scales, configurational entropy and dynamics in glass 
forming liquids "


Abstract

The relationship between dynamics, a growing length scale associated 
with cooperatively rearranging regions, and configurational entropy 
underlie the Adam-Gibbs theory of dynamics in glass forming liquids.
While the Adam-Gibbs relation between relaxation times and 
configurational entropy has been widely employed to rationalize 
experimental and computer simulation data, attempts to directly study 
the length scales associated with cooperatively rearranging regions 
have been relatively few. Fresh impetus in this direction comes from 
recent studies of spatially heterogeneous dynamics, wherein analysis of 
spatial correlations of the mobility of particles allows estimation of 
a dynamical length.  Finite size scaling is employed in the present 
work to evaluate a dynamical length scale in a model glass forming 
liquid, whose relationship to relaxation times and configurational 
entropy are examined.  Comparison with theoretical predictions reveal 
partial agreement, and yield surprises that require further theoretical 
analysis to resolve.  The configurational entropy is found to determine 
relaxation times for all temperatures and system sizes studied through 
the Adam-Gibbs relation, but the configurational entropy of 
cooperatively rearranging regions grows as the temperature is lowered, 
contrary to the assumptions of Adam-Gibbs theory.

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JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR



Thursday, 5 June    -    3:00 p.m.


Lecture Room 'B' - terrace leve  ICTP Leonardo Building



M. BERRY  ( Bristol University )


Series of lectures on: 'Singularities and asymptotics'


Sixth lecture


" Boundary-varying boundary conditions: The Dirichlet singularity "


Abstract

Waves in a two-dimensional domain with Robin (mixed) boundary 
conditions that vary smoothly along the boundary exhibit unexpected 
phenomena. If the variation includes a ‘D point’ where the boundary 
condition is Dirichlet (vanishing wavefunction), the system is 
singular. For a circle billiard, the boundary condition fails to 
determine a discrete set of levels, so the spectrum is continuous. For 
a diffraction grating defined by periodically-varying boundary 
conditions on the edge of a half-plane, the phase of a diffracted beam 
amplitude remains undetermined.  In both cases, the wavefunction on the 
boundary has a singularity at a D point, described by the polylogarithm 
function.