For distribution

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR



Tuesday, 15 January    -    12:30 hrs.

Lecture Room 'D' - SISSA Main Building


G. FALKOVICH   ( The Weizmann Institute of Science, Rehovot )

" Broken and emerging symmetries of turbulence "


Abstract

This is a review of most fundamental (symmetry) aspects of turbulence 
for a physical audience.  To excite turbulence, one needs an external 
pumping;  to keep it in a steady state one needs dissipation. Pumping 
and dissipation break symmetries like time-reversibility, isotropy, 
scale invariance.  Since pumping and dissipation act on vastly 
different scales, the question appears what are the statistical 
properties of a system at the intermediate scales (called inertial 
interval or transparency window).   I shall describe both anomalies 
(when the symmetry is not restored even when the symmetry-breaking 
factor goes to zero) and emerging symmetries like conformal invariance. 
In the latter case, by using the language of Schramm-Loewner Evolution 
for analysis of fractal clusters, one discovers a surprising similarity 
between critical phenomena and turbulence.

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JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

	
Wednesday, 16 January    -    11:30 a.m.


Seminar Room - ICTP Main Building   (first floor)

	

A.C.C. COOLEN   ( King's College London )

"Spin models on random graphs with controlled topologies beyond degree 
constraints"



Abstract

We study Ising spin models on finitely connected random interaction 
graphs which are drawn from an ensemble in which not only the degree 
distribution p(k) can be chosen arbitrarily, but which allows for 
further fine-tuning of the topology via preferential attachment of 
edges on the basis of an arbitrary function Q(k,k') of the degrees of 
the vertices involved. We solve these models using finite connectivity 
equilibrium replica theory, within the replica symmetric ansatz. In our 
ensemble of graphs, phase diagrams of the spin system are found to 
depend no longer only on the chosen degree distribution, but also on 
the choice made for Q(k,k'). The increased ability to control 
interaction topology in solvable models beyond prescribing only the 
degree distribution of the interaction graph enables a more accurate 
modeling of real-world interacting particle systems by spin systems on 
suitably defined random graphs.