Next weeks' seminars

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR


MONDAY, 14 April    -    3:30 p.m.


Seminar Room- ICTP Leonardo Building-1st floor


S. FLACH  (Max-Planck Institute for the Physics of Complex Systems, 
Dresden)


" Periodic orbits, localization in normal mode space, and the 
Fermi-Pasta-Ulam problem "


Abstract

In 1955 Fermi, Pasta and Ulam (FPU) reported on the nonequipartition of 
a nonlinear atomic chain, with initially one normal mode excited.  
Modern computational studies show, that on a first, relatively short, 
time scale the energy is distributed among a few neighbouring modes in 
modal space, with more distant modes being exponentially weakly excited 
- i.e., one observes localization in normal mode space.  On a much 
larger second time scale (which was not reachable wih the MANIAC I), 
the tail modes are slowly growing, and finally the system does 
equilibrate. The problem then is to explain i) the exponential 
localization of energy in modal space on intermediate time scales, and 
ii) the way the time scales depend on the essential parameters (wave 
number, energy density).  Despite its strong impact on nonlinear 
dynamics and statistical physics, the paradox remained essentially 
unexplained for decades - ideal grounds for the appearance of myths.
Recent studies show that the model allows for exact time-periodic 
solutions (q-breathers), which are exponentially localized in the space 
of normal modes. The trajectory initially computed by FPU is a slight 
perturbation away from an exact q-breather orbit. Consequently most of 
the key observations related to the FPU problem (localization of energy 
in normal mode space for long times, recurrence on relatively short 
times,  system size and energy thresholds) are captured by the 
properties of q-breathers and the phase space flow nearby.  The 
underlying concept is much more general, and can be easily extended to 
two-and three-dimensional finite lattices.  A scaling approach leads to 
nontrivial predictions in the limit of infinite system sizes.

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JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR


Tuesday, 15 April    -    12:30 hrs.


Seminar Room - ICTP Leonardo Building - 1st floor


J.-M. MAILLARD (LPTMC, CNRS and Universite' Pierre et Marie Curie, 
Paris VI)

" From holonomy of the non-critical Ising model form factors to n-fold 
integrals and the theory of elliptic curves, moduli spaces,... and 
beyond "



Abstract

We recall the form factors of the two-point diagonal correlation 
function of the Ising model on the square lattice and their associated 
linear differential equations which exhibit both a "Russian-doll'' 
nesting,  and a decomposition of the linear differential operators as a 
direct sum of operators.
The scaling limit of these differential operators breaks the direct sum 
structure but not the  "Russian doll'' structure, the "scaled'' linear  
differential operators being no longer Fuchsian.
We also discuss the nature of the singularities emergingfrom this 
approach.

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									07/09

JOINT ICTP/SISSA CONDENSED MATTER SEMINARS
Academic Year 2007/08



Seminar Room - Leonardo Building  (first floor)



Tuesday, 15 April -     11:00 a.m.


G. BUSSI  ( E.T.H.  Zürich, Lugano )


" New approaches in molecular dynamics: From stochastic thermostats to 
rare-event sampling "


Abstract

A new molecular-dynamics algorithm for sampling the canonical 
distribution will be presented [1].
In this approach the velocities of all the particles are rescaled by a 
properly chosen random factor.
Its properties will be illustrated for Lennard-Jones and water in the 
solid and liquid phases.
Next, a method for determining the free-energy dependence on a selected 
number of order parameters using an adaptive bias will be introduced 
[2]. This method has metadynamics and canonical sampling as limiting 
cases and allows for easy and rigorous error control.
Finally, a new technique based on a combination of metadynamics and 
parallel-tempering will be discussed [3].
This scheme will be shown to be an affordable method for the 
computation of free-energy landscapes in biomolecules.  The folding of 
the beta-hairpin in explicit water will then be used to illustrate the 
power of this technique.
[1] G. Bussi, D. Donadio and M. Parrinello, J. Chem. Phys. 126, 014101 
(2007)
[2] A. Barducci, G. Bussi and M. Parrinello, Phys. Rev. Lett. 100,  
020603 (2008).
[3] G. Bussi, F. L. Gervasio, A. Laio and M. Parrinello, J. Am. Chem.  
Soc. 128, 13435 (2006).