Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite $N$. The Vlasov stationary solution is shown to give the same consistency equation of the canonical solution and its predictions for rotator angle and momenta distribution functions agree very well with numerical simulations. A link is established between the behavior of the maximal Lyapunov exponent and that of thermodynamical fluctuations, expressed by kinetic energy fluctuations or specific heat. The extensivity of chaos in the $N \to \infty$ limit is tested through the scaling properties of Lyapunov spectra and of the Kolmogorov-Sinai entropy. Chaotic dynamics provides the mixing property in phase space necessary for obtaining equilibration; however, the relaxation time to equilibrium grows with $N$, at least near the critical point. Our results constitute an interesting bridge between Hamiltonian chaos in many degrees of freedom systems and equilibrium thermodynamics.Comment: 19 pages, 10 postscript figures included, Latex, Elsevier macros included. Invited talk at the conference ``Classical Chaos and its quantum manifestations'' in honour of Boris Chirikov, Sputnik conference of STATPHYS 20 - Toulouse, France - July 16-18, 1998. Revised version (added refs, changed part of the text and some figures) accepted for publication in Physica

Coping with poverty in a Cairo community

The monograph, a sociological study by a Western social scientist working in Egypt, on a popular quarter of Cairo. The study of the traditional quarters of the great cities of the Middle East has been a very much neglected area of research; in this monograph, bringing painstaking reseach and impressive sociological insight to bear, is our contribution towards folling the gap

International Development In Practice: Education Assistance In Egypt, Pakistan, And Afghanistan

https://works.swarthmore.edu/alum-books/3955/thumbnail.jp

Family In Contemporary Egypt

https://works.swarthmore.edu/alum-books/3880/thumbnail.jp

The Political Culture Of Leadership In The United Arab Emirates

https://works.swarthmore.edu/alum-books/4190/thumbnail.jp

Simple Gestures: A Cultural Journey Into The Middle East

https://works.swarthmore.edu/alum-books/4105/thumbnail.jp