16,422 research outputs found
Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach
We analyze the Glauber dynamics for a bi-populated Curie-Weiss model. We
obtain the limiting behavior of the empirical averages in the limit of
infinitely many particles. We then characterize the phase space of the model in
absence of magnetic field and we show that several phase transitions in the
inter-groups interaction strength occur.Comment: 18 pages, 3 figure
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
We define the topological entropy per unit volume in parabolic PDE's such as
the complex Ginzburg-Landau equation, and show that it exists, and is bounded
by the upper Hausdorff dimension times the maximal expansion rate. We then give
a constructive implementation of a bound on the inertial range of such
equations. Using this bound, we are able to propose a finite sampling algorithm
which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur
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