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A popular theory of self-organized criticality predicts that the stationary density of the abelian sandpile model equals the threshold density of the corresponding fixed-energy sandpile. We recently a...
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals th...
Quasi-polynomial mixing of the 2D stochastic Ising model with "plus" boundary up to criticality
Ising model Mixing time Phase coexistence Glauber dynamics
2011/1/18
We considerably improve upon the recent result of [34] on the mixing time of Glauber dynamics for the 2d Ising model in a box of side L at low temperature and with random boundary conditions whose dis...
Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/20
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and
v denotes the matrix mu...
Many of life's most fascinating phenomena emerge from interactions among many elements|many
amino acids determine the structure of a single protein, many genes determine the fate of a cell,many neuro...
Self-organized criticality as a precursor of fatigue: application to shape memory alloys
Adaptation and Self-Organizing Systems (nlin.AO)
2010/11/10
Fatigue failure can be thought by studying the collective motions of defects inside materials instead of focusing on the growth of a pre-existing micro-crack. An experimental study of the statistical ...
Notes on factor-criticality, extendibility and independence number
Notes on factor-criticality independence number
2010/11/19
In this paper, we give a sufficient and necessary condition for a $k$-extendable graph to be $2k$-factor-critical when $k=\nu/4$, and prove some results on independence numbers in $n$-factor-critical ...
Equivalence between Extendibility and Factor-Criticality
Extendibility Factor-Criticality
2010/11/19
In this paper, we show that if $k\geq (\nu+2)/4$, where $\nu$ denotes the order of a graph, a non-bipartite graph $G$ is $k$-extendable if and only if it is $2k$-factor-critical. If $k\geq (\nu-3)/4$...
Symmetric Criticality in Classical Field Theory
Symmetric Criticality Classical Field Theory
2010/11/22
This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais' Principle of Symme...