7,264 research outputs found
Phase-ordering kinetics on graphs
We study numerically the phase-ordering kinetics following a temperature
quench of the Ising model with single spin flip dynamics on a class of graphs,
including geometrical fractals and random fractals, such as the percolation
cluster. For each structure we discuss the scaling properties and compute the
dynamical exponents. We show that the exponent for the integrated
response function, at variance with all the other exponents, is independent on
temperature and on the presence of pinning. This universal character suggests a
strict relation between and the topological properties of the
networks, in analogy to what observed on regular lattices.Comment: 16 pages, 35 figure
Point configurations that are asymmetric yet balanced
A configuration of particles confined to a sphere is balanced if it is in
equilibrium under all force laws (that act between pairs of points with
strength given by a fixed function of distance). It is straightforward to show
that every sufficiently symmetrical configuration is balanced, but the converse
is far from obvious. In 1957 Leech completely classified the balanced
configurations in R^3, and his classification is equivalent to the converse for
R^3. In this paper we disprove the converse in high dimensions. We construct
several counterexamples, including one with trivial symmetry group.Comment: 10 page
On the density of sets avoiding parallelohedron distance 1
The maximal density of a measurable subset of R^n avoiding Euclidean
distance1 is unknown except in the trivial case of dimension 1. In this paper,
we consider thecase of a distance associated to a polytope that tiles space,
where it is likely that the setsavoiding distance 1 are of maximal density
2^-n, as conjectured by Bachoc and Robins. We prove that this is true for n =
2, and for the Vorono\"i regions of the lattices An, n >= 2
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