1,389 research outputs found
Modelling quasicrystals at positive temperature
We consider a two-dimensional lattice model of equilibrium statistical
mechanics, using nearest neighbor interactions based on the matching conditions
for an aperiodic set of 16 Wang tiles. This model has uncountably many ground
state configurations, all of which are nonperiodic. The question addressed in
this paper is whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case. In
particular, we define an appropriate order parameter, prove that it is
identically zero at high temperatures, and show by Monte Carlo simulation that
it is nonzero at low temperatures
Local Complexity of Delone Sets and Crystallinity
This paper characterizes when a Delone set X is an ideal crystal in terms of
restrictions on the number of its local patches of a given size or on the
hetereogeneity of their distribution. Let N(T) count the number of
translation-inequivalent patches of radius T in X and let M(T) be the minimum
radius such that every closed ball of radius M(T) contains the center of a
patch of every one of these kinds. We show that for each of these functions
there is a `gap in the spectrum' of possible growth rates between being bounded
and having linear growth, and that having linear growth is equivalent to X
being an ideal crystal. Explicitly, for N(T), if R is the covering radius of X
then either N(T) is bounded or N(T) >= T/2R for all T>0. The constant 1/2R in
this bound is best possible in all dimensions. For M(T), either M(T) is bounded
or M(T) >= T/3 for all T>0. Examples show that the constant 1/3 in this bound
cannot be replaced by any number exceeding 1/2. We also show that every
aperiodic Delone set X has M(T) >= c(n)T for all T>0, for a certain constant
c(n) which depends on the dimension n of X and is greater than 1/3 when n > 1.Comment: 26 pages. Uses latexsym and amsfonts package
Fluid/solid transition in a hard-core system
We prove that a system of particles in the plane, interacting only with a
certain hard-core constraint, undergoes a fluid/solid phase transition
Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
The paper investigates how correlations can completely specify a uniformly
discrete point process. The setting is that of uniformly discrete point sets in
real space for which the corresponding dynamical hull is ergodic. The first
result is that all of the essential physical information in such a system is
derivable from its -point correlations, . If the system is
pure point diffractive an upper bound on the number of correlations required
can be derived from the cycle structure of a graph formed from the dynamical
and Bragg spectra. In particular, if the diffraction has no extinctions, then
the 2 and 3 point correlations contain all the relevant information.Comment: 16 page
Dilatancy transition in a granular model
We introduce a model of granular matter and use a stress ensemble to analyze
shearing. Monte Carlo simulation shows the model to exhibit a second order
phase transition, associated with the onset of dilatancy.Comment: Future versions can be obtained from:
http://www.ma.utexas.edu/users/radin/papers/shear2.pd
Eficiência de uso da radiação fotossinteticamente ativa de três forrageiras nativas dos campos sulinos sob dois níveis de sombra e a pleno sol.
Este trabalho teve como objetivo determinar a eficiência de uso da radiação fotossinteticamente ativa (EUR) de Paspalum notatum, Paspalum regnellii e Paspalum dilatatum sob 50% e 80% de sombra artificial e a pleno sol, buscando avaliar o potencial de uso destas espécies em sistemas silvipastoris na região sul do país e a utilização de forrageiras nativas nestes sistemas integrados
Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone
The original publication is available at www.springerlink.comNon peer reviewedPostprin
Ground state at high density
Weak limits as the density tends to infinity of classical ground states of
integrable pair potentials are shown to minimize the mean-field energy
functional. By studying the latter we derive global properties of high-density
ground state configurations in bounded domains and in infinite space. Our main
result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the
density increases, while high-density ground states show some pattern if the
Fourier transform is partially negative. The latter confirms the conclusion of
earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and
Likos et al. (2007). Other results include the proof that there is no Bravais
lattice among high-density ground states of interactions whose Fourier
transform has a negative part and the potential diverges or has a cusp at zero.
We also show that in the ground state configurations of the penetrable sphere
model particles are superposed on the sites of a close-packed lattice.Comment: Note adde
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