730 research outputs found
Watersheds are Schramm-Loewner Evolution curves
We show that in the continuum limit watersheds dividing drainage basins are
Schramm-Loewner Evolution (SLE) curves, being described by one single parameter
. Several numerical evaluations are applied to ascertain this. All
calculations are consistent with SLE, with ,
being the only known physical example of an SLE with . This lies
outside the well-known duality conjecture, bringing up new questions regarding
the existence and reversibility of dual models. Furthermore it constitutes a
strong indication for conformal invariance in random landscapes and suggests
that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT)
with central charge .Comment: 5 pages and 4 figure
Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
The universality class, even the order of the transition, of the
two-dimensional Ising model depends on the range and the symmetry of the
interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the
critical temperature is generally the same due to self-duality. Here we
consider a sudden change in the form of the interaction and study the
nonequilibrium critical dynamical properties of the nearest-neighbor model. The
relaxation of the magnetization and the decay of the autocorrelation function
are found to display a power law behavior with characteristic exponents that
depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.
On the thermodynamics of first-order phase transition smeared by frozen disorder
The simplified model of first-order transition in a media with frozen
long-range transition-temperature disorder is considered. It exhibits the
smearing of the transition due to appearance of the intermediate inhomogeneous
phase with thermodynamics described by the ground state of the short-range
random-field Ising model. Thus the model correctly reproduce the persistence of
first-order transition only in dimensions d > 2, which is found in more
realistic models. It also allows to estimate the behavior of thermodynamic
parameters near the boundaries of the inhomogeneous phase.Comment: 4 page
Symmetry relation for multifractal spectra at random critical points
Random critical points are generically characterized by multifractal
properties. In the field of Anderson localization, Mirlin, Fyodorov,
Mildenberger and Evers [Phys. Rev. Lett 97, 046803 (2006)] have proposed that
the singularity spectrum of eigenfunctions satisfies the exact
symmetry at any Anderson transition. In the
present paper, we analyse the physical origin of this symmetry in relation with
the Gallavotti-Cohen fluctuation relations of large deviation functions that
are well-known in the field of non-equilibrium dynamics: the multifractal
spectrum of the disordered model corresponds to the large deviation function of
the rescaling exponent along a renormalization trajectory
in the effective time . We conclude that the symmetry discovered on
the specific example of Anderson transitions should actually be satisfied at
many other random critical points after an appropriate translation. For
many-body random phase transitions, where the critical properties are usually
analyzed in terms of the multifractal spectrum and of the moments
exponents X(N) of two-point correlation function [A. Ludwig, Nucl. Phys. B330,
639 (1990)], the symmetry becomes , or equivalently
for the anomalous parts .
We present numerical tests in favor of this symmetry for the 2D random
state Potts model with various .Comment: 15 pages, 3 figures, v2=final versio
Critical Behavior of the Random Potts Chain
We study the critical behavior of the random q-state Potts quantum chain by
density matrix renormalization techniques. Critical exponents are calculated by
scaling analysis of finite lattice data of short chains () averaging
over all possible realizations of disorder configurations chosen according to a
binary distribution. Our numerical results show that the critical properties of
the model are independent of q in agreement with a renormalization group
analysis of Senthil and Majumdar (Phys. Rev. Lett.{\bf 76}, 3001 (1996)). We
show how an accurate analysis of moments of the distribution of magnetizations
allows a precise determination of critical exponents, circumventing some
problems related to binary disorder. Multiscaling properties of the model and
dynamical correlation functions are also investigated.Comment: LaTeX2e file with Revtex, 9 pages, 8 eps figures, 4 tables; typos
correcte
Quenched bond dilution in two-dimensional Potts models
We report a numerical study of the bond-diluted 2-dimensional Potts model
using transfer matrix calculations. For different numbers of states per spin,
we show that the critical exponents at the random fixed point are the same as
in self-dual random-bond cases. In addition, we determine the multifractal
spectrum associated with the scaling dimensions of the moments of the spin-spin
correlation function in the cylinder geometry. We show that the behaviour is
fully compatible with the one observed in the random bond case, confirming the
general picture according to which a unique fixed point describes the critical
properties of different classes of disorder: dilution, self-dual binary
random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure
Observation and control of quantized scattering halos
We investigate the production of s-wave scattering halos from collisions
between the momentum components of a Bose-Einstein condensate released from an
optical lattice. The lattice periodicity translates in a momentum comb
responsible for the quantization of the halos' radii. We report on the
engineering of those halos through the precise control of the atom dynamics in
the lattice: we are able to specifically enhance collision processes with given
center-of-mass and relative momenta. In particular, we observe quantized
collision halos between opposite momenta components of increasing magnitude, up
to 6 times the characteristic momentum scale of the lattice.Comment: 11 pages, 7 figure
The distribution of biodiversity richness in the tropics
We compare the numbers of vascular plant species in the three major tropical areas. The Afrotropical Region (Africa south of the Sahara Desert plus Madagascar), roughly equal in size to the Latin American Region (Mexico southward), has only 56,451 recorded species (about 170 being added annually), as compared with 118,308 recorded species (about 750 being added annually) in Latin America. Southeast Asia, only a quarter the size of the other two tropical areas, has approximately 50,000 recorded species, with an average of 364 being added annually. Thus, Tropical Asia is likely to be proportionately richest in plant diversity, and for biodiversity in general, for its size. In the animal groups we reviewed, the patterns of species diversity were mostly similar except for mammals and butterflies. Judged from these relationships, Latin America may be home to at least a third of global biodiversity
Effect of machining parameters on the uncut fibers of a unidirectional flax fiber reinforced composite
In recent years, flax fiber-reinforced polymers (FFRP) are being widely used due to their inherent properties comparable to those of glass fiber reinforced polymers (GFRP). They are partially biodegradable and light weight with good intrinsic modulus and strength. However, milling these composites introduces defects like a poor surface quality with a lot of uncut fibers. The main objective of this study is to analyze the effect of machining parameters and fiber orientation on the uncut fibers (characterized by the number and length of the uncut fibers) of unidirectional FFRP. A full Split-Split Plot Block design of experiment approach was conducted for the analysis. It is shown that the uncut fibers extent depends significantly on the feed rate, the fiber orientation and the cutting tool geometry. The cutting speed does not influence the quantity of uncut fibers. A low feed rate (0.05 mm/rev) and a cutting tool geometry which enhances the fibers shear with a zero-helix angle are shown to minimize the delamination during the up-milling process of unidirectional flax/epoxy composite
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