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 $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_\kappa$, with $\kappa=1.734\pm0.005$, being the only known physical example of an SLE with $\kappa<2$. 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 $c\approx-7/2$.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 $f(\alpha)$ of eigenfunctions satisfies the exact symmetry $f(2d-\alpha)=f(\alpha)+d-\alpha$ 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 $\gamma=(\alpha-d)$ along a renormalization trajectory in the effective time $t=\ln L$. 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 $H(a)$ and of the moments exponents X(N) of two-point correlation function [A. Ludwig, Nucl. Phys. B330, 639 (1990)], the symmetry becomes $H(2X(1) -a)= H(a) + a-X(1)$, or equivalently $\Delta(N)=\Delta(1-N)$ for the anomalous parts $\Delta(N) \equiv X(N)-NX(1)$. We present numerical tests in favor of this symmetry for the 2D random $Q-$state Potts model with various $Q$.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 ($L \leq 16$) 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