575 research outputs found
Force--induced depinning of directed polymers
We present an approach to studying directed polymers in interaction with a
defect line and subject to a force, which pulls them away from the line. We
consider in particular the case of inhomogeneous interactions. We first give a
formula relating the free energy of these models to the free energy of the
corresponding ones in which the force is switched off. We then show how to
detect the presence of a re-entrant transition without fully solving the model.
We discuss some models in detail and show that inhomogeneous interaction, e.g.
disordered interactions, may induce the re-entrance phenomenon.Comment: 15 pages, 2 figure
Continuum limit of random matrix products in statistical mechanics of disordered systems
We consider a particular weak disorder limit ("continuum limit") of matrix
products that arise in the analysis of disordered statistical mechanics
systems, with a particular focus on random transfer matrices. The limit system
is a diffusion model for which the leading Lyapunov exponent can be expressed
explicitly in terms of modified Bessel functions, a formula that appears in the
physical literature on these disordered systems. We provide an analysis of the
diffusion system as well as of the link with the matrix products. We then apply
the results to the framework considered by Derrida and Hilhorst [J. Phys. A
(1983)], which deals in particular with the strong interaction limit for
disordered Ising model in one dimension and that identifies a singular behavior
of the Lyapunov exponent (of the transfer matrix), and to the two dimensional
Ising model with columnar disorder (McCoy-Wu model). We show that the continuum
limit sharply captures the Derrida and Hilhorst singularity. Moreover we
revisit the analysis by McCoy and Wu [Phys. Rev. 1968] and remark that it can
be interpreted in terms of the continuum limit approximation. We provide a
mathematical analysis of the continuum approximation of the free energy of the
McCoy-Wu model, clarifying the prediction (by McCoy and Wu) that, in this
approximation, the free energy of the two dimensional Ising model with columnar
disorder is but not analytic at the critical temperature.Comment: 46 pages, one figure. Introduction reorganized, Proposition 1.5
corrects Proposition 1.6 of v2. Several other scattered modification
Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder
We consider disordered models of pinning of directed polymers on a defect
line, including (1+1)-dimensional interface wetting models, disordered
Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional
polymers in interaction with columnar defects. We consider also random
copolymers at a selective interface. These models are known to have a
(de)pinning transition at some critical line in the phase diagram. In this work
we prove that, as soon as disorder is present, the transition is at least of
second order: the free energy is differentiable at the critical line, and the
order parameter (contact fraction) vanishes continuously at the transition. On
the other hand, it is known that the corresponding non-disordered models can
have a first order (de)pinning transition, with a jump in the order parameter.
Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made.
To appear on Phys. Rev. Let
Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case
We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only log-Hölder continuous
The Zeros of the Partition Function of the Pinning Model
We aim at understanding for which (complex) values of the potential the pinning partition function vanishes. The pinning model is a Gibbs measure based on discrete renewal processes with power law inter-arrival distributions. We obtain some results for rather general inter-arrival laws, but we achieve a substantially more complete understanding for a specific one parameter family of inter-arrivals. We show, for such a specific family, that the zeros asymptotically lie on (and densely fill) a closed curve that, unsurprisingly, touches the real axis only in one point (the critical point of the model). We also perform a sharper analysis of the zeros close to the critical point and we exploit this analysis to approach the challenging problem of Griffiths singularities for the disordered pinning model. The techniques we exploit are both probabilistic and analytical. Regarding the first, a central role is played by limit theorems for heavy tail random variables. As for the second, potential theory and singularity analysis of generating functions, along with their interplay, will be at the heart of several of our arguments
Two new species from the brevantherum clade of solanum (solanaceae) from eastern Brazil
pre-printTwo new species of Solanum (Solanaceae) from eastern Brazil are described. Solanum anisocladum Giacomin & Stehmann is similar to S. megalochiton Mart., but differs by the indument of the adaxial leaf surface, which is composed of long porrect-stellate and unbranched trichomes. It also has a more robust habit and a unique branching pattern of the flowering stems. It is restricted to the Atlantic Rainforest of northeastern Brazil and was previously misidentified as S. megalochiton. The other species, Solanum caelicolum Giacomin & Stehmann, is endemic to Espírito Santo state and is most similar to S. hirtellum (Spreng.) Hassl., but differs mainly by its adaxial leaf indument, with porrect-stellate trichomes with a central ray smaller than the lateral ones, by its comparatively larger fruiting calyx that can reach up to three times the diameter of the mature berry and by its sessile to subsessile unbranched congested inflorescence. Both species belong to the Brevantherum clade, one of the main lineages identified in the genus Solanum, and are placed together in a clade which contains species from S. sects. Extensum D'Arcy and Stellatigeminatum Child. Complete descriptions, distributions, and preliminary conservation assessments of the new species are given
Shear Stress Measurements of Non-Spherical Particles in High Shear Rate Flows
The behavior of liquid-solid flows varies greatly depending on fluid viscosity; particle and liquid inertia; and collisions and near-collisions between particles. Shear stress measurements were made in a coaxial rheometer with a height to gap ratio (b/r0) of 11.7 and gap to outer radius ratio (h/b) of 0.166 that was specially designed to minimize the effects of secondary flows. Experiments were performed for a range of Reynolds numbers, solid fractions and ratio of particle to fluid densities. With neutrally buoyant particles, the dimensional shear stress exhibits a linear dependence on Reynolds number: the slope is monotonic but a non-linear function of the solid fraction. Though non-neutrally buoyant particles exhibit a similar linear dependence at higher Reynolds numbers, at lower values the shear stress exhibits a non-linear behavior in which the stress increases with decreasing Reynolds number due to particle settling
Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits
We present and discuss the derivation of a nonlinear non-local
integro-differential equation for the macroscopic time evolution of the
conserved order parameter of a binary alloy undergoing phase segregation. Our
model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics,
i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to
the Gibbs measure for a Hamiltonian which includes both short range (local) and
long range (nonlocal) interactions. A rigorous derivation is presented in the
case in which there is no local interaction. In a subsequent paper (part II),
we discuss the phase segregation phenomena in the model. In particular we argue
that the phase boundary evolutions, arising as sharp interface limits of the
family of equations derived in this paper, are the same as the ones obtained
from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page
Time Evolution of Spin Waves
A rigorous derivation of macroscopic spin-wave equations is demonstrated. We
introduce a macroscopic mean-field limit and derive the so-called
Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic
Heisenberg model at T=0 and finally extend our analysis to general spin
hamiltonians for the same class of ferromagnetic ground states.Comment: 4 pages, to appear in PR
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