相关论文: Statistical Topography of Glassy Interfaces

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the…

We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition,…

Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling…

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…

We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical…

We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta-pinning at height zero. There is a detailed mathematical understanding of the depinning transition in 2 dimensions without…

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…

Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…

The kinetic roughening of a stable oil--air interface, moving in a Hele--Shaw cell which contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough…

Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of…

Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…

We present numerical evidence that there are two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of $\lambda$, the coefficient of the…

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the…

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…

To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly…

The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and…

The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in…

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for…

The three dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with X-ray Computed Tomography. We search for signatures of organization, we classify local…