相关论文: Statistical Topography of Glassy Interfaces
We study 1-dimensional coupled map lattices consisting of diffusively coupled Tchebyscheff maps of N-th order. For small coupling constants a we determine the invariant 1-point and 2-point densities of these nonhyperbolic systems in a…
Finite size scaling is shown to work very well for the block variables used in intermittency studies on a 2-d Ising lattice. The intermittency exponents so derived exhibit the expected relations to the magnetic critical exponent of the…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented…
We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…
We study a modified model of the Kardar-Parisi-Zhang equation with quenched disorder, in which the driving force decreases as the interface rises up. A critical state is self-organized, and the anomalous scaling law with roughness exponent…
We apply new techniques developed in a previous paper to the study of some surface effects in the 2D Ising model. We examine in particular the pinning-depinning transition. The results are valid for all subcritical temperatures. By duality…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
The effect of open boundary conditions for four models with quenched disorder are studied in finite samples by numerical ground state calculations. Extrapolation to the infinite volume limit indicates that the configurations in ``windows''…
We present an alternative finite-size approach to a set of parity conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general…
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…
We discuss the universal dynamics of elastic interfaces in quenched random media. We focus in the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow…