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The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics,…
In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to…
These are lecture notes of a course given at the 9th International Summer School on Fundamental Problems in Statistical Mechanics, held in Altenberg, Germany, in August 1997. In these notes, we discuss at an elementary level three themes…
We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with…
A novel type of shallow interface state in junctions of two semiconductors without band inversion is identified within the envelope function approximation, using the two-band model. It occurs in abrupt junctions when the interband velocity…
In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with…
We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…
We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct…
We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two…
This letter addresses the issue of interfacial crack propagation mechanisms on various interfaces with using molecular dynamics. Four different interfacial crack propagation manners are recognized by MD simulations: 1, the crack propagates…
Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…
We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles…
From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…
A phase field model of a crack front propagating in a three dimensional brittle material is used to study the fractographic patterns induced by the branching instability. The numerical results of this model give rise to crack surfaces that…
We examine theoretically and numerically fast propagation of a tensile crack along unidimensional strips with periodically evolving toughness. In such dynamic fracture regimes, crack front waves form and transport front disturbances along…
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell…
Exploring the internal mechanism of information spreading is critical for understanding and controlling the process. Traditional spreading models often assume individuals play the same role in the spreading process. In reality, however,…
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…