Related papers: Vertical Discontinuities in Self-Affine Surfaces L…
Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces…
The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open…
We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the…
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…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
Affinity graphs are widely used in deep architectures, including graph convolutional neural networks and attention networks. Thus far, the literature has focused on abstracting features from such graphs, while the learning of the affinities…
We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied…
Computing the gradients of a rendering process is paramount for diverse applications in computer vision and graphics. However, accurate computation of these gradients is challenging due to discontinuities and rendering approximations,…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
We study phase separation between coexisting active and passive fluids in three-dimensions, using numerical simulation and experiments. Chaotic flows of the active phase drive giant interfacial deformations, causing the co-existing phases…
We approximate functionals depending on the gradient of $u$ and on the behaviour of $u$ near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise…
In the present work the instability of a flat horizontal thin layer of a magnetic fluid (the depth of no more than 50 \mum) under the action of a uniform magnetic field is studied experimentally. It was revealed that the development of…
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front…
The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both…
Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$…
The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend…
We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent…
The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…