Related papers: The three-dimensional statistical characterization…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
In light of the race towards macroscale superlubricity of graphitic contacts, the effect of grain boundaries on their frictional properties becomes of central importance. Here, we elucidate the unique frictional mechanisms characterizing…
The study of random surfaces, especially in the asymptotics of large genus, has been of increasing interest in recent years. Many geometrical questions have analogous formulations in the theory of random graphs with a large number of…
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…
In this paper we compute the distributions of various markings on smooth cubic surfaces defined over the finite field $\mathbb{F}_q$, for example the distribution of pairs of points, `tritangents' or `double sixes'. We also compute the…
Optical instruments for measuring surface-wave characteristics provide a better spatial and temporal resolution than other methods, but they face difficulties while converting the results of indirect measurements into absolute levels of the…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the…
The objective of the current study is to utilize an innovative method called 'change probabilities' for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional…
Many devices, including touchscreens and robotic hands, involve frictional contacts. Optimizing these devices requires fine control of the interface's friction law. We lack systematic methods to create dry contact interfaces whose…
We investigate the surface width $W$ of solid-on-solid surfaces in the vicinity of the roughening temperature $T_r$. Above $T_r$, $W^2$ is expected to diverge with the system size $L$ like $\ln L$. However, close to $T_r$ a clean $\ln{L}$…
We have defined pinning fields as those random fields that keep some of the magnetic moments unreversed in the region of negative external applied field during the demagnetizing process. An analysis of the statistical properties of such…
Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study…
Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global…
Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling…
Earth's relief is approximately self-affine, meaning a zoom-in on a small region looks statistically similar to a large region upon rescaling. Fractional Brownian surfaces give an idealized self-affine model of Earth's relief with one…
The interaction between a fluid and a wall is described with a certain boundary condition for the fluid velocity at the wall. To understand how fluids behave near a rough wall, the fluid velocity at every point of the rough surface may be…
Surface topography strongly modifies adhesion of hard-material contacts, yet roughness of real surfaces typically exists over many length scales. This investigation aims to determine which scales of topography have the strongest effect on…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
In this paper we analyze several strategies for the estimation of the roughness parameter of the $\mathcal G_I^0$ distribution. It has been shown that this distribution is able to characterize a large number of targets in monopolarized SAR…