Related papers: Vertical Discontinuities in Self-Affine Surfaces L…
We show that smoothing of multiaffine surfaces that are generated by simulating a crosslinked polymer gel by a frustrated, triangular network of springs of random equilibrium lengths [G.M. Buend{\'\i}a, S.J. Mitchell, P.A. Rikvold, Phys.…
We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self affine with a Hurst exponent equal to 2/3 up to a cutoff-length proportional to…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
Most natural and man-made surfaces appear to be rough on many length scales. There is presently no unifying theory of the origin of roughness or the self-affine nature of surface topography. One likely contributor to the formation of…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of post-mortem fracture surfaces in home-made materials of adjustable…
We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.
We report the scaling behavior of the Earth and Venus over a wider range of length scales than reported by previous researchers. All landscapes (not only mountains) together follow a consistent scaling behavior, demonstrating a crossover…
We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule.…
The scaling properties of one-dimensional deconstructed surfaces are studied by numerical simulations of a disaggregation model. The model presented here for the disaggregation process takes into account the possibility of having quenched…
We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi,…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
We study complements of hypersurfaces in schemes with respect to the property being affine.
Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in…
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
Deep-learning based salient object detection methods achieve great progress. However, the variable scale and unknown category of salient objects are great challenges all the time. These are closely related to the utilization of multi-level…
Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations.…