Related papers: On the Optical Role of Randomness for Structured S…
We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…
The present study focuses on the optical properties of functionalized surfaces and how the surface geometry impacts them. Physical measurements of reflected light are required to understand the visual aspect of such surfaces. Bidirectional…
A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivariate normal distribution.
Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute…
It is a well observed phenomenon that natural images are smooth, in the sense that nearby pixels tend to have similar values. We describe a mathematical model of images that makes no assumptions on the nature of the environment that images…
Inspired by structural colors in avian species, various synthetic strategies have been developed to produce non-iridescent, saturated colors using nanoparticle assemblies. Mixtures of nanoparticles varying in particle chemistry (or complex…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
This study is about the properties of the sets of objects associated in a structure resulting from multiple-processes involving chance as are materials whose texture is unordered and random. Being a paper scientist the author refers to the…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
For plasmonic nanoparticles, we investigate the influence of surface roughness inherent to top-down fabrication on the optical properties, and find that it has a surprisingly small influence on the position and width of the plasmon peaks.…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
Nanostructured surfaces usually exhibit complicated morphologies that cannot be described in terms of Euclidean geometry. Simultaneously, they do not constitute fully random noise fields to be characterized by simple stochastics and…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…