Related papers: Multifractal Distribution of Dendrite on One-dimen…
We study the phase distribution of the complex reflection coefficient in different configurations as a disordered 1D system evolves in length, and its effect on the distribution of the 4-probe resistance $R_4$. The stationary ($L \to…
The characterization of the long-range order and fractal properties of DNA sequences has proved a difficult though highly rewarding task due mainly to the mosaic character of DNA consisting of many interwoven patches of various lengths with…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
We systematically study a collection of refractive phenomena that can possibly occur at the interface of a two-dimensional photonic crystal, with the use of the wave vector diagram formalism. Cases with a single propagating beam (in the…
An analytical expression of the strain distribution due to lattice mismatch is obtained in an infinite isotropic elastic medium (a matrix) with a three-dimensional polyhedron-shaped inclusion (a quantum dot). The expression was obtained…
We study dendritic growth numerically with a phase field model. Tip oscillation and regular side-branching are observed in a parameter region where the anisotropies of the surface tension and the kinetic effect compete. The transition from…
Quasiperiodic moir\'e materials provide a new platform for realizing critical electronic states, yet a direct and experimentally practical method to characterize this criticality has been lacking. We show that a multifractal analysis of the…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and…
This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
In this article: a) a method is developed for calculating volumetric diagrams of elastic scattering of microparticles (in particular, electrons and photons) on single-layer and multi-layer statistically uneven surfaces; b) the diffraction…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…
Diffraction analysis in four dimensional scanning transmission electron microscopy now enables the mapping of local structures including symmetry, strain, and polarization of materials. However, measuring the distribution of these…
The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc.
Utilizing discrete phase distribution to fit continuous phase distribution has been a primary routine for designing metasurfaces. In the existing method, the validation of the discrete designs is guaranteed only by using the sub-wavelength…
Stochastic features of decay of a metastable phase have been investigated with the help of a new monodisperse approximation. This approximation is more precise than the already used one and namely it allows to give a very simple but rather…
Droplet patterns condensing on solid substrates (breath figures) tend to evolve into a self-similar regime, characterized by a bimodal droplet size distribution. The distributions comprise a bell-shaped peak of monodisperse large droplets,…