Related papers: Revisiting Pollock's Drip Paintings
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
In this work, we propose a novel technique for obtaining descriptors of gray-level texture images. The descriptors are provided by applying a multiscale transform to the fractal dimension of the image estimated through the probability…
In this paper, we prove intractability results about sampling from the set of partitions of a planar graph into connected components. Our proofs are motivated by a technique introduced by Jerrum, Valiant, and Vazirani. Moreover, we use…
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…
Fractal channels have significant applications in fields such as microfluidic chips and in vitro diagnostics. However, there is currently insufficient understanding and recognition of fluid flow within fractal channels. In this paper, the…
Summarizing results from Joseph Mecke's last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept of thickening of a random variable, as an inverse operation…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
In this study, we consider a topological derivative-based imaging technique for the fast identification of short, linear perfectly conducting cracks completely embedded in a two-dimensional homogeneous domain with smooth boundary. Unlike…
In an effort to understand the fundamental physics of turbulent transport of particles and heat in a tokamak, the floating potential fluctuations in the the scrape-off layer plasma of ohmically heated ADITYA tokamak are analysed for…
We consider fractal graphs invariant by a skew product $F:\mathbb{T}^k\times \mathbb{R}\rightarrow \mathbb{T}^k\times \mathbb{R}$ of the form $F(x,y)=(Ax, \lambda y+p(x))$ where $0<\lambda<1$, $p\colon\mathbb{T}^k\to\mathbb{R}$ is a…
The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics, and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties.…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
Temporal broadening of pulsar signals results from electron density fluctuations in the interstellar medium that cause the radiation to travel along paths of different lengths. The Gaussian theory of fluctuations predicts that the pulse…
The propagation of an interfacial crack front through a weak plane of a transparent Plexiglas block has been studied experimentally. A stable crack in mode I was generated by loading the system by an imposed displacement. The local…
The Doppler shifts of optical emission lines which have been scattered by surrounding dust and electrons can provide useful information about the kinematics, geometry and physical conditions of astrophysical flows. In principle, the…
We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary…
We study artifacts in the reconstruction of X-ray tomography due to nonlinear effects. For non-convex metal objects, we analyze the new phenomena of streak artifacts from inflection points on the boundary of metal objects. We characterize…
Paint marbling refers to techniques for creating intricate designs in colored paints floating on a liquid surface. If the marbling motions are executed slowly, then this layer of paints can be modeled as a two-dimensional incompressible…
Recent step strain experiments in well-entangled polymeric liquids demonstrated a bulk fracture-like phenomenon. We have studied this instability using a modern version of the Doi-Edwards theory for entangled polymers, and we find close…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…