Related papers: Revisiting Pollock's Drip Paintings
We establish a connection between the scattering inverse problem and the determination of the distribution of the position of the Levy process at the exit time of a bounded interval in term of its Levy exponent.
This paper presents the graphic representation in the z-plane of the first three iterations of the algorithm that generates the Sierpinski Gasket. It analyzes the influence of the f(z) map when we represent fractal images.
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of…
For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…
Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly…
To help understand the underlying mechanisms of neural networks (NNs), several groups have, in recent years, studied the number of linear regions $\ell$ of piecewise linear functions generated by deep neural networks (DNN). In particular,…
Experiments on dry granular matter flowing down an inclined plane are performed in order to study the dynamics of dense pyroclastic flows. The plane is rough, and always wider than the flow, focusing this study on the case of laterally…
The study of human dynamics has attracted much interest from many fields recently. In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matrix). Fractures can act as drains or as barriers, since…
We used optical microscopy to investigate flows inside water rivulets that were inkjet-printed onto different surfaces and under different ambient conditions. The acquired fluid dynamics videos were submitted to the 2013 Gallery of Fluid…
Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)), we propose a discrete model of linear springs for studying fracture in thin and elastically isotropic brittle films. The method enables us to draw a map of the…
This paper modifies a box-counting method of estimating a fractal dimension of a graph, and applies it to estimate the roughness of a sample function of a stochastic process such as a Levy process or a Gaussian process with stationary…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other are prime number indexed basis entities taken…
Recent confocal experiments on colloidal solids motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several…
Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…