Search results for "FRACTAL"

A Random Walk Through Fractal Dimensions. VonB. H. Kaye. VCH Verlagsgesellschaft, Weinheim/VCH Publishers, New York 1989. XXV, 421 S., geb. DM 138.00…

1991

The p-Laplacian with respect to measures

2013

We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.

Fractal Dimension Logarithmic Differences Method for Low Voltage Series Arc Fault Detection

2021

Series arc faults introduce singularities in the current signal and changes over time. Fractal dimension can be used to characterize the dynamic behaviour of the current signal by providing a degree of signal chaos. This measure of irregularity exhibits changes in signal behaviour that can suitably be used as a basis for series arc fault detection. In this paper, an efficient low voltage series arc fault detection method based on the logarithmic differences of the estimate of the fractal dimension of the current signal using the multiresolution length-based method is presented. The discrete wavelet transform and the hard thresholding denoising with the universal threshold are also used. Exp…

Structure of distributions generated by the scenery flow

2015

We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution in the sense of Hochman is generated by a uniformly scaling measure, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of fractal distributions is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all fractal distributions as tangent …

Assessing forest landscape structure using geographic windows.

2001

Landscape structure, interpreted as indicator of functional processes, has become a main attribute of multiresource forest inventories, enhancing its value with respect to society needs. This approach implies effective use of earth observation techniques and geographic information systems to obtain a global view of the inventoried landscapes and to understand the ecological functions of large spatially-heterogeneous landscape mosaics. Landscape structure often reveal extremely complex patterns that can only be very roughly characterized by methods of Euclidean geometry. Conversely, fractals can be applied to adequately describe many of the irregular, fragmented patterns found in nature. In …

Difract: Un nuevo laboratorio virtual para la modelización matemática de las propiedades de difracción de redes fractales

2011

[EN] This work presents a new virtual laboratory, Difract, developed with Easy Java Simulations, for using in Optics courses as a computer tool for the mathematical modelling of the diffraction properties of 1D and 2D fractal gratings. This virtual laboratory enables students to quickly and easily analyze the influence on the Fraunhofer diffraction pattern of the different construction parameters of the fractal grating. As an application example, the Cantor fractal set has been considered.

Fractal Grid – towards the future smart grid

2017

International audience; In the last two decades, electricity grids have faced many challenges that they were not designed to handle. These include integrating weather-dependent renewables, distributed generators, storage units and other advanced components, as well as taking into account active demand. These challenges, together with the ageing of infrastructures, make it more difficult to deliver cost-effective, reliable power. To overcome these issues requires creating new network architectures. The research project Fractal Grid proposes fractality as a core concept to model, analyze and design smart grids in their evolution up to 2030 and beyond. This paper presents the project, its meth…

La morphologie des tissus urbains et périurbains à travers une lecture fractale

2005

Urban expansion produces an irregular urban fabric. This phenomenon influences areas which are distant from urban centres, a problem for sustainable development. Solutions proposed to reduce urban expansion are modelled on the pattern of the compact town. Generally, it is believed that these solutions are unacceptable to the people concerned. In this article we present an alternative approach to the study of urban fabric, which shows that, despite their irregular form, it is possible to describe their development using fractal analysis. This permits understanding of the socio-economic causes of this process and the development an alternative conceptual approach to the management of urban ex…

Fractal surfaces from simple arithmetic operations

2015

Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is shown that these models give rise to a roughness exponent $H$ that shapes the resulting spatial patterns, larger values of the exponent leading to coarser surfaces.

Using the Scaling Analysis to Characterize Financial Markets

2003

We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent approach. We verify the robustness of this approach and we compare the results with the scaling properties in the frequency-domain. We find evidence of deviations from the pure Brownian motion behavior. We show that these deviations are associated with characteristics of the specific markets and they can be, therefore, used to distinguish the different degrees of development of the markets.