Search results for "FRACTAL"
showing 10 items of 329 documents
Random cutout sets with spatially inhomogeneous intensities
2015
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.
Fractal geometry of higher derivative gravity
2019
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances.
Fractal Spacetime Structure in Asymptotically Safe Gravity
2005
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
FLUCTUATION-INDUCED LOCAL OSCILLATIONS AND FRACTAL PATTERNS IN THE LATTICE LIMIT CYCLE MODEL
2003
The fractal properties of the Lattice Limit Cycle model are explored when the process is realized on a 2-dimensional square lattice support via Monte Carlo Simulations. It is shown that the structure of the steady state presents inhomogeneous fluctuations in the form of domains of identical particles. The various domains compete with one another via their borders which have self-similar, fractal structure. The fractality is more prominent, (fractal dimensions df < 2), when the parameter values are near the critical point where the Hopf bifurcation occurs. As the distance from the Hopf bifurcation increases in the parameter space the system becomes more homogeneous and the fractal dimens…
LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY
2002
We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
Multiplexing of encrypted data using fractal masks
2012
In this Letter, we present to the best of our knowledge a new all-optical technique for multiple-image encryption and multiplexing, based on fractal encrypting masks. The optical architecture is a joint transform correlator. The multiplexed encrypted data are stored in a photorefractive crystal. The fractal parameters of the key can be easily tuned to lead to a multiplexing operation without cross talk effects. Experimental results that support the potential of the method are presented.
Theoretical approaches for geometric optimization of urban forms : towards a fractal development of the city
2017
This thesis aims to establish a urban structure that optimizes inhabitant's preferences. In other words, we want to find out which city shape answers the best the residents' aspirations, according to their consumption preferences for urban and green amenities. By considering a theoretical field of study and by characterizing the population by a Cobb-Douglas behavioral pattern, we will build step by step a city, assuming successive arrivais of new individuals, in order to find out which geometric shape gives the most suitable answer. The final goal of this thesis is there to suggest a city with a fractal shape as an appro- priate answer to the resident's expectations. We will show that this …
Morphometry of microstromatolites in calcrete laminar crusts and a fractal model of their growth
1996
The laminar crust, constituting the upper part of calcretes (terrestrial CaCO3 accumulations inside surficial sediments), is a succession of thin layers of various colors and shapes resembling micro-stromatolites. The crust structure and its diagenetic evolution are similar to stromatolites. A quantitative study of its structure was made using image analysis. Euclidian parameters were calculated to describe lamina shape. Eight hundred and eighty-six laminae were divided into six classes from the flatest forms to columnar shapes. The geometrical relationships between the shapes are interpreted as steps in the growth process of the microstromatolite. A fractal model of laminar crust growth wa…
FRACTAL STRUCTURES IN SINGLE CRYSTALS OF FERROELECTRIC LITHIUM NIOBATE GROWN UNDER STRONGLY UNSTABLE CONDITIONS
2009
Atomic force microscopy studies of lithium niobate single crystals containing heterogeneously distributed lanthanide (Gd) admixture and a regular domain structure of 100 nm to 1 μm steps obtained under conditions of severe thermal instability have revealed fractal structures of the size of 10 to 100 nm within regions of the regular domain structures. A super-structure of clustered defects with 1–2 nm steps explaining results of Raman spectra analysis is supposed to exist in the cation sub-lattice and formation of periodic fractal structures of the size of ∼1 nm–100 μm is suggested to take place in lithium niobate single crystals containing lanthanide admixture.
Two-Length-Scale Structure in Some Computer-Generated Aggregates Grown by Diffusion-Limited Aggregation
1994
AbstractThe properties of some aggregates “grown” on a computer by diffusion-limited aggregation have been investigated. Calculations showed that the intensity of the small-angle x-ray and neutron scattering from the aggregates was proportional to q−D for qL ≫ 1, where D > 0, L is a length that characterizes the large-scale structure of the aggregate, q = 4πλ−1 sin(θ/2), γ is the wavelength, and θ is the scattering angle. The magnitude of the exponent D was appreciably smaller than the fractal dimensions that many simulations have shown to be typical of the mass fractal aggregates grown by diffusion-limited aggregation. The calculations suggest that the aggregates have structure on two d…