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The scattering from generalized Cantor fractals
, 2010 We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in ...
A. I. Kuklin +28 more
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The Maximum Entropy principle and the nature of fractals [PDF]
, 1998 We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in those patterns.
J Wagensberg +4 more
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Optimizing the Adaptive Fast Multipole Method for Fractal Sets [PDF]
SIAM Journal on Scientific Computing, 2015 We have performed a detailed analysis of the fast multipole method (FMM) in the adaptive case, in which the depth of the FMM tree is nonuniform. Previous works in this area have focused mostly on special types of adaptive distributions, for example, when
H. Pouransari, Eric F Darve
semanticscholar +1 more source
Sets which are not tube null and intersection properties of random measures [PDF]
, 2014 We show that in $\mathbb{R}^d$ there are purely unrectifiable sets of Hausdorff (and even box counting) dimension $d-1$ which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and ...
Alberti +15 more
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Maxwell’s Equations on Cantor Sets: A Local Fractional Approach
Advances in High Energy Physics, 2013 Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields.
Yang Zhao +4 more
doaj +1 more source
Atomic Scale Fractal Dimensionality in Proteins
, 2002 The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low temperatures (quantum
Allan Widom, Duccio Medini, Lehnert U.
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Fractal-fractional estimations of Bullen-type inequalities with applications
Ain Shams Engineering JournalThe study of inequalities inside fractal domains has been stimulated by the growing interest in fractional calculus for the applied and mathematical sciences.
Saad Ihsan Butt +3 more
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Fractals from Regular Behaviours [PDF]
Logical Methods in Computer ScienceWe forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric space.
Todd Schmid +2 more
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Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems
, 2002 A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control ...
Klages, R., Korabel, N.
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Advanced Functional Materials, EarlyView.Herein presented supraparticles combine the nanoparticulate photocatalyst graphitic carbon nitride with the enzyme horseradish peroxidase, which is immobilized on silica nanoparticles. In an optimized compatibility range, both catalysts operate effectively within the hybrid supraparticles and catalyze a cascade reaction consisting of the photocatalytic
Bettina Herbig +11 more
wiley +1 more source