Search results for " Fractals"
showing 6 items of 6 documents
Fractional calculus in solid mechanics: local versus non-local approach
2009
Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
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.
Evolution of grain-size distribution of pumice sands in 1-D compression
2016
Abstract Crushing is one of the micromechanisms that govern the mechanical behaviour of sands at medium-high stresses. It depends on mineralogy, form and strength of single particle, mean stress level, coordination number, time, etc.. It causes changes of grain-size distribution, porosity, number and type of grain contacts, fabric, structure of the material, etc.. Results of an experimental research on the crushing of pumice sands compressed under 1-D conditions to vertical effective stresses σ′v up to 100MPa are reported here. They show marked crushing already at σ′v of about 200kPa. The evolution of the grain-size distribution can be represented by ΔDi= h/(K(1+C exp(–hlgσ′v))) in which ΔD…
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
Simulation de scénarios fractals d’urbanisation et des mobilités quotidiennes résultantes
2017
International audience