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Self-similar asymptotics in non-symmetrical convergent viscous gravity currents
(Institute of Physics Publishing, 2009-12)
We investigate the evolution of the ridge produced by the non-symmetrical convergent motion of two substrates over which an initially uniform layer of a Newtonian liquid rests. The lack of symmetry of the flow arises because ...
Assouad dimension and local structure of self-similar sets with overlaps in Rd
(Academic Press Inc Elsevier Science, 2020-08)
For a self-similar set in Rd that is the attractor of an iterated function system that does not verify the weak separation property, Fraser, Henderson, Olson and Robinson showed that its Assouad dimension is at least 1. ...
Axisymmetric self-similar finite-time singularity solution of the Euler equations
(2023)
Abstract
Self-similar finite-time singularity solutions of the axisymmetric Euler equations in an infinite system with a swirl are provided. Using the Elgindi approximation of the Biot–Savart kernel for the ...
Self-similarity in a kantowski-sachs universe with a string cloudSelf-similarity in a kantowski-sachs universe with a string cloud
(Revista Mexicana de Física, 2009)
Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
(Suomalainen Tiedeakatemia, 2018-02)
R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with ...
Absolute continuity of self-similar measures, their projections and convolutions
(American Mathematical Society, 2016-07)
We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely continuous is very small—of co-dimension ...
Absolute continuity of non-homogeneous self-similar measures
(Academic Press Inc Elsevier Science, 2018-09)
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there ...
On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions
(Annal Mathematics, 2019-03)
We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measures such as Bernoulli convolutions as special ...