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math-ph2011★ 1 cited
A self-similar field theory for 1D linear elastic continua and self-similar diffusion problem
Thomas Michelitsch, Gérard A. Maugin, Rahman Mujibur +3
This paper is devoted to the analysis of some fundamental problems of linear elasticity in 1D continua with self-similar interparticle interactions. We introduce a self-similar con…
math-ph2009★ 27 cited
Dispersion Relations and Wave Operators in Self-Similar Quasi-Continuous Linear Chains
Thomas M. Michelitsch, Gérard A. Maugin, Franck C. G. A Nicolleau +2
We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-sim…