112 citations · 293 across the 10 of their papers we have counts for
10 papers
On microcontinuum field theories: the Eshelby stress tensor and incompatibility conditions
Markus Lazar, Gerard A. Maugin
We investigate linear theories of incompatible micromorphic elasticity, incompatible microstretch elasticity, incompatible micropolar elasticity and the incompatible dilatation the…
A regularized representation of the fractional Laplacian in n dimensions and its relation to Weierstrass-Mandelbrot type fractal functions
Thomas Michelitsch, Gérard Maugin, Shahram Derogar +1
We demonstrate that the fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with {\it self-similar} interparticle interactions. We show that the…
An approach to anomalous diffusion in the n-dimensional space generated by a self-similar Laplacian
Thomas Michelitsch, Gérard Maugin, Andrzej F. Nowakowski +2
We analyze a quasi-continuous linear chain with self-similar distribution of harmonic interparticle springs as recently introduced for one dimension (Michelitsch et al., Phys. Rev.…
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…
Analysis of the Vibrational Mode Spectrum of a Linear Chain with Spatially Exponential Properties
Thomas Michelitsch, Gérard A. Maugin, Andrzej. F. Nowakowski +1
We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We…
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…