Effective dynamics in lattices with random mass perturbations

Autor:	Garnier, Josselin, Sharma, Basant Lal
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematical Physics Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning due to substrate interaction, we discuss a transient dynamics problem and a time-harmonic transmission problem. By a stochastic, multiscale analysis we provide asymptotic expressions for the displacement field that propagates through the random perturbations and for the time-harmonic transmission coefficients. These theoretical predictions are supported by illustrations of their agreements with numerical simulations. Comment: 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.03090 Zobrazit plný text záznamu View this record from Arxiv