Effective dynamics in lattices with random mass perturbations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909084191555584 |
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| author | Garnier, Josselin Sharma, Basant Lal |
| author_facet | Garnier, Josselin Sharma, Basant Lal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03090 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective dynamics in lattices with random mass perturbations Garnier, Josselin Sharma, Basant Lal Probability Mathematical Physics Classical Analysis and ODEs 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. |
| title | Effective dynamics in lattices with random mass perturbations |
| topic | Probability Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2309.03090 |