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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08456 |
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| _version_ | 1866910523077951488 |
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| author | Touboul, Marie Lombard, Bruno Assier, Raphaël Guenneau, Sébastien Craster, Richard |
| author_facet | Touboul, Marie Lombard, Bruno Assier, Raphaël Guenneau, Sébastien Craster, Richard |
| contents | The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization which results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading therefore to a corrective advective term which cancels out non-reciprocity at the leading order but not at the second order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization Touboul, Marie Lombard, Bruno Assier, Raphaël Guenneau, Sébastien Craster, Richard Analysis of PDEs Numerical Analysis The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization which results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading therefore to a corrective advective term which cancels out non-reciprocity at the leading order but not at the second order. |
| title | Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2407.08456 |