تقرير
Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization
| العنوان: | Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization |
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| المؤلفون: | Touboul, Marie, Lombard, Bruno, Assier, Raphaël, Guenneau, Sébastien, Craster, Richard |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.08456 |
| رقم الأكسشن: | edsarx.2407.08456 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |