Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization
<|reference_start|>Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization: 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.<|reference_end|>
@article{touboul2024propagation,
    title={Propagation and non-reciprocity in time-modulated diffusion through the
  lens of high-order homogenization},
    author={Marie Touboul, Bruno Lombard, Rapha"el Assier, S'ebastien Guenneau,
  Richard Craster},
    journal={arXiv preprint arXiv:2407.08456},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.08456},
    primaryClass={math.AP cs.NA math.NA}
}