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math.AP2026

Finite Spectral-Band Optimal Control of Acoustic Waves via Subwavelength Point-Like Resonant Actuators

Arpan Mukherjee, Mourad Sini

We study finite-band optimal control of acoustic waves actuated by local clusters of subwavelength resonators. The acoustic problem reduces to a time-domain Foldy-Lax approximation…

math.AP2026

Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control

Arpan Mukherjee, Mourad Sini

We study finite-time acoustic wave tracking using effective interior Dirac-type actuators generated by clusters of subwavelength resonant bubbles driven from exterior transducers.…

math.AP2026

Feedback Stabilization and Tracking for Heat Equations Using Thermo-Plasmonic Nanoparticles as Actuators

Arpan Mukherjee, Sérgio S. Rodrigues, Mourad Sini

We propose a feedback strategy to track prescribed heat profiles using plasmonic nanoparticles as actuators. Starting from a thermo--plasmonic Maxwell--heat model, we use a time-do…

math.AP2025

Functional-Analytic Justification of the Time-Domain Foldy-Lax Approximation for Dispersive Acoustic Media: A Feynman-Diagram Viewpoint

Arpan Mukherjee, Mourad Sini

This work provides a rigorous functional-analytic justification for a time-domain Foldy-Lax framework that describes multiple acoustic scattering by a cluster of dispersive resonat…

math.AP2024

Dispersive Effective Metasurface Model for Bubbly Media

Arpan Mukherjee, Mourad Sini

We derive the effective transmission condition for a cluster of acoustic subwavelength resonators, modeled as small-scaled bubbles distributed not necessarily periodically along a…

math.AP2024

Effective Medium Theory for Heat Generation Using Plasmonics: A Parabolic Transmission Problem Driven by the Maxwell System

Xinlin Cao, Arpan Mukherjee, Mourad Sini

The excitation of plasmonic nanoparticles by incident electromagnetic waves at frequencies near their subwavelength resonances induces localized heat generation in the surrounding…

math.AP2024

Dispersive Effective Model in the Time-Domain for Acoustic Waves Propagating in Bubbly Media

Arpan Mukherjee, Mourad Sini

We derive the effective medium theory for the linearized time-domain acoustic waves propagating in a bubbly media. The analysis is done in the time-domain avoiding the need to use…