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Updated: Jan 12, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Resonant transparency and multistability of waves scattered by a frequency-dependent and nonlinear effective mass
Samila F da S Oliveira1, Marcelo L Lyra1
1Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil.
Abstract:
We investigate wave scattering in a one-dimensional harmonic chain containing a single defect whose effective mass depends dynamically on the local properties of oscillations, specifically frequency, displacement amplitude, and velocity amplitude. Motivated by systems exhibiting inertial nonlinearities, such as resonant metamaterials, granular media, and relativistic plasmas, we analyze how these forms of mass variability affect spectral transmission. For frequency-dependent masses, transparent modes emerge when the defect inertia matches that of the surrounding lattice at a specific frequency, allowing near-flat-band transmission. In amplitude-dependent scenarios, nonlinearity induces reentrant and multistable transmission behavior, with fully transparent modes appearing for critical nonlinear strengths. The case of velocity-dependent mass exhibits features of both prior cases, including isolated high-transmission branches and multistability near the Brillouin zone edge. Our results provide new insight into wave-defect interactions in nonlinear lattices and suggest mechanisms for tunable transmission and nonlinear filtering in structured media.
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