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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Mathematics and Statistics Department Faculty Publication Series
We present a dynamically tunable mechanism of wave transmission in 1D helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion towards an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on/off through …
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. …
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one …
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Mathematics and Statistics Department Faculty Publication Series
In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant …