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1. Noise influenced response movement in coupled oscillator arrays with multi-stability

   https://doi.org/10.1016/j.jsv.2022.116951  

   Alofi, A. ; Acar, G ; Balachandran, B. ( April 2022 , Journal of sound and vibration)

   In this work, the authors explore the influence of noise on the dynamics of coupled nonlinear oscillators. Numerical studies based on the Euler–Maruyama scheme and experimental studies with finite duration noise are undertaken to examine how the response can be moved from one response state to another by using noise addition to a harmonically forced system. In particular, jumps from a high amplitude state of each oscillator to a low amplitude state of each oscillator and the converse are demonstrated along with noise-influenced localizations. These events are found to occur in a region of multi-stability for the system, and the corresponding noise levels are reported. A method for recognizing how much noise is required to induce a change the system dynamics is developed by using the response basins of attraction. The findings of this work have implications for weakly coupled, nonlinear oscillator arrays and the manner in which noise can be used to influence energy localization and system dynamics in these systems. 

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2. Using noise to augment synchronization among oscillators

   https://doi.org/10.1038/s41598-021-83806-9  

   Vaidya, Jaykumar ; Bashar, Mohammad Khairul ; Shukla, Nikhil ( December 2021 , Scientific Reports)

   null (Ed.)

   Abstract Noise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms. 

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3. Energy Exchange between Two Sub-systems Coupled with a Nonlinear Elastic Path

   Sen, O.T. ; Singh, R. ( May 2018 , NOVEM 2018 Conference)

   The chief objective of this paper is to explore energy transfer mechanism between the sub-systems that are coupled by a nonlinear elastic path. In the proposed model (via a minimal order, two degree of freedom system), both sub-systems are defined as damped harmonic oscillators with linear springs and dampers. The first sub-system is attached to the ground on one side but connected to the second sub-system on the other side. In addition, linear elastic and dissipative characteristics of both oscillators are assumed to be identical, and a harmonic force excitation is applied only on the mass element of second oscillator. The nonlinear spring (placed in between the two sub-systems) is assumed to exhibit cubic, hardening type nonlinearity. First, the governing equations of the two degree of freedom system with a nonlinear elastic path are obtained. Second, the nonlinear differential equations are solved with a semi-analytical (multi-term harmonic balance) method, and nonlinear frequency responses of the system are calculated for different path coupling cases. As such, the nonlinear path stiffness is gradually increased so that the stiffness ratio of nonlinear element to the linear element is 0.01, 0.05, 0.1, 0.5 and 1.0 while the absolute value of linear spring stiffness is kept intact. In all solutions, it is observed that the frequency response curves at the vicinity of resonant frequencies bend towards higher frequencies as expected due to the hardening effect. However, at moderate or higher levels of path coupling (say 0.1, 0.5 and 1.0), additional branches emerge in the frequency response curves but only at the first resonant frequency. This is due to higher displacement amplitudes at the first resonant frequency as compared to the second one. Even though the oscillators move in-phase around the first natural frequency, high amplitudes increase the contribution of the stored potential energy in the nonlinear spring to the total mechanical energy. The out-of-phase motion around the second natural frequency cannot significantly contribute due to very low motion amplitudes. Finally, the governing equations are numerically solved for the same levels of nonlinearity, and the motion responses of both sub-systems are calculated. Both in-phase and out-of-phase motion responses are successfully shown in numerical solutions, and phase portraits of the system are generated in order to illustrate its nonlinear dynamics. In conclusion, a better understanding of the effect of nonlinear elastic path on two damped harmonic oscillators is gained. 

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4. Analysis and optimization of a nonlinear dual‐mode floor isolation system subjected to earthquake excitations

   https://doi.org/10.1002/eqe.3449  

   Bin, Puthynan ; Tehrani, Mohammad H. ; Nisa, Mehrun ; Harvey, Jr., P. Scott ; Taflanidis, Alexandros A. ( April 2021 , Earthquake Engineering & Structural Dynamics)

   Floor isolation systems (FISs) are used to mitigate earthquake‐induced damage to sensitive building contents. Dynamic coupling between the FIS and primary structure (PS) may be nonnegligible or even advantageous when strong nonlinearities are present under large isolator displacements. This study investigates the influence of dynamic coupling between the PS and FIS in the presence of nonsmooth (impact‐like) nonlinearity in the FIS under intense earthquakes. Using component mode analysis, a nonlinear reduced order model of the combined FIS–PS system is developed by coupling a condensed model of the linear PS to the nonlinear FIS. A bilinear Hertz‐type contact model is assumed for the FIS, with the gap and the impact stiffness and damping providing parametric variation. The performance of the FIS–PS system is quantified through a multiobjective, risk‐based design criterion considering both the total acceleration sustained by the isolated mass under a service‐level earthquake and the interstory drift under a maximum considered earthquake. The results of a parametric study shed light on understanding the valid range that the decoupled approach can be reliably applied for nonlinear FISs experiencing impacts. It is also shown that the nonlinear FIS can be tuned in such a way to mitigate seismic responses of the supporting PS under strong shaking, in addition to protecting the isolated mass at low to moderate shaking. The FIS, therefore, functions as a dual‐mode vibration isolator/absorber system, with displacement‐dependent response adaptation. Guidelines to the optimal tuning of such a dual‐mode system are presented based on the risk‐based stochastic design optimization.

    

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5. Plasmon-induced coherence, exciton-induced transparency, and Fano interference for hybrid plasmonic systems in strong coupling regime

   https://doi.org/10.1063/5.0083197  

   Scott, Zoe ; Muhammad, Shafi ; Shahbazyan, Tigran V. ( May 2022 , The Journal of Chemical Physics)

   We present an analytical model describing the transition to a strong coupling regime for an ensemble of emitters resonantly coupled to a localized surface plasmon in a metal–dielectric structure. The response of a hybrid system to an external field is determined by two distinct mechanisms involving collective states of emitters interacting with the plasmon mode. The first mechanism is the near-field coupling between the bright collective state and the plasmon mode, which underpins the energy exchange between the system components and gives rise to exciton-induced transparency minimum in scattering spectra in the weak coupling regime and to emergence of polaritonic bands as the system transitions to the strong coupling regime. The second mechanism is the Fano interference between the plasmon dipole moment and the plasmon-induced dipole moment of the bright collective state as the hybrid system interacts with the radiation field. The latter mechanism is greatly facilitated by plasmon-induced coherence in a system with the characteristic size below the diffraction limit as the individual emitters comprising the collective state are driven by the same alternating plasmon near field and, therefore, all oscillate in phase. This cooperative effect leads to scaling of the Fano asymmetry parameter and of the Fano function amplitude with the ensemble size, and therefore, it strongly affects the shape of scattering spectra for large ensembles. Specifically, with increasing emitter numbers, the Fano interference leads to a spectral weight shift toward the lower energy polaritonic band.

    

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