scholarly journals Vibrational and stochastic resonances in driven nonlinear systems

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200226 ◽  
Author(s):  
U. E. Vincent ◽  
P. V. E. McClintock ◽  
I. A. Khovanov ◽  
S. Rajasekar
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Quantum Control ◽  
Resonance Phenomenon ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
Potential Applications ◽  
Mathematical Sciences ◽  
External Forces ◽  
Photonic Band

Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties—one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances—addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

scholarly journals Vibrational and stochastic resonances in driven nonlinear systems: part 2

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
U. E. Vincent ◽  
P. V. E. McClintock ◽  
I. A. Khovanov ◽  
S. Rajasekar
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
State Of The Art ◽  
Ambient Vibration ◽  
Nonlinear Phenomena ◽  
Engineering Systems ◽  
Stochastic Excitation ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
And Control

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

scholarly journals Delay-induced resonance suppresses damping-induced unpredictability

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200232 ◽  
Author(s):  
M. Coccolo ◽  
J. Cantisán ◽  
J. M. Seoane ◽  
S. Rajasekar ◽  
M. A. F. Sanjuán
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Duffing Oscillator ◽  
Critical Values ◽  
Minimal Amount ◽  
Combined Effects ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
The Right

Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyse the generation of a certain damping-induced unpredictability due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

scholarly journals Stochastic and vibrational resonance in complex networks of neurons

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
Ali Calim ◽  
Tugba Palabas ◽  
Muhammet Uzuntarla
Keyword(s):  
Nonlinear Systems ◽  
Complex Networks ◽  
Stochastic Resonance ◽  
Network Architecture ◽  
External Perturbation ◽  
Neural System ◽  
Neural Systems ◽  
Vibrational Resonance ◽  
Resonance Phenomena ◽  
Information Signal

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

Construction of logic gates exploiting resonance phenomena in nonlinear systems

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200238 ◽  
Author(s):  
K. Murali ◽  
S. Rajasekar ◽  
Manaoj V. Aravind ◽  
Vivek Kohar ◽  
W. L. Ditto ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Logic Gates ◽  
Bistable System ◽  
Periodic Forcing ◽  
Vibrational Resonance ◽  
Logic Function ◽  
Excitable Systems ◽  
Influence Of Noise ◽  
Optimal Window

A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

scholarly journals Topological guided-mode resonances at non-Hermitian nanophotonic interfaces

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ki Young Lee ◽  
Kwang Wook Yoo ◽  
Youngsun Choi ◽  
Gunpyo Kim ◽  
Sangmo Cheon ◽  
...  
Keyword(s):  
Fundamental Study ◽  
One Dimensional ◽  
Guided Mode ◽  
Wall Structures ◽  
Potential Applications ◽  
Photonic Microstructures ◽  
Guided Mode Resonance ◽  
The One ◽  
Photonic Band ◽  
Topological Correlations

Abstract The topological properties of photonic microstructures are of great interest because of their experimental feasibility for fundamental study and potential applications. Here, we show that robust guided-mode-resonance states exist in photonic domain-wall structures whenever the complex photonic band structures involve certain topological correlations in general. Using the non-Hermitian photonic analogy of the one-dimensional Dirac equation, we derive essential conditions for photonic Jackiw-Rebbi-state resonances taking advantage of unique spatial confinement and spot-like spectral features which are remarkably robust against random parametric errors. Therefore, the proposed resonance configuration potentially provides a powerful method to create compact and stable photonic resonators for various applications in practice.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200229 ◽  
Author(s):  
V. Sorokin ◽  
I. Demidov
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Stochastic Systems ◽  
Signal To Noise Ratio ◽  
Nonlinear Damping ◽  
Resonance Phenomenon ◽  
Oscillatory Systems ◽  
Stochastic Excitations ◽  
Viable Approach ◽  
Stochastic Resonance Phenomenon

Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

scholarly journals Dynamic energy budget theory restores coherence in biology

2010 ◽  
Vol 365 (1557) ◽  
pp. 3413-3428 ◽  
Author(s):  
Tânia Sousa ◽  
Tiago Domingos ◽  
J.-C. Poggiale ◽  
S. A. L. M. Kooijman
Keyword(s):  
Energy Budget ◽  
State Of The Art ◽  
Theme Issue ◽  
Dynamic Energy Budget ◽  
Dynamic Energy Budget Theory ◽  
Potential Applications ◽  
Set Up ◽  
Budget Theory ◽  
Near Future ◽  
Consistent Application

We present the state of the art of the development of dynamic energy budget theory, and its expected developments in the near future within the molecular, physiological and ecological domains. The degree of formalization in the set-up of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occam's razor, is discussed. We place the various contributions in the theme issue within this theoretical setting, and sketch the scope of actual and potential applications.

scholarly journals Development and Testing of Woven FRP Flexure Hinges for Pressure-Actuated Cellular Structures with Regard to Morphing Wing Applications

Aerospace ◽  
2019 ◽  
Vol 6 (11) ◽  
pp. 116
Author(s):  
Patrick Meyer ◽  
Johannes Boblenz ◽  
Cornelia Sennewald ◽  
Michael Vorhof ◽  
Christian Hühne ◽  
...  
Keyword(s):  
Operating Conditions ◽  
Cellular Structures ◽  
High Lift ◽  
Reinforced Plastics ◽  
Flexure Hinges ◽  
Key Factor ◽  
Potential Applications ◽  
Fiber Reinforced Plastics ◽  
The One ◽  
External Forces

Shape-variable structures can change their geometry in a targeted way and thus adapt their outer shape to different operating conditions. The potential applications in aviation are manifold and far-reaching. The substitution of conventional flaps in high-lift systems or even the deformation of entire wing profiles is conceivable. All morphing approaches have to deal with the same challenge: A conflict between minimizing actuating forces on the one hand, and maximizing structural deflections and resistance to external forces on the other. A promising concept of shape variability to face this challenging conflict is found in biology. Pressure-actuated cellular structures (PACS) are based on the movement of nastic plants. Firstly, a brief review of the holistic design approach of PACS is presented. The aim of the following study is to investigate manufacturing possibilities for woven flexure hinges in closed cellular structures. Weaving trials are first performed on the material level and finally on a five-cell PACS cantilever. The overall feasibility of woven fiber reinforced plastics (FRP)-PACS is proven. However, the results show that the materials selection in the weaving process substantially influences the mechanical behavior of flexure hinges. Thus, the optimization of manufacturing parameters is a key factor for the realization of woven FRP-PACS.

Optimizing the Electrical Power in an Energy Harvesting System

2015 ◽  
Vol 25 (12) ◽  
pp. 1550171 ◽  
Author(s):  
Mattia Coccolo ◽  
Grzegorz Litak ◽  
Jesús M. Seoane ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
High Frequency ◽  
Energy Harvester ◽  
Electrical Power ◽  
Low Frequency ◽  
Electrical Energy ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Energy Harvesting System

In this paper, we study the vibrational resonance (VR) phenomenon as a useful mechanism for energy harvesting purposes. A system, driven by a low frequency and a high frequency forcing, can give birth to the vibrational resonance phenomenon, when the two forcing amplitudes resonate and a maximum in amplitude is reached. We apply this idea to a bistable oscillator that can convert environmental kinetic energy into electrical energy, that is, an energy harvester. Normally, the VR phenomenon is studied in terms of the forcing amplitudes or of the frequencies, that are not always easy to adjust and change. Here, we study the VR generated by tuning another parameter that is possible to manipulate when the forcing values depend on the environmental conditions. We have investigated the dependence of the maximum response due to the VR for small and large variations in the forcing amplitudes and frequencies. Besides, we have plotted color coded figures in the space of the two forcing amplitudes, in which it is possible to appreciate different patterns in the electrical power generated by the system. These patterns provide useful information on the forcing amplitudes in order to produce the optimal electrical power.

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