Resonance-like Phenomenon Research Articles

Field-driven polyelectrolyte-polymer collisions in nanochannels.

Even though dilute (unentangled) polymer solutions cannot act as gel-like sieving media, it has been shown that they can be used to separate DNA molecules in capillary electrophoresis. The separation then comes from sporadic, independent DNA-polymer collisions. We study polymer-polymer collisions in nanochannels (i.e., channels that are smaller than the normal size of the polymers), a situation where a polyelectrolyte is forced to migrate "through" isolated uncharged molecules during electrophoresis. We use Langevin dynamics simulations to explore the nature of these collisions and their effect on the net motion of the two polymer chains. We identify several types of collisions, including some that are unique to nanochannels. When the uncharged polymer is much larger than the polyelectrolyte, the system is reminiscent of gel electrophoresis, and we propose a modified empirical reptation model to explain the data, with an orientation factor that depends on the tube diameter. We also observe that the duration of a collision is a non-monotonic function of the polymer size ratio when the two chains are of comparable size, a surprising resonance-like phenomenon, which, combined with the asymmetric nature of molecular conformations during collision, suggests possible ratchet-like mechanisms that could be used to sort polyelectrolytes in nanodevices.

Vortex-Induced Vibrations of an Elastic Micro-Beam with Gas Modeled by DSMC.

The fluid-structure interaction is one of the most important coupled problems in mechanics. The topic is crucial for many high-technology areas. This work considers the interaction between an elastic obstacle and rarefied gas flow, seeking specific problems that arise during this interaction. The Direct Simulation Monte Carlo method was used to model the rarefied gas flow and the linear Euler-Bernoulli beam theory was used to describe the motion of the elastic obstacle. It turned out that the vibrations caused by the gas flow could provoke a resonance-like phenomenon when the frequency of vortex shedding of the flow was close to the natural frequency of the beam. This phenomenon could be useful in certain high-technology applications.

Contrarian Voter Model under the Influence of an Oscillating Propaganda: Consensus, Bimodal Behavior and Stochastic Resonance.

We study the contrarian voter model for opinion formation in a society under the influence of an external oscillating propaganda and stochastic noise. Each agent of the population can hold one of two possible opinions on a given issue—against or in favor—and interacts with its neighbors following either an imitation dynamics (voter behavior) or an anti-alignment dynamics (contrarian behavior): each agent adopts the opinion of a random neighbor with a time-dependent probability , or takes the opposite opinion with probability . The imitation probability is controlled by the social temperature T, and varies in time according to a periodic field that mimics the influence of an external propaganda, so that a voter is more prone to adopt an opinion aligned with the field. We simulate the model in complete graph and in lattices, and find that the system exhibits a rich variety of behaviors as T is varied: opinion consensus for , a bimodal behavior for , an oscillatory behavior where the mean opinion oscillates in time with the field for , and full disorder for . The transition temperature vanishes with the population size N as in complete graph. In addition, the distribution of residence times in the bimodal phase decays approximately as . Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature . Furthermore, mean-field analytical results show that the opinion oscillations reach a maximum amplitude at an intermediate temperature, and that exhibit a lag with respect to the field that decreases with T.

Ion Cyclotron Resonance: Results and Prospects for Psychiatry

The Ion Cyclotron Resonance-like (ICR-like) phenomenon is a physical model for the ionic currents through cellular membranes obtained by application of very weak, extremely low frequency electromagnetic fields (ELF-EMF). It was proposed in 1984 by the American physicist Abraham Liboff as a hypothesis to explain the results of the physicists Adey and Blackman in their studies of these currents. Liboff postulated that the ELF-EMF applied in the experiments interacted with the geomagnetic field (GMF), inducing facilitated movement of ion species through cellular membranes and so acting as modulators for the degree of movement of the ions.

Phase Diagram and Optimal Information Use in a Collective Sensing System.

We consider a population of individuals living in an uncertain environment. Individuals are able to make noisy observations of the environment and communicate using signals. We show that the model shows an order-disorder transition from an ordered phase in low communication noise in which a consensus about the environmental state is formed to a disordered phase in high communication noise in which no consensus is formed. There are different consensus states: informed consensus in which consensus on the correct belief about the environmental state is formed, and misinformed consensus in which consensus on a wrong belief is formed. Based on the consensus state reached, the ordered phase is decomposed into multistable states separated by first order transitions. We show that the inference capability of the population in a changing environment is maximized on the edge of bistability: on the border between an informed consensus phase and a bistable phase in which both informed and misinformed consensuses are stable. In addition, we show that an optimal level of noise in communication increases the responsiveness of the population to environmental changes in a resonancelike phenomenon. Furthermore, the beneficial effect of noise is the most crucial in a fast changing environment.

Multichannel Interference in Resonancelike Enhancement of High-Order Above-Threshold Ionization.

The intensity-dependent resonancelike enhancement phenomenon in the high-order above-threshold ionization spectrum is a typical quantum effect for atoms or molecules in an intense laser field, which has not been well understood. The calculations of the time-dependent Schrödinger equation (TDSE) are in remarkable agreement with the experimental data, but they cannot clarify the contributions of the bound states. The semiclassical approach of strong field approximation, in which no excited states are involved, can obtain a similar phenomenon, but the laser intensities of enhanced regions predicted by the strong field approximation are inconsistent with the results of the TDSE. In this Letter, a new fully quantum model is established from the TDSE without any excited states. Two types of enhanced structures, unimodal and multimodal structures, are found in the results of the TDSE and model. In addition, the calculations of the model reproduce the key features of the results of the TDSE. It shows that the excited states are not the key factor in the resonancelike enhancements in our calculated system, since there are no excited states in our model. Based on the calculations of our model, we show that such resonancelike enhancements are caused by the constructive interference of different momentum transfer channels. Last, the Fano-like line shapes are also discussed for the features of multichannel interference.

Pattern selection and regulation using noise in a liquid metal.

Electric forcing can be used to select and to regulate the shape of liquid metals. In this work, we present a transition among different patterns in a liquid mercury drop regulated by noise. A stochastic resonancelike phenomenon was observed for two different structural transitions of the liquid metal. In the first set of experiments, the transition from irregular (I) → triangular (T) → irregular (I) patterns was obtained by increasing the amplitude of biased white noise. In the second part, we observed the transition from irregular (I) → elliptical (E) → irregular (I) patterns using the same kind of noise. Periodic stochastic resonance was corroborated in our experiments by employing the cross-correlation coefficient technique.

Resonance-like cooperation due to transaction costs in the prisoner’s dilemma game

Cooperation is omnipresent in the evolution of social species. In human societies, people voluntarily associate and cooperate with each other to exchange payments, which results in the inclusion of transaction costs during the process. This paper applies transaction costs to the spatial prisoner’s dilemma game to better understand the evolution of cooperation by introducing an active–passive mechanism. In particular, a player who actively proposes the game should pay a transaction costs, while the passive responder pays nothing. Using Monte Carlo simulations and pair-approximation analysis, we investigate the frequency of cooperators in the stationary state for different values of the transaction cost, which maintain the same trend. It is found that there exists an optimal value of the transaction cost at which cooperation is optimally promoted. For small or large values of the transaction cost, the promotive effect decreases, and the evolution of cooperation may be impaired if compared to the absence of the active–passive mechanism. Finally, we explain the emergence of large clusters and theoretically confirm the existence of the optimal transaction cost. The mechanism of transaction costs enhancing cooperation resembles a resonance-like phenomenon, which may be helpful in understanding the cooperative behavior induced by the different behaviors between individuals in society.

Analysis of resonance effect for a railway track on a layered ground

Abstract When a train runs on soft ground it can approach or even exceed the speed of surface waves in the ground. Under such conditions the amplitudes of the track response increase considerably. Moreover, a resonance-like phenomenon can occur in which a clear oscillation trail can be observed behind the moving axle loads. An investigation is presented of this resonance frequency and the critical speed effect for a track on a layered half-space subject to a moving load. Three different methods are used to investigate this resonance frequency: (i) the spectrum of the response to a moving load, (ii) analysis of the dispersion curves of the ground, and (iii) frequency analysis of the response to a stationary load. A parameter study is presented of a layered half-space ground with different P-wave speeds, S-wave speeds, and depth of the upper layer. The critical speeds are found in each case; in such a layered ground, the critical speed is greater than the Rayleigh wave speed of the soft upper layer due to the influence of the underlying half-space. The oscillating frequencies are shown to vary with the speed of the moving load, tending to reduce when the load speed increases. The P-wave speeds of both the upper layer and the underlying half-space are found to have negligible influence on the critical velocity and on the oscillating frequency; the S-wave speed of the half-space has only a small influence. Larger differences are found when the depth of the layer is varied. Finally, a formula for calculating this resonance frequency is proposed.

An Investigation of the Dynamical Transitions in Harmonically Driven Random Networks of Firing-Rate Neurons

Continuous-time recurrent neural networks are widely used as models of neural dynamics and also have applications in machine learning. But their dynamics are not yet well understood, especially when they are driven by external stimuli. In this article, we study the response of stable and unstable networks to different harmonically oscillating stimuli by varying a parameter ρ, the ratio between the timescale of the network and the stimulus, and use the dimensionality of the network’s attractor as an estimate of the complexity of this response. Additionally, we propose a novel technique for exploring the stationary points and locally linear dynamics of these networks in order to understand the origin of input-dependent dynamical transitions. Attractors in both stable and unstable networks show a peak in dimensionality for intermediate values of ρ, with the latter consistently showing a higher dimensionality than the former, which exhibit a resonance-like phenomenon. We explain changes in the dimensionality of a network’s dynamics in terms of changes in the underlying structure of its vector field by analysing stationary points. Furthermore, we uncover the coexistence of underlying attractors with various geometric forms in unstable networks. As ρ is increased, our visualisation technique shows the network passing through a series of phase transitions with its trajectory taking on a sequence of qualitatively distinct figure-of-eight, cylinder, and spiral shapes. These findings bring us one step closer to a comprehensive theory of this important class of neural networks by revealing the subtle structure of their dynamics under different conditions.

Impact of bounded noise on the formation and instability of spiral wave in a 2D Lattice of neurons

Spiral waves in the neocortex may provide a spatial framework to organize cortical oscillations, thus help signal communication. However, noise influences spiral wave. Many previous theoretical studies about noise mainly focus on unbounded Gaussian noise, which contradicts that a real physical quantity is always bounded. Furthermore, non-Gaussian noise is also important for dynamical behaviors of excitable media. Nevertheless, there are no results concerning the effect of bounded noise on spiral wave till now. Based on Hodgkin-Huxley neuron model subjected to bounded noise with the form of Asin[ωt + σW(t)], the influences of bounded noise on the formation and instability of spiral wave in a two-dimensional (2D) square lattice of neurons are investigated in detail by separately adjusting the intensity σ, amplitude A, and frequency f of bounded noise. It is found that the increased intensity σ can facilitate the formation of spiral wave while the increased amplitude A tends to destroy spiral wave. Furthermore, frequency of bounded noise has the effect of facilitation or inhibition on pattern synchronization. Interestingly, for the appropriate intensity, amplitude and frequency can separately induce resonance-like phenomenon.

Mechanical Motion Induced by Spatially Distributed Limit-Cycle Oscillators

Spatially distributed limited-cycle oscillators are seen in various physical and biological systems. In internal organs, mechanical motions are induced by the stimuli of spatially distributed limit-cycle oscillators. We study several mechanical motions by limit-cycle oscillators using simple model equations. One problem is deformation waves of radius oscillation induced by desynchronized limit-cycle oscillators, which is motivated by peristaltic motion of the small intestine. A resonance-like phenomenon is found in the deformation waves, and particles can be transported by the deformation waves. Another is the beating motion of the heart. The expansion and contraction motion is realized by a spatially synchronized limit-cycle oscillation; however, the strong beating disappears by spiral chaos, which is closely related to serious arrhythmia in the heart.

Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling

Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage (p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.

Noise-induced resonance-like phenomena in InP crystals embedded in fluctuating electric fields

We explore and discuss the complex electron dynamics inside a low-doped n-type InP bulk embedded in a sub-THz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise. The results presented in this study derive from numerical simulations obtained by means of a multi-valley Monte Carlo approach to simulate the nonlinear transport of electrons inside the semiconductor crystal. The electronic noise characteristics are statistically investigated by calculating the correlation function of the velocity fluctuations, its spectral density and the integrated spectral density, i.e. the total noise power, for different values of both amplitude and frequency of the driving oscillating electric field and for different correlation times of the field fluctuations. Our results show that the nonlinear response of electrons is strongly affected by the field fluctuations. In particular, crucially depending on the relationship between the correlation times of the external Gaussian noise and the timescales of complex phenomena involved in the electron dynamical behavior: (i) electrons self-organize among different valleys, giving rise to intrinsic noise suppression; (ii) this cooperative behavior causes the appearance of a resonance-like phenomenon in the noise spectra.

Dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation

We present measurements of the azimuthal rotation velocity $\dot{{\it\theta}}(t)$ and thermal amplitude ${\it\delta}(t)$ of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation. Both $\dot{{\it\theta}}(t)$ and ${\it\delta}(t)$ exhibit clear oscillations at the modulation frequency ${\it\omega}$. Fluid acceleration driven by oscillating Coriolis force causes an increasing phase lag in $\dot{{\it\theta}}(t)$ when ${\it\omega}$ increases. The applied modulation produces oscillatory boundary layers and the resulting time-varying viscous drag modifies ${\it\delta}(t)$ periodically. Oscillation of $\dot{{\it\theta}}(t)$ with maximum amplitude occurs at a finite modulation frequency ${\it\omega}^{\ast }$. Such a resonance-like phenomenon is interpreted as a result of optimal coupling of ${\it\delta}(t)$ to the modulated rotation velocity. We show that an extended large-scale circulation model with a relaxation time for ${\it\delta}(t)$ in response to the modulated rotation provides predictions in close agreement with the experimental results.

Nano watermill driven by revolving charge**Project supported by the National Natural Science Foundation of China (Grant Nos. 11005093 and 61274099), the Research Fund of Education Department of Zhejiang Province, China (Grant No. Y201223336), the Zhejiang Provincial Science and Technology Key Innovation Team, China (Grant No. 2011R50012), the Key Laboratory of Zhejiang Province, China (Grant No. 2013E10022), and the Hong Kong

A novel nanoscale watermill for the unidirectional transport of water molecules through a curved single-walled carbon nanotube (SWNT) is proposed and explored by molecular dynamics simulations. In this nanoscale system, a revolving charge is introduced to drive a water chain confined inside the SWNT, the charge and the tube together serving as a nano waterwheel and nano engine. A resonance-like phenomenon is found, and the revolving frequency of the charge plays a key role in pumping the water chain. The water flux across the SWNT increases with respect to the revolving frequency of the external charge and it reaches its maximum when the frequency is 4 THz. Correspondingly, the number of hydrogen bonds in the water chain inside the SWNT decreases dramatically as the frequency increases from 4 THz to 25 THz. The mechanism behind the resonance phenomenon has been investigated systematically. Our findings are helpful for the design of nanoscale fluidic devices and energy converters.

Frequency dielectric response of ferroelectric–magnetic ceramic composites like PbZr0.65Ti0.35O3–BaFe12O19

The dielectric properties of PbZr0.65Ti0.35O3–BaFe12O19 (PZT–BaM) multiferroic ceramic composites, obtained from the conventional solid-state reaction method, have been investigated. While there is some dielectric dispersion at low frequencies, the highly-stable values of dielectric permittivity over a wide frequency range, together with low dielectric losses (~10−3), make these composites suitable for practical radio-frequency and potential microwave device applications. Toward high frequencies, the data reveal an anomalous resonance-like phenomenon. This resonance phenomenon is connected to an over-damped resonance mechanism for the vibration of the boundaries of polar regions, associated with the ferroelectric phase. A noticeable dependence of the parameters characterizing this last dielectric dispersion with the BaM concentration is found, indicating a strong influence of the magnetic phase on the dynamics of the ferroelectric domain-wall motion.

Controlling extreme events on complex networks.

Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.

Stochastic resonance for information flows on hierarchical networks

A simple model of information flows represented by package delivery on networks with hierarchical structures is considered. The packages should be transferred from one network node to another and the delivery process is influenced by two types of noise. The first type of noise is related to a partially false knowledge of network topology (topological noise), i.e. membership of nodes in communities in a shipping algorithm include a number of errors corresponding to a random rewiring of a fraction of network links. The second type of noise (dynamical noise) is related to a diffusive part in packet dynamics, i.e. package paths do not follow from completely deterministic rules. In the case of a pure topological noise and in the case of combination of both types of noises, we observe a resonance-like phenomenon for communication efficiency. The system performance measured as a fraction of packages that are delivered in a certain time period or as an inverse of time of a package delivery is maximal for intermediate levels of noise. This effect resembles the phenomenon of stochastic resonance that exists in many complex systems where a noise can enhance the information transfer.

Effect of nonidentical signal phases on signal amplification of two coupled excitable neurons

In this paper, we study the response of two coupled excitable neurons to external subthreshold periodic signals. We find that the neurons' response to the subthreshold signals can be enhanced when the signal phases are nonidentical. Moreover, we find that the response can be strongly improved if the level of nonidentical signal phases is at an intermediate value and thus resulting in a resonance-like phenomenon. Furthermore, under the influence of nonidentical signal phases, the response also exhibits a resonance-like dependency on the coupling coefficient. Moreover, we give an analysis to understand the mechanism of these two types of resonance behaviors. Finally, we discuss the robustness of the resonances induced by nonidentical signal phases to neuronal diversity, noise perturbation and different neuron model. We believe that the phenomena found in this paper will be useful for understanding neural information processing.