Resonance-like Phenomena Research Articles

Synchronization, Multiresonance Phenomena, and Discrete Oscillation Periods in a Hopfield Neural Network with Two Time Delays

Hopfield neural network attracts particular attention as it serves as a relatively simple mathematical model that describes some properties of the brain function. We investigate analog Hopfield neural networks with two time delays. It is shown that the neural network with all inhibitory connections demonstrates growing oscillations after exceeding the threshold, and oscillations become synchronous after a relatively short period of time of the order of the larger time delay. The oscillation amplitude of the neural network as function of the time delay in one subnetwork demonstrates resonance-like phenomena with multiple peaks. The oscillation period of the neural network with two time delays shows discrete structure and changes within relatively narrow intervals in contrast to the oscillation period of the neural network with one time delay, which shows continuous changes of oscillation amplitude and period with time delay. Multiresonance behavior is sustained for both inhibitory and excitatory connections of the second subnetwork, while the first subnetwork possesses only inhibitory connections. The oscillation period of the subnetwork with smaller time delay and equal coupling strengths dominates the whole neural network activity. Turning on and off smaller time delay in one subnetwork allows for the control of the oscillation period and demonstrates memory-like behavior. Mechanisms of the simulated phenomena are disclosed and their similarity to brain function is discussed.

Effects of pulse-like earthquake motions on a typical subway station structure obtained in shaking-table tests

A series of large-scale shaking table tests on a typical subway station structure were carried out for pulse-like earthquake motions. The propagation of earthquake motions in soils is explored. The effects of velocity pulse parameters (i.e., pulse shape, pulse frequency (fp), and pulse duration (Tpd)) on dynamic responses of the structure are analyzed from the viewpoint of the dynamic characteristics of soils. It is found that the site amplifies the frequency components of dynamic excitation in specific frequency bands (i.e., the amplification frequency band, AFB). With an increase in earthquake motion intensity, the AFB gradually moves towards low frequencies. Additionally, the bandwidth gradually narrows. The velocity pulse increases the amplitude of the first-mode shear deformation of soils and thus the seismic internal force response of underground structures. In addition, the effect of a one-sided pulse in terms of increasing the first-order shear deformation amplitude of soil is more pronounced than the effect of a two-sided pulse. Pulse-like earthquake motions with long pulse duration and multiple pulse cycles may trigger remarkable resonance-like phenomena of soils and further aggravate soil and structure responses when the main pulse frequencies are located in the AFB of soils.

Tracking Critical Points on Evolving Curves and Surfaces

In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution N(t) of the number N of static balance points of the abrading particle. Static balance points correspond to the critical points of the particle’s surface represented as a scalar distance function r, measured from the center of mass of the particle, so their time evolution can be expressed as . The mathematical model of the particle can be constructed on two scales: on the macro (global) scale the particle may be viewed as a smooth, convex manifold described by the smooth distance function r with equilibria, while on the micro (local) scale the particle’s natural model is a finely discretized, convex polyhedral approximation r Δ of r, with equilibria. There is strong intuitive evidence suggesting that under some particular evolution models (e.g., curvature-driven flows) N(t) and N Δ(t) primarily evolve in the opposite manner (i.e. if one is increasing then the other is decreasing and vice versa). This observation appears to be a key factor in tracking geophysical abrasion. Here we create the mathematical framework necessary to understand these phenomena more broadly, regardless of the particular evolution equation. We study micro and macro events in one-parameter families of curves and surfaces, corresponding to bifurcations triggering the jumps in N(t) and N Δ(t). Based on this analysis we show that the intuitive picture developed for curvature-driven flows is not only correct, it has universal validity, as long as the evolving surface r is smooth. In this case, bifurcations associated with r and r Δ are coupled to some extent: resonance-like phenomena in N Δ(t) can be used to forecast downward jumps in N(t) (but not upward jumps). Beyond proving rigorous results in the case of evolving planar curves for the limit on the nontrivial interplay between singularities in the discrete and continuum approximations we also show that our mathematical model is structurally stable. This property serves as the basis for the second, experimental part of our research where we demonstrate via computer simulations that the phenomena on evolving surfaces appear to be closely analogous to the planar case, however, they also show additional geometric features which are still not completely understood.

Role of spin-transfer torques on synchronization and resonance phenomena in stochastic magnetic oscillators

A theoretical study on how synchronization and resonance-like phenomena in superparamagnetic tunnel junctions can be driven by spin-transfer torques is presented. We examine the magnetization of a superparamagnetic free layer that reverses randomly between two well-defined orientations due to thermal fluctuations, acting as a stochastic oscillator. When subject to an external ac forcing, this system can present stochastic resonance and noise-enhanced synchronization. We focus on the roles of the mutually perpendicular damping-like and field-like torques, showing that the response of the system is very different at low and high frequencies. We also demonstrate that the field-like torque can increase the efficiency of the current-driven forcing, especially at sub-threshold electric currents. These results can be useful for possible low-power, more energy efficient applications.

Strong perturbations in nonlinear systems

A novel case of probabilistic coupling for hybrid stochastic systems with chaotic components via Markovian switching is presented. We study its stability in the norm, in the sense of Lyapunov and present a quantitative scheme for detection of stochastic stability in the mean. In particular we examine the stability of chaotic dynamical systems in which a representative parameter undergoes a Markovian switching between two values corresponding to two qualitatively different attractors. To this end we employ, as case studies, the behaviour of two representative chaotic systems (the classic Rossler and the Thomas-Rossler models) under the influence of a probabilistic switch which modifies stochastically their parameters. A quantitative measure, based on a Lyapunov function, is proposed which detects regular or irregular motion and regimes of stability. In connection to biologically inspired models (Thomas-Rossler models), where strong fluctuations represent qualitative structural changes, we observe the appearance of stochastic resonance-like phenomena i.e. transitions that lead to orderly behavior when the noise increases. These are attributed to the nonlinear response of the system.

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.

A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells.

Experimental studies recently performed on single cancer and healthy cells have demonstrated that the former are about 70% softer than the latter, regardless of the cell lines and the measurement technique used for determining the mechanical properties. At least in principle, the difference in cell stiffness might thus be exploited to create mechanical-based targeting strategies for discriminating neoplastic transformations within human cell populations and for designing innovative complementary tools to cell-specific molecular tumour markers, leading to possible applications in the diagnosis and treatment of cancer diseases. With the aim of characterizing and gaining insight into the overall frequency response of single-cell systems to mechanical stimuli (typically low-intensity therapeutic ultrasound), a generalized viscoelastic paradigm, combining classical and spring-pot-based models, is introduced for modelling this problem by neglecting the cascade of mechanobiological events involving the cell nucleus, cytoskeleton, elastic membrane and cytosol. Theoretical results show that differences in stiffness, experimentally observed ex vivo and in vitro, allow healthy and cancer cells to be discriminated, by highlighting frequencies (from tens to hundreds of kilohertz) associated with resonance-like phenomena—prevailing on thermal fluctuations—that could be helpful in targeting and selectively attacking tumour cells.

Resonance-like phenomena in a submerged cylindrical shell subjected to two consecutive shock waves: The effect of the inner fluid

A submerged fluid-filled cylindrical shell subjected to a sequence of two shock waves originated at the same source is considered. It is demonstrated that, unlike in the case of a submerged evacuated shell, there exists a certain critical range of the values of the delay between the incident wavefronts where both the peak compressive and the peak tensile stress observed in the structure are significantly (60% or more) higher than the respective stresses in the same system subjected to a single-front loading. It is further demonstrated that the highest and the lowest hydrodynamic pressure attained in the system is also dramatically affected for certain values of the delay between the incident wavefronts, with the maximum double-front pressure being more than 30% higher than its single-front counterpart. The practical relevance of the findings is discussed in the context of the pre-design analysis of industrial systems subjected to shock loading.

Submerged circular cylindrical shell subjected to two consecutive shock waves: Resonance-like phenomena

A submerged evacuated circular cylindrical shell subjected to a sequence of two external shock waves generated at the same source is considered. A semi-analytical model combining the classical methods of mathematical physics with the finite-difference methodology is developed and employed to simulate the interaction. Both the hydrodynamic and structural aspects of the problem are considered, and it is demonstrated that varying the delay between the first and second wavefronts has a very significant effect on the stress–strain state of the structure. In particular, it is shown that for certain values of the delay, the constructive superposition of the elastic waves travelling around the shell results in a ‘resonance-like’ increase of the structural stress in certain regions. The respective stress can be so high that it sometimes exceeds the overall maximum stress observed in the same structure but subjected to a single-front shock wave with the same parameters, in some cases by as much as 50%. A detailed parametric analysis of the observed phenomenon is carried out, and an easy-to-use diagram summarizing the finding is proposed to aim the pre-design analysis of engineering structures.

Resonancelike phenomena in the mobility of a chain of nonlinear coupled oscillators in a two-dimensional periodic potential

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

Investigation of the wall friction in the pipe induced by the oscillating flow

The wall friction induced by the oscillating flow of the fractional derivative Maxwell viscoelastic fluid in the pipe is investigated. The velocity and the shear stress solutions of the flow are solved. The friction is derived from the shear stress expression and analysed by numerical simulation. From analysis, it is found that the friction amplitude exhibits resonance-like phenomena. Moreover, the number of the resonance-like peaks, the enhancement magnitude, and the resonance-like frequency of the same order vary with the pipe radius and rheological parameters of fluids. When the radius overtakes the critical value, the friction curve monotonously decreases, and when the radius is big enough, the enhancement disappears.

Here and there, near and far: How proximity and separation affect scattering in concert halls

Classical theory of scattering deals with plane waves, waves which are so far from their source that they form straight fronts of sound, with pressure amplitude and particle velocity exactly in phase. If such waves are much larger than objects they encounter inverse fourth power (Rayleigh) scattering obtains; if the waves are about the same size as the objects resonant (Mie) scattering occurs; if waves are much shorter than the objects specular (Ufimtsev) scattering is the rule. These all affect sound in the far field. But if sources are closer than a wavelength to objects their waves encounter the plane approximation is not valid; pressure amplitude and particle velocity are not in phase, so resonance-like phenomena occur. These occur on stages of concert halls: bass instruments producing waves 2 m or longer always are close to the floor; some, like tympani and viols, can be close to vertical surfaces too. This sort of scat-tering enhances fundamentals of notes with respect to the overtones, strongly affecting the timbre of such instruments.

Laser-induced recollision phenomena: interference resonances at channel closings.

An analytical theory of the resonancelike phenomena in high-order above-threshold ionization is presented that explains details of the experimental spectra and theoretical simulations. It traces the observed features to the constructive interference of "quantum orbits" with long travel times at laser intensities where the N-photon ionization channels close. Characteristic differences show up between even and odd N. The effects are generic to all laser-induced recollision phenomena. For nonsequential double ionization, their signature in the momentum distribution of the final electrons is identified.

Resonance behavior of viscoelastic fluids in Poiseuille flow and application to flow enhancement

Resonance-like phenomena in axisymmetric Poiseuille flows of viscoelastic fluids are studied. It is shown that instantaneous flow velocities of the upper convected Maxwell fluid with a spectrum of relaxation times drastically increase at certain frequencies of the oscillating pressure gradient. This effect becomes more pronounced as the tube radius gets smaller. Non-linear constitutive structures are also considered to show that the most effective mean flow rate enhancement for pulsating flows can be reached at the resonance frequencies.

Resonance-like phenomena in Lyapunov calculations from data reconstructed by the time-delay method

The time-delay method introduces a certain structure in form of symmetries into reconstructed data sets. We show, that this structure may cause resonance-like phenomena in Lyapunov calculations. The “resonance effects” can be avoided by a small modification of the algorithms.

Fluctuations in the cross section and the dibaryon

Microscopic calculations for the transition from the resonance picture to the fluctuator picture of nuclear reaction cross sections at low energies are performed. The two pictures can clearly be distinguished experimentally. The observation of resonances is evidence of the fact that the long-living stationary modes are relevant and the process is irreversible due to their memory. The observation of fluctuations, however, corresponds to the fact that the dynamical short-living reversible modes are relevant. Nevertheless, this process is also microscopically irreversible, due to the existence of the long-living traps in which the many-body properties of the system are conserved. As a consequence, irreversibility on a microscopic level and dynamical behaviour of the interaction are not in contradiction with one another. The calculations performed for the nuclear system may be considered as model calculations for the dibaryon. In order to obtain information on the dibaryon, it is necessary to clarify whether the observed resonance-like phenomena correspond to resonances or fluctuations.

Resonance-like phenomena in activated dissociative adsorption: N+2 on Ni(100) and Ni(111)

Atomic nitrogen adsorption on Ni(100) and Ni(111) surfaces was studied by using very low energy (1–20 eV) N+2 and N+ ion beams. The amount of adsorbed nitrogen was measured by Auger electron spectroscopy as a function of the incident energy of the ions. The adsorption rate for N+ is almost a constant, whereas the dissociative-adsorption rate for N+2 is strongly energy dependent. In the latter case, there exist two channels; one has a low apparent activation barrier of about 1 eV and the other of about 5 eV. A resonance-like feature in the low-activation-barrier reaction was observed at the incident energy of 2–3 eV on Ni(100) and ∼4 eV on Ni(111). The adsorption rate is independent of the angle of incidence. The resonance-like feature is explained by a model which assumes that electronically excited molecules produced by resonance neutralization of the incident ions are dissociatively adsorbed over the low activation barrier and the excited molecules are deexcited on the surface at higher incident energies.