Reduced transport of swimming particles in chaotic flow due to hydrodynamic trapping

We computationally study the transport of active, self-propelled particles suspended in a two-dimensional chaotic flow. The pointlike, spherical particles have their own intrinsic swimming velocity, which modifies the dynamical system so that the particles can break the transport barriers present in the carrier flow. Surprisingly, we find that swimming does not necessarily lead to enhanced particle transport. Small but finite swimming speed can result in reduced transport, as swimmers get stuck for long times in traps that form near elliptic islands in the background flow. Our results have implications for models of transport and encounter rates for small marine organisms.     

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.     

Flow-induced oscillations of a cantilevered pipe conveying fluid with base excitation

It is known that a plain cantilevered pipe conveying fluid loses its stability by a Hopf bifurcation, leading to either planar or non-planar flutter for flow velocities beyond the critical flow velocity for Hopf bifurcation. If an external mass is attached to the end of the pipe (an end-mass), the resulting dynamics become much richer, showing 2D and 3D quasiperiodic and chaotic oscillations at high flow velocities. In this paper, a cantilevered pipe, with and without an end-mass, subjected to a small-amplitude periodic base excitation is considered. A set of three-dimensional nonlinear equations is used to analyze the pipe?s response at various flow velocities and with different amplitudes and frequencies of base excitation. The nonlinear equations are discretized using the Galerkin technique and the resulting set of equations is solved using Houbolt?s finite difference method. It is shown that for a plain pipe (with no end-mass), non-planar post-instability oscillations can be reduced to planar periodic oscillations for a range of base excitation frequencies and amplitudes. For a pipe with an end-mass, similarly to a plain pipe, three-dimensional period oscillations can be reduced to planar ones. At flow velocities beyond the critical flow velocity for torus instability, the three-dimensional quasiperiodic oscillations can be reduced to two-dimensional quasiperiodic or periodic oscillations, depending on the frequency of base excitation. In all these cases, a low-amplitude base excitation results in reducing the three-dimensional oscillations of the pipe to purely two-dimensional oscillations, over a range of excitation frequencies. These numerical results are in agreement with the previous experimental work.     

Features of the dynamics of particles and fields at cyclotron resonances

Some features of the dynamics of particles and fields at cyclotron resonances have been discussed with the focus on chaotic dynamical regimes. It has been shown that the known criterion of the transition of the regular dynamics of particles to chaotic dynamics at cyclotron resonances sometimes describes this transition incorrectly. The reason for such a feature of the criterion has been revealed. The anomalous sensitivity of the dynamics of particles to external fluctuations at autoresonance has been analyzed. A theory of excitation of electromagnetic waves by a beam of phased oscillators under the conditions of isolated nonlinear cyclotron resonance has been developed. It has been shown that the chaotic dynamical regime is due to the periodic change in the structure of the phase portrait of particles in the wave field. It has been shown that higher moments can play a more significant role than lower moments in almost all chaotic dynamical regimes at cyclotron resonances. In this case, the known kinetic diffusion equations should be generalized with the inclusion of these higher moments.     

Statistics of resonances and time reversal reconstruction in aluminum acoustic chaotic cavities

The statistical properties of wave propagation in classical chaotic systems are of fundamental interest in physics and are the basis for diagnostic tools in materials science. The statistical properties depend in particular also on the presence of time reversal invariance in the system, which can be verified independently by time reversal reconstruction experiments. As a model system to test the combination of statistical properties with the ability to perform time reversal reconstruction we investigated chaotic systems with time reversal invariance using ultrasonic waves in aluminum cavities. After excitation of the samples with a short acoustic pulse the reverberation responses were recorded and analyzed. In the analysis of the spectral density of the recorded responses we explicitly included the fact that not all resonances are detected. Reversibility of the excited wave dynamics in the cavity after a time delay was studied by reconstruction of the excitation pulse in time reversal experiments. The statistical properties of resonance frequencies in the cavities were obtained from the reverberant responses. The distribution of the transmission intensities displays random division of intensity between cavity waves in narrow frequency bands. The distribution of frequency spacing between neighboring cavity resonances and the spectral rigidity agree with the predictions for the Gaussian Orthogonal Ensemble. This agreement is achieved if a fraction of typically 25 percent of resonances is not detected in the experiment. The normalized amplitude of the pulse that is reconstructed in the time reversal experiments decays exponentially with the time delay between the original excitation pulse and the end of the reversed oscillation track. The exponential behavior exists for time delays longer than the inverse of the nearest neighbor resonance spacing.     

Experimental evidence of simultaneous multi-resonance noise reduction using an absorber with essential nonlinearity under two excitation frequencies

The addition of an essentially nonlinear membrane absorber to a linear vibroacoustic system with multiple resonances is studied experimentally, using quasiperiodic excitation. An extended experimental dataset of the system response is analyzed under steady-state excitation at two frequencies. Thresholds between low and high damping states within the system and associated noise reduction are observed and quantified thanks to frequency conversion and RMS efficiency indicators. Following previous numerical results, it is shown that the membrane NES (Nonlinear Energy Sink) acts simultaneously and efficiently on two acoustic resonances. In all cases, the introduction of energy at a second excitation frequency appears favorable to lower the frequency conversion threshold and to lower the noise within the system. In particular, a simultaneous control of two one-to-one resonances by the NES is observed. Exploration of energy conversion in the two excitation amplitudes plane advocates for a linear dependence of the frequency conversion thresholds on the two excitation amplitudes.     

Controlling the ratchet effect for cold atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.     

Brillouin spectroscopy of nonlinear magnetoacoustic resonances in a layered YIG/GGG structure

Brillouin light scattering spectroscopy is used to visualize the spatial structure of magnetoacoustic resonances in an yttrium iron garnet (YIG) film on a gadolinium–gallium garnet (GGG) substrate under the strong influence of nonlinear processes of three magnon decay. It is shown that the decay processes result in the simultaneous excitation of magnetoacoustic resonances at two frequencies: those of the input signal and its half frequency. The distribution of coupled magnetic and elastic waves becomes much more complicated and the excitation threshold of magnetoacoustic resonances arises.     

What is the role of chaotic scattering in irreversible processes?

We study kinetic properties of simple mechanical models of deterministic diffusion like the scattering of a point particle in a billiard of Lorentz type and the multibaker area-preserving map. We show how dynamical chaos and, in particular, chaotic scattering are related to the transport property of diffusion. Moreover, we show that the Liouvillian dynamics of the multibaker map can be decomposed into the eigenmodes of diffusive relaxation associated with the Ruelle resonances of the Perron-Frobenius operator.     

A novel excitation scheme to enhance image resolution in dynamic atomic force microscopy

We propose a novel multifrequency excitation technique for the non-contact atomic force microscopy (AFM). The probe is excited at two frequencies that are far from resonances while their subtraction is close to the fundamental frequency. Due to combination resonance occurring in nonlinear systems, the response includes a term with frequency equal to subtraction of excitation frequencies. We suggest to employ this term as the main signal for imaging. It is found that the present excitation improves signal sensitivity to sample topography and increases resolution. This technique is especially convenient for highly-damped environments where non-contact AFMs are very difficult to use.     

The effect of Lagrangian chaos on locking bifurcations in shear flows

The effect of an externally imposed perturbation on an unstable or weakly stable shear flow is investigated, with a focus on the role of Lagrangian chaos in the bifurcations that occur. The external perturbation is at rest in the laboratory frame and can form a chain of resonances or cat's eyes where the initial velocity v(x0)(y) vanishes. If in addition the shear profile is unstable or weakly stable to a Kelvin-Helmholtz instability, for a certain amplitude of the external perturbation there can be an unlocking bifurcation to a nonlinear wave resonant around a different value of y, with nonzero phase velocity. The interaction of the propagating nonlinear wave with the external perturbation leads to Lagrangian chaos. We discuss results based on numerical simulations for different amplitudes of the external perturbation. The response to the external perturbation is strong, apparently because of non-normality of the linear operator, and the unlocking bifurcation is hysteretic. The results indicate that the observed Lagrangian chaos is responsible for a second bifurcation occurring at larger external perturbation, locking the wave to the wall. This bifurcation is nonhysteretic. The mechanism by which the chaos leads to locking in this second bifurcation is by means of chaotic advective transport of momentum from one chain of resonances to the other (Reynolds stress) and momentum transport to the vicinity of the wall via chaotic scattering. These results suggest that locking of waves in rotating tank experiments in the presence of two unstable modes is due to a similar process. (c) 2002 American Institute of Physics.     

Deterministic chaos in the dynamics of charged particles near a magnetic field reversal

The charged particle motion near magnetic field reversals shows a miscellaneous picture, alternating between chaotic and regular trajectories. A general scheme for the different types of solutions in dependence on the initial phase space domain has been obtained as for as the chaotization thresshold and a velocity-space diffusion coefficient in strongly curved fields.     

Period multiplication and chaotic behaviour in a driven non-linear piezoelectric resonator

Experimental observations show that the frequencies of piezoelectrically active vibrational resonances of Rochelle salt can be tuned over a 2 : 1 range by an applied voltage. At high driving amplitudes, subharmonics of the driving frequency occur, accompanied by regions of chaotic behaviour, due to the non-linear nature of the resonant system.     

Enhanced evanescent coupling to whispering-gallery modes due to gold nanorods grown on the microresonator surface

The evanescent fields of whispering-gallery modes of a high-Q dielectric microresonator are locally enhanced via excitation of the surface plasmon resonances of gold nanorods grown on the microresonator’s surface. This results in enhanced coupling between the microresonator and an adjacent tapered optical fiber for frequencies in the vicinity of the surface plasmon resonance. The experimental results presented here demonstrate coupling enhancement by a factor of 100–1000, accompanied by an increase in absorption and scattering loss that is very small by comparison.     

Chaos in composite billiards

The mechanisms and features of the chaotic behavior in billiards with ray splitting (refraction) are considered. In contrast to ordinary billiards, the law of motion in composite billiards that is coded with a sequence of ray visits to different media is shown to be deterministically chaotic. The analysis is performed in terms of a geometrical-dynamical approach in which a symmetric phase space is used instead of the ordinary Hamiltonian phase space. The chaotization elements in composite billiards of a general position are studied. The dynamics of rays in ring billiards consisting of two concentric media with different refractive indices is considered.     

Electric and magnetic excitations in anisotropic broadside-coupled triangular-split-ring resonators

The electric and magnetic resonances of anisotropic broadside-coupled triangular-split-ring resonators are studied for different incident wave excitations. It is shown that the higher order modes exist in both electric and magnetic resonances. It is observed that the incident electric field couples to the magnetic resonance of the designed structure under different excitations. Multiple resonance features due to the anisotropy of the structure are found in the case of different excitations and the nature of these resonances can be regulated as either an electric or a magnetic mode for different frequencies. In this way, a resonant effective permittivity or permeability can be obtained. Hence, controllable properties of the constitutive material parameters (i.e. electric or magnetic resonances, negative values, etc.) can be determined by changing the incident wave excitation.     

Bubble acoustical scattering cross section under multi-frequency acoustic excitation

The acoustical scattering cross section is usually employed to evaluate the scattering ability of the bubbles when they are excited by the incident acoustic waves. This parameter is strongly related to many important applications of performance prediction for search sonar or underwater telemetry, acoustical oceanography, acoustic cavitation, volcanology, and medical and industrial ultrasound. In the present paper, both the analytical and numerical analysis results of the acoustical scattering cross section of a single bubble under multi-frequency excitation are obtained. The nonlinear characteristics(e.g.,harmonics, subharmonics, and ultraharmonics) of the scattering cross section curve under multi-frequency excitation are investigated compared with single-frequency excitation. The influence of several paramount parameters(e.g., bubble equilibrium radius, acoustic pressure amplitude, and acoustic frequencies) in the multi-frequency system on the predictions of scattering cross section is discussed. It is shown that the combination resonances become significant in the multi-frequency system when the acoustic power is big enough, and the acoustical scattering cross section is promoted significantly within a much broader range of bubble sizes and acoustic frequencies due to the generation of more resonances.     

Chaotization of the virtual cathode oscillations in the external magnetic field created by a ring magnet

The physical mechanisms leading to the chaotization of the virtual cathode oscillations in a low-voltage vircator system at an increase in the amplitude of the external inhomogeneous magnetic field created by a ring magnet have been studied within a two-dimensional numerical model. It has been established that the chaotization of the virtual cathode oscillations in a strongly inhomogeneous external magnetic field is due to the formation of the secondary electronic structure (electron beam) in the electron flow resulting from the magnetic trap in the outer layers of the electron beam.     

Superconductor-proximity effect in hybrid structures: fractality versus chaos

We study the proximity effect of a superconductor to a normal system with a fractal spectrum. We find that there is no gap in the excitation spectrum, even in the case where the underlying classical dynamics of the normal system is chaotic. An analytical expression for the distribution of the smallest excitation eigenvalue E1 of the hybrid structure is obtained. On small scales it decays algebraically as P(E1) approximately E1(-D0), where D0 is the fractal dimension of the spectrum of the normal system. Our theoretical predictions are verified by numerical calculations performed for various models.     

Wheel/rail noise generation due to nonlinear effects and parametric excitation

Two models are developed, one in the time domain and another in the frequency domain, to explain when a wheel/rail noise generation model requires the inclusion of discrete supports, parametric excitation, and the nonlinear contact spring. Numerical simulations indicate the inclusion of discrete supports to describe low frequency response, and also at higher frequencies, especially where the rail is very smooth or has a corrugation/wavelength corresponding to the pinned-pinned frequency. With a corrugation, it may become essential to include the nonlinear contact spring, as contact loss occurs at high corrugation amplitudes. As nonlinearity causes force generation over a broad frequency range, some contributions excite wheel resonances, resulting in high radiation levels, that require the inclusion of wheel/rail nonlinear effects and parametric excitation for accurate prediction.