Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the intergrain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self-interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolution of the modulated wave packet, which is described by a nonlinear Schrodinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward. (C) 2004 American Institute of Physics.

Weakly nonlinear effects associated with transverse oscillations in dusty plasma crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Discrete breather modes associated with vertical dust grain oscillations in dusty plasma crystals

Accounting for the lattice discreteness and the sheath electric field nonlinearity in dusty plasma crystals, it is demonstrated that highly localized structures (discrete breathers) involving vertical (transverse, off-plane) oscillations of charged dust grains may exist in a dust lattice. These structures correspond to either extremely localized bright breather excitations (pulses) or dark excitations composed of dips/voids. Explicit criteria for selecting different breather modes are presented. (C) 2005 American Institute of Physics.

The Oscillations of Tau Pegasi

We present extensive spectroscopic time series observations of the multiperiodic, rapidly rotating, delta Scuti star tau Pegasi. Information about the oscillations is contained within the patterns of line-profile variation of the star's blended absorption-line spectrum. We introduce the new technique of Doppler deconvolution with which to extract these patterns by modeling the intrinsic stellar spectrum and the broadening functions for each spectrum in the time series. Frequencies and modes of oscillation are identified from the variations using the technique of Fourier-Doppler imaging and a two-dimensional least-squares cleaning algorithm. We find a rich mode spectrum with degrees up to l = 20 and with frequencies below about 35 cycles day-1. Those modes with the largest amplitudes have frequencies that lie within a narrow band. We conclude that the observed spectrum can be explained if the modes of tau Peg propagate in the prograde direction with l ~= |m| and with frequencies that are about equal in the corotating frame of the star. We discuss the implications of these results for the prospect of delta Scuti seismology.

The Origin of Type I Spicule Oscillations

We use images of high spatial and temporal resolution, obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, to reveal how the generation of transverse waves in Type I spicules is a direct result of longitudinal oscillations occurring in the photosphere. Here we show how pressure oscillations, with periodicities in the range of 130–440 s, manifest in small-scale photospheric magnetic bright points, and generate kink waves in the Sun’s outer atmosphere with transverse velocities approaching the local sound speed. Through comparison of our observations with advanced two-dimensional magnetohydrodynamic simulations, we provide evidence for how magnetoacoustic oscillations, generated at the solar surface, funnel upward along Type I spicule structures, before undergoing longitudinal-to-transverse mode conversion into waves at twice the initial driving frequency. The resulting kink modes are visible in chromospheric plasma, with periodicities of 65–220 s, and amplitudes often exceeding 400 km. A sausage mode oscillation also arises as a consequence of the photospheric driver, which is visible in both simulated and observational time series. We conclude that the mode conversion and period modi?cation is a direct consequence of the 90? phase shift encompassing opposite sides of the photospheric driver. The chromospheric energy ?ux of these waves are estimated to be ˜3 × 105 W m-2, which indicates that they are suf?ciently energetic to accelerate the solar wind and heat the localized corona to its multi-million degree temperatures.

Transverse Oscillations in Chromospheric Mottles

A number of recent investigations have revealed that transverse waves are ubiquitous in the solar chromosphere. The vast majority of these have been reported in limb spicules and active region fibrils. We investigate long-lived, quiet-Sun, on-disk features such as chromospheric mottles (jet-like features located at the boundaries of supergranular cells) and their transverse motions. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. The data set is comprised of simultaneous imaging in the Ha core, Ca II K, and G band of an on-disk quiet-Sun region. Time-distance techniques are used to study the characteristics of the transverse oscillations. We detect over 40 transverse oscillations in both bright and dark mottles, with periods ranging from 70 to 280 s, with the most frequent occurrence at ~165 s. The velocity amplitudes and transverse displacements exhibit characteristics similar to limb spicules. Neighboring mottles oscillating in-phase are also observed. The transverse oscillations of individual mottles are interpreted in terms of magnetohydrodynamic kink waves. Their estimated periods and damping times are consistent with phase mixing and resonant mode conversion.

Calcium oscillations in interstitial cells of the rabbit urethra.

Measurements were made (using fast confocal microscopy) of intracellular Ca2+ levels in fluo-4 loaded interstitial cells isolated from the rabbit urethra. These cells exhibited regular Ca2+ oscillations which were associated with spontaneous transient inward currents recorded under voltage clamp. Interference with D-myo-inositol 1,4,5-trisphosphate (IP3) induced Ca2+ release using 100 microm 2-aminoethoxydiphenyl borate, and the phospholipase C (PLC) inhibitors 2-nitro-4-carboxyphenyl N,N-diphenylcarbamate and U73122 decreased the amplitude of spontaneous oscillations but did not abolish them. However, oscillations were abolished when ryanodine receptors were blocked with tetracaine or ryanodine. Oscillations ceased in the absence of external Ca2+, and frequency was directly proportional to the external Ca2+ concentration. Frequency of Ca2+ oscillation was reduced by SKF-96365, but not by nifedipine. Lanthanum and cadmium completely blocked oscillations. These results suggest that Ca2+ oscillations in isolated rabbit urethral interstitial cells are initiated by Ca2+ release from ryanodine-sensitive intracellular stores, that oscillation frequency is very sensitive to the external Ca2+ concentration and that conversion of the primary oscillation to a propagated Ca2+ wave depends upon IP3-induced Ca2+ release.

Long-range synchronization and local desynchronization of alpha oscillations during visual short-term memory retention in children

Local alpha-band synchronization has been associated with both cortical idling and active inhibition. Recent evidence, however, suggests that long-range alpha synchronization increases functional coupling between cortical regions. We demonstrate increased long-range alpha and beta band phase synchronization during short-term memory retention in children 6-10 years of age. Furthermore, whereas alpha-band synchronization between posterior cortex and other regions is increased during retention, local alpha-band synchronization over posterior cortex is reduced. This constitutes a functional dissociation for alpha synchronization across local and long-range cortical scales. We interpret long-range synchronization as reflecting functional integration within a network of frontal and visual cortical regions. Local desynchronization of alpha rhythms over posterior cortex, conversely, likely arises because of increased engagement of visual cortex during retention.

Optical super-resolution through super-oscillations

We demonstrate that a quasi-periodic array of nanoholes in a metal screen can focus light into subwavelength spots in the far-field without contributions from evanescent fields. The subwavelength spots were observed with a conventional optical microscope and mapped to the far-field. We relate the formation of subwavelength light localizations in the far-field to the phenomenon of super-oscillations. This effect offers a new way to achieve subwavelength imaging, which differs from approaches based on the recovery of evanescent fields.

The Source of 3 Minute Magnetoacoustic Oscillations in Coronal Fans

We use images of high spatial, spectral, and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the coupling between wave phenomena observed at numerous heights in the solar atmosphere. Analysis of 4170 Å continuum images reveals small-scale umbral intensity enhancements, with diameters ~0."6, lasting in excess of 30 minutes. Intensity oscillations of ˜3 minutes are observed to encompass these photospheric structures, with power at least three orders of magnitude higher than the surrounding umbra. Simultaneous chromospheric velocity and intensity time series reveal an 87?±8? out-of-phase behavior, implying the presence of standing modes created as a result of partial wave re?ection at the transition region boundary. We ?nd a maximum waveguide inclination angle of˜40? between photospheric and chromospheric heights, combined with a radial expansion factor of <76%. An average blueshifted Doppler velocity of ˜1.5 km s-1, in addition to a time lag between photospheric and chromospheric oscillatory phenomena, con?rms the presence of upwardly propagating slow-mode waves in the lower solar atmosphere. Propagating oscillations in EUV intensity are detected in simultaneous coronal fan structures, with a periodicity of 172±17 s and a propagation velocity of 45±7 km s-1. Numerical simulations reveal that the damping of the magnetoacoustic wave trains is dominated by thermal conduction. The coronal fans are seen to anchor into the photosphere in locations where large-amplitude umbral dot (UD) oscillations manifest. Derived kinetic temperature and emission measure time series display prominent outof-phase characteristics, and when combined with the previously established sub-sonic wave speeds, we conclude that the observed EUV waves are the coronal counterparts of the upwardly propagating magnetoacoustic slow modes detected in the lower solar atmosphere. Thus, for the ?rst time, we reveal how the propagation of 3 minute magnetoacoustic waves in solar coronal structures is a direct result of amplitude enhancements occurring in photospheric UDs.photospheric UDs.

Analog of Rabi oscillations in resonant electron-ion systems

Quantum coherence between electron and ion dynamics, observed in organic semiconductors by means of ultrafast spectroscopy, is the object of recent theoretical and computational studies. To simulate this kind of quantum coherent dynamics, we have introduced in a previous article [L. Stella, M. Meister, A. J. Fisher, and A. P. Horsfield, J. Chem. Phys. 127, 214104 (2007)] an improved computational scheme based on Correlated Electron-Ion Dynamics (CEID). In this article, we provide a generalization of that scheme to model several ionic degrees of freedom and many-body electronic states. To illustrate the capability of this extended CEID, we study a model system which displays the electron-ion analog of the Rabi oscillations. Finally, we discuss convergence and scaling properties of the extended CEID along with its applicability to more realistic problems. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3589165]

Standing wave oscillations in an electrocatalytic reaction

Experimental standing wave oscillations of the interfacial potential across an electrode have been observed in the electrocatalytic oxidation of formic acid on a Pt ring working electrode. The instantaneous potential distribution was monitored by means of equispaced potential microprobes along the electrode. The oscillatory standing waves spontaneously arose from a homogeneous stationary state prior to a Hopf bifurcation if the reference electrode was placed close to the working electrode. Reduced electrolyte concentrations resulted in aperiodic potential patterns, while the presence of a sufficiently large ohmic resistance completely suppressed spatial inhomogeneities. The experimental findings confirm numerical predictions of a reaction-migration formalism: under the chosen geometry, a long-range negative potential coupling between distant points across the ring electrode can lead to oscillatory potential domains of distinct phase. It is further shown that the occurrence of oscillatory standing waves can be rationalized as the electrochemical equivalent of Turing's second bifurcation (wave bifurcation). In the presence of an external resistance, the coupling becomes positive throughout and leads to spatial synchronization.