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In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}$Rb. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.

In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}$Rb. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.

In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}$Rb. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.

A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation follows directly from the Euler-Lagrange equation in its general form. It is defined solely by the homogeneity orders. If the potential energy is represented by a single homogeneous function, as well as the kinetic energy, the partition between these energies is defined uniquely. Finite discrete systems, finite continual bodies, homogeneous and periodic-structure waveguides are considered. The general results are illustrated by examples of various types of oscillations and waves, linear and nonlinear, homogeneous and forced, steady-state and transient, periodic, non-periodic and solitary, regular, parametric and resonant. The reduced energy partition relation for statics is also presented.

A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation follows directly from the Euler-Lagrange equation in its general form. It is defined solely by the homogeneity orders. If the potential energy is represented by a single homogeneous function, as well as the kinetic energy, the partition between these energies is defined uniquely. Finite discrete systems, finite continual bodies, homogeneous and periodic-structure waveguides are considered. The general results are illustrated by examples of various types of oscillations and waves, linear and nonlinear, homogeneous and forced, steady-state and transient, periodic, non-periodic and solitary, regular, parametric and resonant. The reduced energy partition relation for statics is also presented.

A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation follows directly from the Euler-Lagrange equation in its general form. It is defined solely by the homogeneity orders. If the potential energy is represented by a single homogeneous function, as well as the kinetic energy, the partition between these energies is defined uniquely. Finite discrete systems, finite continual bodies, homogeneous and periodic-structure waveguides are considered. The general results are illustrated by examples of various types of oscillations and waves, linear and nonlinear, homogeneous and forced, steady-state and transient, periodic, non-periodic and solitary, regular, parametric and resonant. The reduced energy partition relation for statics is also presented.

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In the past few years observations by high-resolution space imaging telescopes and spectrometers have confirmed that a great variety of MHD waves are supported in the solar corona of a low-beta plasma and fine structure. MHD waves are an important diagnostic tool for the determination of the physical parameters of coronal loops, dubbed {\em coronal seismology}. In this paper, I will review recent results of both propagating and standing waves observed with SOHO and TRACE, and discuss the wave damping and excitation mechanisms as well as some applications of coronal seismology based on recent numerical simulations and theories in relation to the observations.

We investigate the non-linear coupling between radial and non-radial oscillations of static spherically symmetric neutron stars as a possible mechanism for the generation of gravitational waves that may lead to observable signatures. In this paper we concentrate on the axial sector of the non-radial perturbations. By using a multi-parameter perturbative framework we introduce a complete description of the non-linear coupling between radial and axial non-radial oscillations; we study the gauge invariant character of the associated perturbative variables and develop a computational scheme to evolve the non-linear coupling perturbations in the time domain. We present results of simulations corresponding to different physical situations and discuss the dynamical behaviour of this non-linear coupling. Of particular interest is the occurrence of signal amplifications in the form of resonance phenomena when a frequency associated with the radial pulsations is close to a frequency associated with one of the axial w-modes of the star. Finally, we mention possible extensions of this work and improvements towards more astrophysically motivated scenarios.

We study the non-radial oscillations of relativistic neutron stars, in particular the (fundamental) f-modes, which are believed to be the most relevant for the gravitational wave emission of perturbed isolated stars. The expected frequencies of the f-modes are compared to the sensitivity range of Mario Schenberg, the Brazilian gravitational wave spherical detector.

In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfv\'en waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfv\'en waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.

Book Source: Digital Library of India Item 2015.74162 dc.contributor.author: George W. Pierce dc.date.accessioned: 2015-06-30T14:08:43Z dc.date.available: 2015-06-30T14:08:43Z dc.date.digitalpublicationdate: 2004-07-09 dc.date.citation: 1920 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 3506 dc.identifier.origpath: /data7/upload/0177/293 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/74162 dc.description.numberedpages: 517 dc.description.numberedpages: 19 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 536 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Mcgraw-hill Book Company, Inc. dc.rights: Public Domain dc.title: Electric Oscillations And Electric Waves dc.rights.holder: Mcgraw-hill Book Company, Inc.

We analyze flare-associated transverse oscillations in a quiescent solar prominence on 8-9 September, 2010. Both the flaring active region and the prominence were located near the West limb, with a favorable configuration and viewing angle. The fulldisk extreme ultraviolet (EUV) images of the Sun obtained with high spatial and temporal resolution by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory, show flare-associated lateral oscillations of the prominence sheet. The STEREO-A spacecraft, 81.5 degrees ahead of the Sun-Earth line, provides on-disk view of the flare-associated coronal disturbances. We derive the temporal profile of the lateral displacement of the prominence sheet by using the image cross-correlation technique. The displacement curve was de-trended and the residual oscillatory pattern was derived. We fit these oscillations with a damped cosine function with a variable period and find that the period is increasing. The initial oscillation period (P0) is 28.2 minutes and the damping time (t_D) of 44 minutes. We confirm the presence of fast and slow EUV wave components. Using STEREO-A observations we derive a propagation speed of 250 km/s for the slow EUV wave by applying time-slice technique to the running difference images. We propose that the prominence oscillations are excited by the fast EUV wave while the increase in oscillation period of the prominence is an apparent effect, related to a phase change due to the slow EUV wave acting as a secondary trigger. We discuss implications of the dual trigger effect for coronal prominence seismology and scaling law studies of damping mechanisms.

We analyze flare-associated transverse oscillations in a quiescent solar prominence on 8-9 September, 2010. Both the flaring active region and the prominence were located near the West limb, with a favorable configuration and viewing angle. The fulldisk extreme ultraviolet (EUV) images of the Sun obtained with high spatial and temporal resolution by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory, show flare-associated lateral oscillations of the prominence sheet. The STEREO-A spacecraft, 81.5 degrees ahead of the Sun-Earth line, provides on-disk view of the flare-associated coronal disturbances. We derive the temporal profile of the lateral displacement of the prominence sheet by using the image cross-correlation technique. The displacement curve was de-trended and the residual oscillatory pattern was derived. We fit these oscillations with a damped cosine function with a variable period and find that the period is increasing. The initial oscillation period (P0) is 28.2 minutes and the damping time (t_D) of 44 minutes. We confirm the presence of fast and slow EUV wave components. Using STEREO-A observations we derive a propagation speed of 250 km/s for the slow EUV wave by applying time-slice technique to the running difference images. We propose that the prominence oscillations are excited by the fast EUV wave while the increase in oscillation period of the prominence is an apparent effect, related to a phase change due to the slow EUV wave acting as a secondary trigger. We discuss implications of the dual trigger effect for coronal prominence seismology and scaling law studies of damping mechanisms.

We analyze flare-associated transverse oscillations in a quiescent solar prominence on 8-9 September, 2010. Both the flaring active region and the prominence were located near the West limb, with a favorable configuration and viewing angle. The fulldisk extreme ultraviolet (EUV) images of the Sun obtained with high spatial and temporal resolution by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory, show flare-associated lateral oscillations of the prominence sheet. The STEREO-A spacecraft, 81.5 degrees ahead of the Sun-Earth line, provides on-disk view of the flare-associated coronal disturbances. We derive the temporal profile of the lateral displacement of the prominence sheet by using the image cross-correlation technique. The displacement curve was de-trended and the residual oscillatory pattern was derived. We fit these oscillations with a damped cosine function with a variable period and find that the period is increasing. The initial oscillation period (P0) is 28.2 minutes and the damping time (t_D) of 44 minutes. We confirm the presence of fast and slow EUV wave components. Using STEREO-A observations we derive a propagation speed of 250 km/s for the slow EUV wave by applying time-slice technique to the running difference images. We propose that the prominence oscillations are excited by the fast EUV wave while the increase in oscillation period of the prominence is an apparent effect, related to a phase change due to the slow EUV wave acting as a secondary trigger. We discuss implications of the dual trigger effect for coronal prominence seismology and scaling law studies of damping mechanisms.

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

"Electromagnetic Waves and Oscillations at the Surface of Conductors" is an article from American Journal of Mathematics, Volume 11 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369349

"Electromagnetic Waves and Oscillations at the Surface of Conductors" is an article from American Journal of Mathematics, Volume 11 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369349

"Electromagnetic Waves and Oscillations at the Surface of Conductors" is an article from American Journal of Mathematics, Volume 11 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369349

"Electromagnetic Waves and Oscillations at the Surface of Conductors" is an article from American Journal of Mathematics, Volume 11 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369349

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e < < m_i, \bar{v_i} < < \bar{v_e}, and T_e m_e < < T_i m_i results in expressions for transversal plasma-electron oscillation/wave decrements with a damping of the low-velocity electron branch \sim n_i^{1/3}/\bar{v}_e^{4/3}, where n_i is the ion density and \bar{v}_e is the mean electron velocity. It ought to rehabilitate Vlasov principal value prescription for relevant integrals, but to supplement it with representation of an asymptotical solution as a sum of exponents (not a single one). "Non-damping" kinematical waves in low-collision plasma transform in the damping ones at reasonably chosen iteration process.

Dispersion relations and polarizations for surface waves in infinite planar samples in the QHE regime are explicitly determined in the small wavevector limit in which the dielectric tensor can be considered as local. The wavelength and frequency regions of applicability of the results extends to the infrared region for typical experimental conditions. Then, standard samples with millimetric sizes seem to be able to support such excitations. Forced oscillations are also determined which should be generated in the 2DEG by external electromagnetic sources. They show an almost frequency independent wavevelength which decreases with the magnetic field. A qualitative model based in these solutions is also presented to describe a recently found new class of resonances appearing near the edge of a 2DEG in the QHE regime.

Dispersion relations and polarizations for surface waves in infinite planar samples in the QHE regime are explicitly determined in the small wavevector limit in which the dielectric tensor can be considered as local. The wavelength and frequency regions of applicability of the results extends to the infrared region for typical experimental conditions. Then, standard samples with millimetric sizes seem to be able to support such excitations. Forced oscillations are also determined which should be generated in the 2DEG by external electromagnetic sources. They show an almost frequency independent wavevelength which decreases with the magnetic field. A qualitative model based in these solutions is also presented to describe a recently found new class of resonances appearing near the edge of a 2DEG in the QHE regime.

QPOs are a common feature in the X-ray power density spectrum of black hole binaries and a potentially powerful tool to probe the spacetime geometry around these objects. Here we discuss their constraining power to test the Kerr black hole hypothesis within the relativistic precession model. We compare our results with the constraints that can be obtained from gravitational waves and iron line. We find that QPOs may provide very precise measurements, but they are strongly affected by parameter degeneracy, and it is difficult to test the Kerr metric with this approach in the absence of independent observations to constrain the mass or the spin.

Presentation about waves and their properties.

The behaviour of the toroidal and meridional components of the solar large-scale magnetic field and linear Alfven and Rossby waves during solar activity cycles and bi-annual time periods are theoretically investigated in this work. We consider the case of periodical velocity shear with bi-annual oscillation period . The large-scale magnetic field toroidal and meridional components are obtained as harmonic functions of the time. The sign reversal of these magnetic field components is studied. The numerical simulations show that, due to the velocity shear oscillations, the toroidal or meridional component of the large-scale magnetic field reverses its sign three times in one of the hemispheres (northern or southern) of the Sun, during the solar activity cycle 23. According to our results the appearance of velocity shear oscillations leads to the modulation of the magnetic field 22-year period oscillations by the bi-annual ones. The presented model is applicable for investigation of the magnetic field evolution at the base of convection zone as well as for understanding the magnetic field properties in the upper solar atmosphere. The excitement of the linear Rossby and Alfven waves in the shear layer at the base of the convection zone is also considered. The periodical impulsive growth is characteristic to the energy density of Alfven and Rossby waves and they propagate as localized in time powerful pulses. Such behavior of waves well explains mechanisms of the solar flare excitement and activity.

The behaviour of the toroidal and meridional components of the solar large-scale magnetic field and linear Alfven and Rossby waves during solar activity cycles and bi-annual time periods are theoretically investigated in this work. We consider the case of periodical velocity shear with bi-annual oscillation period . The large-scale magnetic field toroidal and meridional components are obtained as harmonic functions of the time. The sign reversal of these magnetic field components is studied. The numerical simulations show that, due to the velocity shear oscillations, the toroidal or meridional component of the large-scale magnetic field reverses its sign three times in one of the hemispheres (northern or southern) of the Sun, during the solar activity cycle 23. According to our results the appearance of velocity shear oscillations leads to the modulation of the magnetic field 22-year period oscillations by the bi-annual ones. The presented model is applicable for investigation of the magnetic field evolution at the base of convection zone as well as for understanding the magnetic field properties in the upper solar atmosphere. The excitement of the linear Rossby and Alfven waves in the shear layer at the base of the convection zone is also considered. The periodical impulsive growth is characteristic to the energy density of Alfven and Rossby waves and they propagate as localized in time powerful pulses. Such behavior of waves well explains mechanisms of the solar flare excitement and activity.

The behaviour of the toroidal and meridional components of the solar large-scale magnetic field and linear Alfven and Rossby waves during solar activity cycles and bi-annual time periods are theoretically investigated in this work. We consider the case of periodical velocity shear with bi-annual oscillation period . The large-scale magnetic field toroidal and meridional components are obtained as harmonic functions of the time. The sign reversal of these magnetic field components is studied. The numerical simulations show that, due to the velocity shear oscillations, the toroidal or meridional component of the large-scale magnetic field reverses its sign three times in one of the hemispheres (northern or southern) of the Sun, during the solar activity cycle 23. According to our results the appearance of velocity shear oscillations leads to the modulation of the magnetic field 22-year period oscillations by the bi-annual ones. The presented model is applicable for investigation of the magnetic field evolution at the base of convection zone as well as for understanding the magnetic field properties in the upper solar atmosphere. The excitement of the linear Rossby and Alfven waves in the shear layer at the base of the convection zone is also considered. The periodical impulsive growth is characteristic to the energy density of Alfven and Rossby waves and they propagate as localized in time powerful pulses. Such behavior of waves well explains mechanisms of the solar flare excitement and activity.

Starting from a general relativistic framework a hydrodynamic formalism is derived that yields the mean-square amplitudes and rms surface velocities of normal modes of non-relativistic stars excited by arbitrary gravitational wave (GW) radiation. In particular, stationary GW fields are considered and the resulting formulae are evaluated for two general types of GW radiation: radiation from a particular astrophysical source (e.g., a binary system) and a stochastic background of gravitational waves (SBGW). Expected sources and signal strengths for both types of GW radiation are reviewed and discussed. Numerical results for the Sun show that low-order quadrupolar g modes are excited more strongly than p modes by orders of magnitude. Maximal rms surface velocities in the case of excitation by astrophysical sources are found to be v {\le} 10^(-8) mm/s, assuming GW strain amplitudes of h {\le} 10^(-20). It is shown that current models for an SBGW produced by cosmic strings, with Omega_GW ~ 10^(-8)-10^(-5) in the frequency range of solar g modes, are able to produce maximal solar g-mode rms surface velocities of 10^(-5)-10^(-3) mm/s. This result lies close to or within the amplitude range of 10^(-3)-1 mm/s expected from excitation by turbulent convection, which is currently considered to be responsible for stellar g-mode excitation. It is concluded that studying g-mode observations of stars other than the Sun, in which excitation by GWs could be even more effective due to different stellar structures, might provide a new method to either detect GWs or to deduce a significant direct upper limit on an SBGW at intermediate frequencies between the pulsar bound and the bounds from interferometric detectors on Earth.

Starting from a general relativistic framework a hydrodynamic formalism is derived that yields the mean-square amplitudes and rms surface velocities of normal modes of non-relativistic stars excited by arbitrary gravitational wave (GW) radiation. In particular, stationary GW fields are considered and the resulting formulae are evaluated for two general types of GW radiation: radiation from a particular astrophysical source (e.g., a binary system) and a stochastic background of gravitational waves (SBGW). Expected sources and signal strengths for both types of GW radiation are reviewed and discussed. Numerical results for the Sun show that low-order quadrupolar g modes are excited more strongly than p modes by orders of magnitude. Maximal rms surface velocities in the case of excitation by astrophysical sources are found to be v {\le} 10^(-8) mm/s, assuming GW strain amplitudes of h {\le} 10^(-20). It is shown that current models for an SBGW produced by cosmic strings, with Omega_GW ~ 10^(-8)-10^(-5) in the frequency range of solar g modes, are able to produce maximal solar g-mode rms surface velocities of 10^(-5)-10^(-3) mm/s. This result lies close to or within the amplitude range of 10^(-3)-1 mm/s expected from excitation by turbulent convection, which is currently considered to be responsible for stellar g-mode excitation. It is concluded that studying g-mode observations of stars other than the Sun, in which excitation by GWs could be even more effective due to different stellar structures, might provide a new method to either detect GWs or to deduce a significant direct upper limit on an SBGW at intermediate frequencies between the pulsar bound and the bounds from interferometric detectors on Earth.

This review has two parts. The first part summarizes the current observational constraints on fluctuations in the solar medium deep within the solar Radiative Zone, and shows how the KamLAND and SNO-salt data combine to make the experimental determination of the neutrino oscillation parameters largely insensitive to prior assumptions about the nature of these oscillations. As part of a search for plausible sources of solar fluctuations to which neutrinos could be sensitive, the second part of the talk summarizes a preliminary analysis of the influence of magnetic fields on helioseismic waves. Using simplifying assumptions which should apply to modes in the solar radiative zone, we find a resonance between Alfven waves and helioseismic g-modes which potentially modifies the solar density profile fairly significantly over comparatively short distance scales, too narrow to be ruled out by present-day analyses of p-wave helioseismic spectra.

The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a non-relativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernovae parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.

The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a non-relativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernovae parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.

We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated single- and double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed transport with very little dispersion. The dynamics in the double-periodic system is dominated by Bloch-Zener oscillations, i.e. the interplay of Bloch oscillations and Zener tunneling between the subbands. Apart from directed transport, the latter system permits various interesting applications, such as widely tunable matter wave beam splitters and Mach-Zehnder interferometry. As an application, a method for efficient probing of small nonlinear mean-field interactions is suggested.

Recent observations of giant flares from soft gamma-ray repeaters have exhibited multiple 25-150 Hz oscillations. Frequencies in this range are expected for toroidal shear waves in a neutron star (NS) crust, lending support to Duncan's proposal that such modes may be excited in these events. This motivates a reassessment of how these waves reflect the NS structure and what role the magnetic field plays in setting their frequencies. We calculate the eigenfrequencies and eigenfunctions of toroidal oscillations for a realistic NS crust, including a vertical magnetic field at magnetar strengths ($B\sim10^{14}-10^{15} {\rm G}$). The lowest radial-order mode has a red-shifted frequency of $\approx28 {\rm Hz}[l(l+1)/6]^{1/2}$, with the prefactor depending on the NS's mass and radius, and its crust's depth and composition. This mode is independent of the magnetic field for $B\lesssim4\times10^{15} {\rm G}$, a limit much greater than the inferred dipole magnetic fields for these objects. Though this is a good fit to the observed oscillations, only rather loose constraints can be made for the NSs' properties because all that can be fit is this prefactor (a single parameter). Modes with shorter radial wavelengths are more sensitive to the magnetic field starting at $B\sim2\times10^{14} {\rm G}$ and have higher frequencies (600-2000 Hz). The discovery of these modes, coupled with the oscillations observed thus far, would provide a powerful probe to the NS crustal structure.

The density matrix renormalization group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is groundstate charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyse these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscillations from true charge density waves. We also discuss a different approach to extracting the correlation exponent from the finite size spectrum which uses exclusively open boundary conditions and can therefore take advantage of data for much larger system sizes. A general discussion of the Friedel oscillation wave-vectors is given, and a convenient Fourier transform technique is used to determine it. DMRG results are analysed on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the existence of a long-ranged charge density wave state in the t-J ladder at a filling of n=0.75 and near J/t \approx 0.25.

Using data obtained by the EUV Imaging Spectrometer (EIS) onboard Hinode, we have per- formed a survey of obvious and persistent (without significant damping) Doppler shift oscillations in the corona. We have found mainly two types of oscillations from February to April in 2007. One type is found at loop footpoint regions, with a dominant period around 10 minutes. They are characterized by coherent behavior of all line parameters (line intensity, Doppler shift, line width and profile asymmetry), apparent blue shift and blueward asymmetry throughout almost the en- tire duration. Such oscillations are likely to be signatures of quasi-periodic upflows (small-scale jets, or coronal counterpart of type-II spicules), which may play an important role in the supply of mass and energy to the hot corona. The other type of oscillation is usually associated with the upper part of loops. They are most clearly seen in the Doppler shift of coronal lines with forma- tion temperatures between one and two million degrees. The global wavelets of these oscillations usually peak sharply around a period in the range of 3-6 minutes. No obvious profile asymmetry is found and the variation of the line width is typically very small. The intensity variation is often less than 2%. These oscillations are more likely to be signatures of kink/Alfven waves rather than flows. In a few cases there seems to be a pi/2 phase shift between the intensity and Doppler shift oscillations, which may suggest the presence of slow mode standing waves according to wave theories. However, we demonstrate that such a phase shift could also be produced by loops moving into and out of a spatial pixel as a result of Alfvenic oscillations. In this scenario, the intensity oscillations associated with Alfvenic waves are caused by loop displacement rather than density change.

We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.

This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative order this configuration does not exhibit any gravitational radiation, we have found a new interesting gravitational signal at non-linear order, in which the radial normal modes are precisely mirrored. In addition, a resonance effect is present when the frequencies of the radial pulsations are close to the first axial w-mode. Finally, we have roughly estimated the damping times of the radial pulsations due to the non-linear gravitational emission. The coupling near the resonance results to be a very effective mechanism for extracting energy from the radial oscillations.

We report an analysis of the effects of magnetic field on a quasi-one-dimensional band of interacting electrons with a transverse dimerizing potential. One-particle problem in bond-antibond representation is solved exactly. The resulting propagator is used to calculate the spin-density-wave (SDW) response of the interacting system within the matrix RPA for the SDW susceptibility. We predict the magnetic field induced transition of the first order between interband SDW_0 and intraband SDW_(+-) phases. We reproduce the rapid oscillations with a period of 260 Tesla and the overal profile of the TMTSF_2ClO_4 phase diagram.

In this book some review articles by former and present members of the Dritte are combined, indicating the broadness of the research interests which developed from this theme. Unfortunately, such collection of articles allows only for a limited access to the broad variety of different fields of interest that have been dealt with in the past. The reviews are, therefore, complemented by a short overview which, again, cannot show all aspects of successful work during the sixty years of existence of the institute. Also, a short outlook is given at the end of the book on future research objectives in complex systems and biophysics. FreeScience.info ID2806 Obtained from http://webdoc.sub.gwdg.de/univerlag/2007/oscillations.pdf http://www.freescience.info/go.php?pagename=books&id=2806

In this book some review articles by former and present members of the Dritte are combined, indicating the broadness of the research interests which developed from this theme. Unfortunately, such collection of articles allows only for a limited access to the broad variety of different fields of interest that have been dealt with in the past. The reviews are, therefore, complemented by a short overview which, again, cannot show all aspects of successful work during the sixty years of existence of the institute. Also, a short outlook is given at the end of the book on future research objectives in complex systems and biophysics. FreeScience.info ID2806 Obtained from http://webdoc.sub.gwdg.de/univerlag/2007/oscillations.pdf http://www.freescience.info/go.php?pagename=books&id=2806

Hole-doped high-temperature cuprate superconductors below optimum doping have small electron-like Fermi surfaces occupying a small fraction of the Brillouin zone. There is strong evidence that this is linked to charge density wave (CDW) order, which reconstructs the large hole-like Fermi surfaces predicted by band structure calculations . Recent experiments have revealed the structure of the two CDW components in the benchmark bilayer material YBa$_2$Cu$_3$O$_{7-x}$ in high field where quantum oscillation (QO) measurements are performed. We have combined these results with a tight-binding description of the bands in an isolated bilayer to give a minimal model revealing the essential physics of the situation. Here we show that this approach, combined with the effects of spin-orbit interactions and the pseudogap, gives a good qualitative description of the multiple frequencies seen in the QO observations in this material. Magnetic breakdown through weak CDW splitting of the bands will lead to a field-dependence of the QO spectrum and to the observed fourfold symmetry of the results in tilted fields.

Self-sustained current oscillations in weakly-coupled superlattices are studied by means of a self-consistent microscopic model of sequential tunneling including boundary conditions naturally. Well-to-well hopping and recycling of charge monopole domain walls produce current spikes (high frequency modulation) superimposed on the oscillation. For highly doped injecting contacts, the self-oscillations are due to dynamics of monopoles. As the contact doping decreases, a lower-frequency oscillatory mode due to recycling and motion of charge dipoles is predicted. For low contact doping, this mode dominates and monopole oscillations disappear. At intermediate doping, both oscillation modes coexist as stable solutions and hysteresis between them is possible.

Manipulation with ill-defined notions creates an illusion of a simple derivation of the standard phase of neutrino oscillations in hep-ph/0311241 and hep-ph/0312180.