Normal Mode Spectrum Research Articles

Normal modes of a small bilayer system of binary classical charged particles trapped in a parabolic confinement potential

The normal modes and the melting character of a bilayer system consisting of binary charged particles with different charge and/or different mass, interacting through a Coulomb potential and confined in a parabolic trap are investigated. The normal mode spectrum is discussed as a function of the charge ratio (CR) and mass ratio (MR) of the two kinds of charged particles as well as the interlayer separation. We show that the dependence of the normal modes on the excited states can be tuned by varying the CR, the MR, and the interlayer distance. Once the interlayer distance is larger than a critical value, the first excited state corresponds only to the intershell rotation mode. In addition, the intershell rotation melting temperature is discussed as a function of the CR and MR as well as the interlayer separation.

Ground state and normal-mode spectra of a two-dimensional system of dipole particles confined in a parabolic trap

The ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures like chains and Y-shaped configurations when a magnetic field is applied parallel to the plane of the particles. The normal-mode spectrum of the particles and its dependence on the magnetic field and the strength of the dipole moment of the particles are studied. The vibrational and rotational modes of the spectrum, which are associated with the stability of the system, are investigated in detail. The number of particles is varied and we found different ordering of the particles for different values of the dipole moment and the magnetic field. A ring structure with a large number of particles is observed for high values of the dipole moment of the particles.

Quasi-normal modes in topologically massive gravity

We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a chiral highest weight'' QNM which in turn satisfies a first order equation.

Q-breathers in discrete nonlinear Schrödinger lattices

q-breathers (QBs) are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi–Pasta–Ulam (FPU) paradox. We study QBs in one-, two- and three-dimensional discrete nonlinear Schrödinger (DNLS) lattices—theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of QBs is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter QBs delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into the strong mode–mode interaction regime. In particular, this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of QBs supplements these findings. We relate our findings to previous studies of time-periodic multibreather standing waves. For three-dimensional lattices, we find QB vortices which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.

The energy spectrum of electromagnetic normal modes in dissipative media: modes between two metal half spaces

The energy spectrum of electromagnetic normal modes plays a central role in the theory of the van der Waals and Casimir interaction. Here we study the modes in connection with the van der Waals interaction between two metal half spaces. Neglecting dissipation leads to distinct normal modes with real-valued frequencies. Including dissipation seems to have the effect that these distinct modes move away from the real axis into the complex frequency plane. The summation of the zero-point energies of these modes render a complex-valued result. Using the contour integration, resulting from the use of the generalized argument principle, gives a real-valued and different result. We resolve this contradiction and show that the spectrum of true normal modes forms a continuum with real frequencies.

Molecular states of two vertically coupled systems of classical charged particles confined by a Coulomb potential

We numerically study the structure and the normal-mode spectrum of two vertically coupled finite-size two-dimensional systems of interacting classical charged particles that are confined by a nonuniform distribution of background charge. The structural and dynamical properties of the system are analyzed as a function of the separation between the planes of charges $(d)$, as well as a function of the strength of the confinement potential $(Z)$. We find different asymmetrical ground-state configurations, as well as structural phase transitions induced by the unbinding of particles, which were not present in previous models with a parabolic confinement potential. Depending on the order of the structural transition the normal-mode frequencies exhibit a discontinuity or a softening.

Effect of eccentricity on the spin-wave spectrum of NiFe∕Cu∕NiFe pillars with elliptical cross section

Brillouin light scattering (BLS) has been exploited to study the effect of eccentricity on the magnetic normal-mode spectrum of five arrays of trilayered pillars with an elliptical cross section and different eccentricity ε in the range between 1 and 3. The pillars consist of a pair of 10nm thick Permalloy (NiFe) layers separated by a Cu spacer with thickness of 10nm. Several discrete spin-wave modes were observed in the BLS spectra and their frequencies tracked as a function of the in-plane direction of the applied magnetic field. All mode frequencies exhibit a uniaxial anisotropy, induced by the shape of the elements, which increases with ε. A satisfactory reproduction of the measured frequencies was achieved by three-dimensional micromagnetic simulations, solving the discretized Landau-Lifshitz-Gilbert equation over the layered structure in the time domain and performing a local Fourier transform.

Particle positioning techniques for dusty plasma experiments

Video microscopy is a widely applied diagnostic to investigate the structure and the dynamics of particles in dusty plasmas. Reliable algorithms are required to accurately recover particle positions from the camera images. Here, four different particle positioning techniques have been tested on artificial and experimental data of dusty plasma situations. Two methods that rely on pixel-intensity thresholds were found to be strongly affected by pixel-locking errors and by noise. Two other methods-one applying spatial bandpass filters and the other fitting polynomials to the intensity pattern-yield subpixel resolution under various conditions. These two methods have been shown to be ideally suited to recover particle positions even from small-scale fluctuations that are used to derive the normal mode spectra of finite dust clusters.

Modifications to the resistive MHD spectrum due to changes in the equilibrium

The normal-mode spectrum of the linearized resistive magnetohydrodynamics (MHD) operator is determined numerically for an inhomogeneous plasma slab. The spectrum consists of fast and slow magnetosonic and Alfvén sub-spectra. The obtained Alfvén sub-spectrum consists of discrete resistive Alfvén modes and an ‘ideal quasi-mode’ that originates from a surface mode due to a sharp density transition layer in the plasma. The quasi-mode interacts with the resistive Alfvén modes when the width of the transition layer is modified. Eventually, when the transition layer spreads over a substantial part of the plasma, the quasi-mode even loses its global or ‘collective’ behaviour and gradually transforms into an ordinary resistive Alfvén mode. In other words, it joins the resistive Alfvén sub-spectrum. Avoided crossings occur during the interactions of the ideal quasi-mode and the resistive spectrum.

Propagation of impulsive broadband signals in a coastal ocean setting during the 1996 Shelfbreak Primer experiment

The 1996 Shelfbreak PRIMER experiment provided an opportunity to study the impulse response of a coastal ocean waveguide using broadband acoustic signals from explosive sources. Acoustic transmission paths in the vicinity of the shelfbreak included various orientations ranging from up‐slope to along‐slope, including interactions with a shelfbreak front. Acoustic receptions were acquired with a 16‐element vertical line array (VLA). In addition, thermistor string data acquired at the receiving array suggest that a group of high‐amplitude, internal waves traversed the test site during this portion of the experiment. Modal decomposition of broadband signal arrivals was performed to investigate variation of the impulse response during source deployments. Variations in the received spectra of individual normal modes were compared with numerical predictions for impulsive broadband signals propagating in range‐dependent environments constructed using oceanographic data available for the test site. The potential for mode coupling and three‐dimensional effects to shape the modal and spectral distribution of received energy is being investigated. Numerical and experimental results will be discussed. [Work supported by Office of Naval Research.]

Vibrational spectroscopy and normal-mode analysis of Fe(II) octaethylporphyrin.

The normal-mode spectrum for the four-coordinated heme compound Fe(II) octaethylporphyrin, Fe(OEP), has been determined by refining force constants to the experimental Fe vibrational density of states measured with nuclear resonance vibrational spectroscopy (NRVS). Convergence of the calculated spectrum to the data was achieved by first imposing D4 symmetry on the model structure as well as the force constants, progressively including different internal coordinates of motion, then allowing the true Ci (or S2) point group symmetry of the C(i)1 Fe(OEP) crystal structure. The NRVS-refined normal modes are in good agreement with Raman and IR spectra at high frequencies. Prior density functional theory predictions for a model porphyrin are similar to the core modes computed with the best-fit force field, but significant differences between D4 and Ci modes underline the sensitivity of porphyrin Fe normal modes to structural details. Some differences between the Ci best fit and the NRVS data can be attributed to intermolecular contacts not included in the normal-mode analysis.

Symmetry and entropy of black hole horizons

We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzschild black hole live in the restricted subspace of the Hilbert space of horizon boundary states in which all punctures are equal. Consequently, one value of the Immirzi parameter matches both the Hawking value for the entropy and the quasi normal mode spectrum of the Schwarzschild black hole. The method of noiseless subsystems allows us to understand, in this example and more generally, how symmetries, which take physical states to physical states, can emerge from a diffeomorphism invariant formulation of quantum gravity.

Dynamics in Polymer−Silicate Nanocomposites As Studied by Dielectric Relaxation Spectroscopy and Dynamic Mechanical Spectroscopy

Nanocomposites of organically modified clay nanoparticles and a polyisoprene (PI) matrix were prepared by solution-mediated intercalation, and their dynamics were investigated over a broad range of frequency and temperature by dielectric relaxation spectroscopy (DRS) and dynamic mechanical spectroscopy (DMS). The principal goal was to address the effect of geometric confinement and elucidate how the dynamics vary as a function of the type and concentration of clay and the molecular weight of PI. Dielectric spectra of nanocomposites with low-molecular-weight PI reveal no effect of clay loading on the average relaxation time for segmental and normal mode relaxation, but dc conductivity and interfacial polarization are affected. In nanocomposites with high molecular weight PI (in the entangled regime), however, a clear effect of clay loading on the average relaxation time for the normal mode process is observed. Most interestingly, it is found that the normal mode becomes faster with increasing clay content, and an explanation is offered in terms of the preferential suppression of the longer scale (lower frequency) portion of the normal mode spectrum. The average relaxation times for segmental and normal mode calculated from dielectric and viscoelastic measurements are in excellent agreement. DMS measurements also reveal an increase in the magnitude of storage and loss modulus with increasing clay loading up to the threshold value of 8 wt %. The observed increase originates from the “filler effect”.

Normal Mode Splitting and Mechanical Effects of an Optical Lattice in a Ring Cavity

A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.

Wavelet filter analysis of atmospheric pressure effects in the long-period seismic mode band

The importance of the reduction of atmospheric pressure effects becomes very clear when investigating seismic normal-mode spectra below 1.5 mHz. The usual simple correction method consists in subtracting a term converted from local atmospheric pressure (pressure multiplied by a frequency-independent admittance) from the gravity record in time domain. Thus, estimating an efficient admittance is the key for an improved correction. Band-pass filters derived from dyadic orthogonal wavelet transform, having narrow pass-bands with good frequency response but without Gibbs phenomenon and causing no phase lag, are very helpful to estimate an efficient admittance, which is both time and frequency-dependent. Processing of high quality superconducting gravimeter (SG) records for the great Sumatra earthquake (Mw = 9.3, Dec 26, 2004) with wavelet filters reveal the three very well resolved splitting singlets of overtone 2S 1 with a single gravity record after correction with time-dependent and frequency-dependent admittances. We also observe all coupled toroidal modes below 1.5 mHz, except 0T 5, 0T 7 and 1T 1, with good signal-to-noise ratio (SNR); moreover, toroidal modes 1T 2 and 1T 3 are for the first time unambiguously revealed in vertical components.

Ac conductivity in a DNA charge transport model

We present the ac response of a DNA charge transport model, where the charge in the pi-stack interacts with the base-pair opening dynamics of the double strand. The calculated ac conductivity exhibits prominent peaks at polaron normal modes with electronic character, while weaker response appears at lower frequencies in the vibrational part of the polaron normal mode spectrum. Examples of the former, strong peaks, show redshifts as the amplitude of the ac field increases.

Structure, normal mode spectra, and mixing of a binary system of charged particles confined in a parabolic trap

We study the mixing of two different kinds of particles, having different charge and/or mass, interacting through a pure Coulomb potential, and confined in a parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the ratio of the charges (mass ratio) of the two types of particles. We show that particles are not always arranged in a shell structure. Mixing of the particles goes hand in hand with a large number of metastable states. The normal modes of the system are obtained, and we find that some of the special modes can be tuned by varying the ratio between the charges (masses) of the two species. The degree of mixing of the two type of particles is summarized in a phase diagram, and an order parameter that describes quantitatively the mixing between particles is defined.

Mechanism for singular behavior in vibrational spectra of topologically disordered systems: Short-range attractions

At low-enough fluid densities, we have found some naive singular behavior, like the van Hove singularities in the phonon spectra of lattices, appearing in the instantaneous normal mode spectra of the Lennard-Jones (LJ) 2n-n fluids, which serve as a prototype of topologically disordered systems. The singular behavior cannot be predicted by the mean-field theory, but interpreted by the perturbed binary modes of some special pairs, called the mutual nearest neighbor pairs, at separations corresponding to the extreme binary frequencies, which are solely determined by the attractive part of the LJ 2n-n pair potential. By reducing the range of attraction in the pair potential under the conditions of the same particle diameter and well depth, the tendency for the appearance of the singular behavior shifts to higher fluid densities. From this study, we conclude that pair potential with a short-range attraction can be a mechanism to produce a counterpart of the van Hove singularity in the vibrational spectra of disordered systems without a reference lattice.

Asteroseismology with robotic telescopes

AbstractAsteroseismology explores the interior of pulsating stars by analysing their normal mode spectrum. The detection of a sufficient number of pulsation modes for seismic modelling of main sequence variables requires large quantities of highprecision time resolved photometry. Robotic telescopes have become an asset for asteroseismology because of their stable instrumentation, cost‐ and time‐efficient operation and the potentially large amounts of observing time available.We illustrate these points by presenting selected results on several types of pulsating variables, such as δ Scuti stars (main sequence and pre‐main sequence), γ Doradus stars, rapidly oscillating Ap stars and β Cephei stars, thereby briefly reviewing recent success stories of asteroseismic studies of main sequence stars. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of confinement on the vibrational density of states and the Boson peak in a polymer glass.

We have performed a normal-mode analysis on a glass forming polymer system for bulk and free-standing film geometries prepared under identical conditions. It is found that for free-standing film glasses, the normal-mode spectrum exhibits significant differences from the bulk glass with the appearance of an additional low-frequency peak and a higher intensity at the Boson peak frequency. A detailed eigenvector analysis shows that the low-frequency peak corresponds to a shear-horizontal mode which is predicted by continuum theory. The peak at higher frequency (Boson peak) corresponds to motions that are correlated over a length scale of approximately twice the interaction site diameter. These observations shed some light on the microscopic dynamics of glass formers, and help explain decreasing fragility that arises with decreasing thickness in thin films.