Dynamical Spectrum Research Articles

Nonlinear phenomena in hybrid Couette flow composed of planar and circular shear

Results are presented from an experimental investigation of a novel shear flow. Two parallel sections of planar Couette flow are connected by two semicircular sections of circular Couette flow to give a flow domain with the shape of a running track. Driving the flow with a moving inner boundary leads to centrifugal instability in the curved regions as in conventional Taylor–Couette flow. This is in contrast to the planar regions, which are linearly stable and are characterized instead by finite-amplitude instability. In the steady regime, the entire flow field is dominated by structures akin to Taylor vortices. The mechanism of exchange between a four-cell and a six-cell flow over a range of aspect ratio is qualitatively the same as for the standard Taylor–Couette problem. In the unsteady regime, the flow is characterized by various spatiotemporal modes, the selection of which is dependent on the manner of flow evolution. Quasistatic increase of the Reynolds number from zero typically results in flow with a banded spatial structure and low-dimensional dynamics, both of which are associated with instability in the semicircular regions. However, an abrupt step-like increase of Reynolds number produces a persistent flow state with strong spatial disorder and a broadband dynamical spectrum. The results of this study have implications for the conventional distinctions between the properties of open and closed flows, and suggest the possibility of intermediate flows which are worthy of investigation in their own right.

An Atlas of Burst Oscillations and Spectral Properties in 4U 1728−34

We study correlations between the burst properties and the position in the color-color diagram of the low mass X-ray binary 4U 1728-34 using 21 bursts found in two data sets obtained with the Rossi X-ray Timing Explorer. Using spectral fits we analyze the spectral evolution during the bursts and determine the burst peak flux, temperature, rise time and fluence. Using dynamical power spectra we study the properties of the ~363 Hz burst oscillations. We find correlations between fluence, peak flux, the occurrence of radius expansion and the presence of burst oscillations, and the position of the source in the color-color diagram. The radius expansion bursts with and without burst oscillations differ both with respect to where they occur in the color-color diagram and in how the radius expansion takes place. We compare our results with those of a similar study by Muno et al. (2000) for KS 1731-26. Both KS 1731-260 and 4U 1728-34 show more or less the same behavior with respect to the dependence of the presence/absence of the burst oscillations on the position of the source in the color-color diagram, but the dependence of most of the spectral burst parameters on the position in the color-color diagram is clearly different. We find that the systematic absence in 4U 1728-34 of burst oscillations in the ``island'' state of the color-color diagram is not explained by the bursts involving mixed H-He burning, as may be the case in KS 1731--260 (Cumming & Bildsten 2000).

Anomalous diffusion near structural-glass transformations

A new insight into the relaxation observed in dynamical spectra near structural-glass transformations is given. The following restricted-diffusion universal mechanisms are established: in polymers α-relaxation is driven by subdiffusion controlled by random fields, and in liquids β-relaxation is realized through long-time-waiting random jumps.

Low-Frequency Pulsations of Coronal Magnetic Loops

We analyze low-frequency intensity fluctuations of the microwave emission from solar flares at frequencies 22 and 37 GHz. The three microwave bursts of durations of about 1 h, observed at the Metsahovi Radio Observatory (Finland) with the time resolution of 0.1 and 0.05 s, are studied. To obtain spectral-temporal characteristics of the low-frequency fluctuations, we apply the Wigner-Ville method, i.e., the time-lag Fourier transform of the “local” autocorrelation function of an analytical signal. As a result, we obtain for the first time the dynamical spectra of the low-frequency fluctuations, which are identified as MHD eigenoscillations of coronal magnetic loops. The features of the dynamical spectra testify that several types of low-frequency pulsations are excited in coronal magnetic loops during solar flares: 1) Fast and slow magnetosonic oscillations with periods of 1-1.5 s and 200-280 s, respectively. Fast magnetosonic oscillations appear as pulse trains of duration 100-200 s and have the positive frequency drift dν/ dt≈ 0.125 Hz/min and the frequency splitting δν≈ 0.05 Hz; 2) The eigenoscillations of a coronal magnetic loop as an equivalent electric circuit. The period of these oscillations is about 1 s during the initial stage of a microwave burst and increases gradually up to 4 s during the decay stage of the radio emission; and 3) Intensity modulation of the microwave radiation by a periodic pulse sequence with a period of about 1 s at the burst onset and about 2 s at its end. The parameters of the dynamical spectra and identification of the MHD pulsations allow us to obtain information on the loop parameters, such as the ratio of the loop radius to its length (r/L≈ 0.1), the ratio of the gas pressure to the magnetic-field pressure inside the loop (β ≈ 3· 10-3), the ratio of plasma densities outside and inside the loop, and the electric current in the coronal loop (I≈ 1.5 · 1012 A).

Unsaturated polyester resins cure: Kinetic, rheologic, and mechanical dynamical analysis. II. The glass transition in the mechanical dynamical spectrum of polyester networks

Unsaturated polyester resins cure: Kinetic, rheologic, and mechanical dynamical analysis. II. The glass transition in the mechanical dynamical spectrum of polyester networks

The Development of Nonlinear Dynamics in Astronomy

We present the historical development of Nonlinear Dynamical Astronomy with emphasis on the “third integral” and its applications. The new era started with the use of computers, and of formal analytical developments in the spirit of Poincare. Most dynamical systems were found to contain both ordered and chaotic orbits. The transition from order to chaos is discussed. Recent developments refer to the dynamical spectra, integrals of notion in self-consistent models, systems of 3 or more degrees of freedom, chaos in relativity and cosmology, and chaos in quandum mechanics.

Static and dynamical properties of frustrated two-dimensional square quantum Heisenberg antiferromagnets

Two-dimensional square quantum Heisenberg antiferromagnets with competing interactions up to third neighbors ${(J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ model) are investigated by using the high-temperature series expansion method. From the analyses of the wave-vector-dependent susceptibility $\ensuremath{\chi}(\mathit{k}),$ we find four kinds of the stable paramagnetic phases depending on the coupling constants, i.e., N\'eel, collinear, and two helical paramagnetic phases, ${H}_{1}$ and ${H}_{2}.$ They are characterized by the critical wave vector ${\mathit{k}}_{A}^{c} (A=N,$ C, ${H}_{1},$ or ${H}_{2}),$ at which the functions $\ensuremath{\chi}(\mathit{k})$ show the maximum value. Except around the ${H}_{1}\ensuremath{-}{H}_{2}$ phase boundary, they are destabilized and show the intermediate phases in the neighborhood of the phase boundaries, where the relevant critical wave vector ${\mathit{k}}_{A}^{c}$ is not specified uniquely. The analogy between the paramagnetic phase diagram obtained here and the ordered ones derived by the simple spin wave theory suggests the possibility of the spin liquid state in the intermediate phase at $T=0.$ The first-order transition occurs between ${H}_{1}$ and ${H}_{2}$ phases, so the intermediate phase is not seen there. The dynamical spectrum function $F(\mathit{k},\ensuremath{\omega})$ is calculated in the form of Mori's continued fraction with the frequency moments. The dynamical aspects for the stable paramagnetic phases are also characterized by the critical wave vector ${\mathit{k}}_{A}^{c}.$ While the side peak or shoulder shape appears in $F({\mathit{k}}_{A}^{c},\ensuremath{\omega})$ at $T=\ensuremath{\infty},$ the line shape becomes considerably narrow when decreasing the temperature at ${\mathit{k}}_{A}^{c}.$ These behaviors are attributed to the spin flip-flop motion for the former case, and the quasicollective motion for the latter one. In the intermediate phase, at $T=\ensuremath{\infty}$ the line shape undergoes slow change versus the wave vector $\mathit{k}$ except for the drastic narrowing around $\mathit{k}\ensuremath{\simeq}0,$ due to the absence of the unique critical wave vector. It is found that the high-temperature dynamical aspect keeps there, even though the temperature is decreased, due to the frustration effect.

The Principal Spectrum for Linear Nonautonomous Parabolic PDEs of Second Order: Basic Properties

We put forward a theory extending the notion of principal eigenfunction and principal eigenvalue to the case of linear nonautonomous parabolic PDEs of second orderut=∑i, j=1Naij(t, x)∂2u∂xi∂xj+∑i=1Nai(t, x)∂u∂xi+a0(t, x)u, x∈Ω,on a bounded domain Ω⊂RN, with Dirichlet or Robin boundary conditions. A canonically defined one-dimensional subbundle S (corresponding to the solutions that are globally defined and of the same sign) serves as an analog of principal eigenfunction. The principal spectrum is defined to be the dynamical (Sacker–Sell) spectrum of the linear skew-product flow on S. Characterizations of principal spectrum in terms of (logarithmic) growth rates of positive solutions are given. Finally, monotonicity of the principal spectrum with respect to zero order terms is proved.

Dynamical spectrum for scalar parabolic equations

In this paper we compute the dynamical spectrum for time dependent scalar parabolic equations with both Neumann and Dirichlet boundary conditions. In order to do that, first, we put forward the concepts of negative continuation, exponential dichotomy and Dynamical Spectrum for linear skew product semiflows. Second, we set the problem in the skew product semiflow frame work and compute explicitly the dynamical spectrum for this semiflow. Finally, we compute the dynamical spectrum for a time dependent system of ordinary differential equations that is obtained by spatially discretizing of the parabolic equation

Dynamical chaos and power spectra in toy models of heteropolymers and proteins.

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically nonchaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.

Influence of the additional second-neighbor hopping on the spin response in the t-J model

The influence of the additional second-neighbor hopping ${t}^{\ensuremath{'}}$ on the spin response of the $t\ensuremath{-}J$ model in the underdoped and optimally doped regimes is studied within the fermion-spin theory. Although the additional second-neighbor hopping ${t}^{\ensuremath{'}}$ is systematically accompanied by the reduction of the dynamical spin structure factor and susceptibility, the qualitative behavior of the dynamical spin structure factor and susceptibility of the ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model is the same as in the case of $t\ensuremath{-}J$ model. The integrated dynamical spin structure factor spectrum is almost ${t}^{\ensuremath{'}}$ independent, and the integrated dynamical spin susceptibility still shows the particularly universal behavior as $I(\ensuremath{\omega},T)\ensuremath{\propto}\mathrm{arctan}[{a}_{1}\ensuremath{\omega}{/T+a}_{3}(\ensuremath{\omega}{/T)}^{3}].$

NMR studies on hydrogen bonding and proton transfer in Mannich bases

A review of studies on the ortho Mannich bases containing various substituents in the phenyl ring on the basis of1H,13C and15N nuclear magnetic resonance (NMR) spectra in various solvents over the temperature range 110–298 K is presented. Some new results are also included. The data gathered so far show that there is some critical (inversion) range of ΔpK a (= pK a(NH+) − pK a(OH)) in which the proton transfer equilibrium appears. This inversion range is well reflected in the behaviour of secondary deuterium isotope effect in13C NMR spectra. A strong temperature effect on the strength of hydrogen bonding should be emphasized. The1H chemical shift for trichloroderivative increases from 13.5 at room temperature up to 17 ppm at 130 K when the proton is equally shared between the bridging atoms (1 J(1H,15N) = 30–40 Hz). The potential for the proton motion in such bridges is discussed taking into account the behaviour in the ultraviolet and infrared spectra. The role of dimerization in proton transfer equilibria is shown. In addition the rotation of OH groups involved in hydrogen bond formation and nitrogen pyramidal inversion was studied by the1H dynamical NMR spectra.

Unsaturated polyester resins cure: Kinetic, rheologic, and mechanical dynamical analysis. II. The glass transition in the mechanical dynamical spectrum of polyester networks

Unsaturated polyester networks with various structures built from an orthophtalic polyester, with methyl ethyl ketone peroxide as an initiator and cobalt octoate as a promoter, were studied with dynamic mechanical thermal analysis from −50 to 200 °C to characterize changes in the mechanical properties as a function of the temperature. From these measurements, the glass-transition temperatures of the different networks were determined, their dependence on conversion being fitted to an equation related to the Couchman and DiBenedetto equations. Finally, the different transitions were analyzed as a function of the cure conditions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 146–152, 2001

Complex oscillations in an electrically stimulated membrane model

Este artigo investiga, teoricamente, a dinâmica de um modelo de membrana sob estimulação elétrica externa. Este sistema mostra vários tipos de respostas oscilatórias no potencial da membrana, quando uma corrente sinoidal AC é superposta à corrente DC aplicada através da membrana. À medida que a frequência da corrente AC varia, este comportamento varia de oscilações periódicas, P1, até oscilações do tipo explosivas, através de regiões de quase-periodicidade. As séries temporais que apresentam estes comportamentos são caracterizadas usando métodos de Teoria de Sistemas Dinâmicos, a saber: mapas de retorno, expoentes de Lyapunov, espectro de potências e dimensão de capacidade. Os resultados são discutidos em relação a membranas biológicas sob condições similares.

Solitons and Nondissipative Diffusion

The dynamical correlation spectra of the Toda chain are obtained by a molecular dynamics simulation and analyzed in terms of Bethe-ansatz-based soliton phenomenology. The spectrum of local temperature fluctuations exhibits a feature which can be unambiguously assigned to solitons. Detailed linewidth analysis demonstrates the phenomenon of nondissipative soliton diffusion, i.e., the stochastic sequence of spatial shifts experienced by the soliton as it moves through the lattice and interacts with other excitations without momentum exchange. Our results provide strong support for the dynamical predictions of the finite-temperature Bethe ansatz excitation spectrum.

A new spectral form of decameter type IIID radio bursts

The intensity-time profiles I(t) of narrow-band (δf/f≈10−2) radio bursts, which from the slanted dynamical spectrum (If,t) of type IIId emission, are strongly dependent on the heliolongitudes |l| of their coronal (quasi-monochromatic) sources. In the central sector (|l|<50°), each of these short-time (≈10 s), steep-front bursts generated at the second harmonic f=2fp has a delayed echo-like component, and they usually have a slow exponential decay at the limb (|l|=90°).

Horizontal wavenumber spectra of winds, temperature, and trace gases during the Pacific Exploratory Missions: 1. Climatology

Aircraft‐based meteorological and chemical measurements from NASA's Pacific Exploratory Missions provide a suitable database for studying the climatology of horizontal wavenumber spectra in the troposphere overlying an ocean. The wavenumber spectra of trace gas and meteorological quantities aid in identifying the physical processes producing atmospheric structures as well as provide diagnostics for general circulation models. Flight segments were distributed over altitudes ranging from about ∼50 m to 13 km and 70°S to 60°N in latitude. The spectra were averaged according to altitude and latitude regions. The wavelength range covered was typically ∼0.5–100 km. Quantities processed in this way were horizontal velocity, potential temperature, specific humidity, and the mixing ratios of ozone, methane, carbon monoxide, and carbon dioxide. Spectral power and slope (in log‐log coordinates) corresponding to the wavelength regime of 6–60 km were tabulated for those measured quantities. The spectral slopes of horizontal velocity and potential temperature were generally close to −5/3 with no transition to a steeper slope at short wavelengths as seen in some other studies. Spectral slopes of the tracer species also ranged around −5/3. This agreement in form of the dynamical and tracer spectra is consistent with both the gravity‐wave advection and quasi two‐dimensional turbulence models. In the upper troposphere the spectral power for all quantities except specific humidity tended to be greater at latitudes higher than 30° compared to latitudes lower than 30°. This latitudinal trend confirms the earlier results of the Global Atmospheric Sampling Program.

A generation mechanism for chorus emission

Abstract. A chorus generation mechanism is discussed, which is based on interrelation of ELF/VLF noise-like and discrete emissions under the cyclotron wave-particle interactions. A natural ELF/VLF noise radiation is excited by the cyclotron instability mechanism in ducts with enhanced cold plasma density or at the plasmapause. This process is accompanied by a step-like deformation of the energetic electron distribution function in the velocity space, which is situated at the boundary between resonant and nonresonant particles. The step leads to the strong phase correlation of interacting particles and waves and to a new backward wave oscillator (BWO) regime of wave generation, when an absolute cyclotron instability arises at the central cross section of the geomagnetic trap, in the form of a succession of discrete signals with growing frequency inside each element. The dynamical spectrum of a separate element is formed similar to triggered ELF/VLF emission, when the strong wavelet starts from the equatorial plane. The comparison is given of the model developed using some satellite and ground-based data. In particular, the appearance of separate groups of chorus signals with a duration 2-10 s can be connected with the preliminary stage of the step formation. BWO regime gives a succession period smaller than the bounce period of energetic electrons between the magnetic mirrors and can explain the observed intervals between chorus elements.Key words. Magnetospheric physics (Energetic particles · trapped). Space plasma physics (wave-particle interactions; waves and instabilities)

Detection of Ordered and Chaotic Motion using The Dynamical Spectra

AbstractTwo simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of the “dynamical spectra”. 1) We calculate a “spectral distance”Dof the dynamical spectra for two different initial deviation vectors.D→ 0 in the case of chaotic orbits, whileD→const≠ 0 in the case of ordered orbits. This method is by orders of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity at a rate ∝N= number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM torus of an island of stability, as well as the most important cantori causing stickiness near it.

Macroscopic and microscopic models of nuclear rotations

The longstanding goal of expressing the nuclear rotor model as a submodel of the shell model is achieved by the use of dynamical groups and spectrum generating algebras. One obtains rotational states as eigenstates of a rotationally invariant Hamiltonian with microscopic shell-model wavefunctions.