Characteristic Oscillation Periods Research Articles

Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited o-Fluoroaniline

Quantum beat frequency is the basis for understanding interference effects and vibrational wave packet dynamics and has important applications. Using femtosecond time-resolved mass spectrometry and femtosecond time-resolved photoelectron image combined with theoretical calculations, we study the electronic excited-state relaxation of o-fluoraniline molecule and the time-dependent evolution of vibrational wave packets between different eigenstates. After the molecule absorbs a photon of 288.3 nm and is excited to the S1 state, intramolecular vibrational redistribution first occurs on the time scale τ1 = 349 fs, and then the transition to the triplet state occurs through the intersystem crossing on the time scale τ2 = 583 ps, and finally, the triplet state occurs decays slowly through the time scale τ3 = 2074 ps. We find the intramolecular vibrational redistribution is caused by the 00, 10b1 and 16a1 vibrational modes of the Sl state origin. That is, the 288.3 nm femtosecond laser excites the molecule to the S1 state, and the continuous flow of the vibrational wave packet prepares a coherent superposition state of three vibrational modes. Through extracting the oscillation of different peak intensities in the photoelectron spectrum, we observe reversible changes caused by mutual interference of the S1 00, S1 10b1 and S1 16a1 states when the wave packets flow. When the pump pulse is 280 nm, the beat frequency disappears completely. This is explained in terms of increases in the vibrational field density and characteristic period of oscillation, and statistical averaging makes the quantum effect smooth and indistinguishable. In addition, the Rydberg component of the S1 state is more clearly resolved by combining experiment and theory.

On the quantum and classical control of laser-driven isomerization in the Wigner representation.

We investigate the validity of the classical approximation to the numerically exact quantum dynamics for infrared laser-driven control of isomerization processes. To this end, we simulate the fully quantum mechanical dynamics both by wavepacket propagation in position space and by propagating the Wigner function in phase space employing a quantum-mechanical correction term. A systematic comparison is made with purely classical propagation of the Wigner function. On the example of a one-dimensional double well potential, we identify two complementary classes of pulse sequences that invoke either a quantum mechanically or a classically dominated control mechanism. The quantum control relies on a sequence of excitations and de-excitations between the system's eigenstates on a time scale far exceeding the characteristic vibrational oscillation periods. In contrast, the classical control mechanism is based on a short and strong few-cycle field exerting classical-like forces driving the wavepacket to the target potential well where it is slowed down and finally trapped. While in the first case, only the quantum mechanical propagation correctly describes the field-induced population transfer, the short pulse case is also amenable to a purely classical description. These findings shed light on the applicability of classical approximations to simulate laser-controlled dynamics and may offer a guideline for novel control experiments in more complex systems that can be analyzed and interpreted utilizing efficient state-of-the-art classical trajectory simulations based on ab initio molecular dynamics.

Drainage, rebound and oscillation of a meniscus in a tube

In this paper, the drainage and subsequent rebound of a liquid column in a cylindrical tube is examined experimentally and theoretically. When liquid is drawn up into a capillary and then released under gravity, inertia allows the meniscus to overshoot the equilibrium capillary rise height. The meniscus then rebounds up the tube, again overshooting the equilibrium height and undergoes oscillation. By varying both the immersion depth and radius of the tube, one can observe rich dynamical behavior, with the most dramatic being the formation of a fast liquid jet, barely visible to the naked eye but easily captured with high-speed video. In addition to the flow separation caused by the sudden expansion at the end of the tube, this jet serves as a mechanism of energy dissipation. Some qualitative differences between the works of Quere et al. [“Rebounds in a capillary tube,” Langmuir 15, 3679–3682 (1999)] and Lorenceau et al. [“Gravitational oscillations of a liquid column in a pipe,” Phys. Fluids 14(6), 1985–1992 (2002)] and the present experiment are observed and discussed. A critical condition for oscillatory behavior is derived theoretically and matches well with the experimental observation. Once in the oscillatory regime, both the maximum depth below and the maximum rebound height above the equilibrium level are investigated by performing a systematic sweep through the relevant parameter space, incorporating the initial meniscus height, immersion depth, tube radius, and fluid properties. Lastly, the characteristic period of oscillation, tp, is assessed and found to be largely independent of fluid viscosity, and could be reasonably well-collapsed by a single curve whereby tp∼hi, where hi is the tube immersion depth.

Neutron star bulk viscosity, ‘spin-flip’ and GW emission of newly born magnetars

The viscosity-driven "spin-flip" instability in newborn magnetars with interior toroidal magnetic fields is re-examined. We calculate the bulk viscosity coefficient ($\zeta$) of cold, $npe \mu$ matter in neutron stars (NS), for selected values of the nuclear symmetry energy and in the regime where $\beta$-equilibration is slower than characteristic oscillation periods. We show that: i) $\zeta$ is larger than previously assumed and the instability timescale correspondingly shorter; ii) for a magnetically-induced ellipticity $\epsilon_B \lesssim 4 \times 10^{-3}$, typically expected in newborn magnetars, spin-flip occurs for initial spin periods $\lesssim 2-3$ ms, with some dependence on the NS equation of state (EoS). We then calculate the detectability of GW signals emitted by newborn magnetars subject to "spin-flip", by accounting also for the reduction in range resulting from realistic signal searches. For an optimal range of $\epsilon_B \sim (1-5) \times 10^{-3}$, and birth spin period $\lesssim 2$ ms, we estimate an horizon of $\gtrsim 4$ Mpc, and $\gtrsim 30$ Mpc, for Advanced and third generation interferometers at design sensitivity, respectively. A supernova (or a kilonova) is expected as the electromagnetic counterpart of such GW events. Outside of the optimal range for GW emission, EM torques are more efficient in extracting the NS spin energy, which may power even brighter EM transients.

Flow characteristics and instability analysis of pressure drop in parallel multiple microchannels

Instability analysis is vital for the safety of the system with microchannels, in which the microchannels could be used as a heat sink component with high heat efficiency. In this study, flow visualization and measurements of two-phase flow boiling in six parallel microchannels with a hydraulic diameter of 517 µm were conducted in order to investigate the dynamic instability in a microchannel system. The tests were performed in the range of mass flux 23.04–111.89 kg/(m2·s), heat flux 4.2–67.7 kW/m2, inlet temperature 40–60 °C and exit vapor quality −0.06 to 0.12. The wavelet decomposition method was used for the oscillation characteristic analysis and the signal noise was identified successfully within the decomposition process. Combination of time-domain and frequency-domain analysis as well as the high speed visualization were performed for the characteristics analysis of the pressure drop. Entropy method was first used for the flow instability analysis in the microchannel system and noticeable differences of stable and unstable flow states were found due to its inherent flow patterns in microchannel system. A strong bearing was found between the characteristic oscillation period of dynamic flow and the corresponding boiling number.

The Long-Term Pattern of Temperature and Precipitation in the Southern Urals

The dynamics of the average annual temperature in the near-surface air and total annual precipitation in the South Urals are studied on the basis of observation data from ten meteorological stations of the Orenburg region, with the observation period being 90 years on average. By using wavelet transform and cross wavelet transform methods, the characteristic oscillation periods are revealed in the initial meteorological data series and correlations to the main climatic indices (AMO, NAO, and NAM) are calculated.

МЕДЛЕННАЯ ДИНАМИКА СТЕПЕНИ СИНХРОНИЗОВАННОСТИ КОНТУРОВ ВЕГЕТАТИВНОЙ РЕГУЛЯЦИИ РИТМА СЕРДЕЧНО-СОСУДИСТОЙ СИСТЕМЫ

Introduction: The main problem in analyzing low-frequency components of biological processes is conducting specialized experiments with long-term signal recording. However, the information about the system behavior on long scales can make an invaluable contribution to understanding the nature of the interaction between separate elements of the system. Purpose: Analyzing the features of the dynamics of the proposed quantitative index which characterizes the degree of phase synchronization of complex non-stationary biological systems (contours of autonomic regulation of the cardiovascular system) on time scales about tens and hundreds of characteristic oscillation periods (hundreds of seconds) using long experimental records. Results: During the experiments, we obtained simultaneous registration of two-hour signals from 23 healthy subjects: cardiointervalogram and photoplethysmogram vessels. The dynamics of the total percentage of phase synchronization (S index) of 0.1 Hz oscillations in the PPG and CIG was estimated in sliding windows. Similarly, we investigated the powers of so-called low-frequency (LF, 0.1 Hz) and high-frequency (HF, > 0.1 Hz) components of the spectrum of the original signals. The features of the interaction between the studied indices were evaluated using correlation analysis methods. We have found that the S index dynamics shows signs of its oscillatory nature with a characteristic oscillation period about 1000 s. The interaction between LF and HF oscillations in the autonomic circulatory regulation is of a complex nonlinear character. We have also identified signs of oscillations with a period about 1000 s in the dependencies of the total percentage of the phase synchronization of 0.1 Hz contours in circulatory regulation. A structural model of the interaction between circulatory regulatory contours is formed which explains the observed effects. Practical relevance: Obtaining fundamental knowledge about the interaction and regulation of the cardiovascular system elements will allow us to improve the methods we are developing for the diagnostics and therapy of pathological disturbances in the cardiovascular system.

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

Self-organization in cells often manifests itself in oscillations and waves. Here, we address deformation waves in protoplasmic droplets of the plasmodial slime mould Physarum polycephalum by modelling and experiments. In particular, we extend a one-dimensional model that considered the cell as a poroelastic medium, where active tension caused mechanochemical waves that were regulated by an inhibitor (Radszuweit et al., 2013). Our extension consists of a simple, qualitative chemical reaction–diffusion model (Brusselator) that describes the regulation of the inhibitor by another biochemical species. The biochemical reaction enhances the formation of mechanochemical waves if the reaction rates and input concentrations are near or inside an oscillatory regime. The period of the waves is found to be controlled by the characteristic oscillation period, whereas their wavelength is set by mechanical parameters. The model also allows for a systematic study of the chemical activity at the onset of mechanochemical waves. We also present examples for pattern formation in protoplasmic droplets of Physarum polycephalum including global oscillations where the central region of the droplets is in antiphase to the boundary zone, as well as travelling and standing wave-like uniaxial patterns. Finally, we apply our model to reproduce these experimental results by identifying the active tension inhibitor with the intracellular calcium concentration in the Physarum droplets and by using parameter values from mechanical experiments, respectively knowledge about the properties of calcium oscillations in Physarum. The simulation results are then found to be in good agreement with the experimental observations.

Non-Tidal Water Level Variability in Lianyungang Coastal Area

The non-tidal water level fluctuation at four locations in Lianyungang coastal area was analyzed by using tide data. Results show that the non-tidal water level fluctuation was associated with the spatial distribution. The combined effects of shoaling and attenuation due to the shape and bottom topography contribute to the spatial distribution of non-tidal water level fluctuation. Two characteristic oscillation periods of about 12 h and 24 h which highly coherent throughout the four stations were revealed. Analysis of the exciting mechanisms indicates that the variability was mainly generated by fluctuation in wind speed.

Implementation of a three-qubit Toffoli gate in a single step

Single-step implementations of multi-qubit gates are generally believed to provide a simpler design, a faster operation, and a lower decoherence. For coupled three qubits interacting with a photon field, a realizable scheme for a single-step Toffoli gate is investigated. We find that the three qubit system can be described by four effective modified Jaynes-Cummings models in the states of two control qubits. Within the rotating wave approximation, the modified Jaynes-Cummings models are shown to be reduced to the conventional Jaynes-Cummings models with renormalized couplings between qubits and photon fields. A single-step Toffoli gate is shown to be realizable with tuning the four characteristic oscillation periods that satisfy a commensurate condition. Possible values of system parameters are estimated for single-step Toffli gate. From numerical calculation, further, our single-step Toffoli gate operation errors are discussed due to imperfections in system parameters, which shows that a Toffoli gate with high fidelity can be obtained by adjusting pairs of the photon-qubit and the qubit-qubit coupling strengthes. In addition, a decoherence effect on the Toffoli gate operation is discussed due to a thermal reservoir.

10.1007/s11443-008-3004-3

We develop new approaches to the numerical simulations of slowly evolving stellar systems with characteristic times of the order of the precession period for a typical orbit. This period is assumed to be long compared to the characteristic oscillation periods of individual stars in their orbits. For such processes, the standard numerical simulations using various N-body methods become inadequate, since the bulk of the computational time is spent on the repeated calculations of almost invariable orbits. We suggest a new N-orbit approach (called so by analogy and by contrast with N-body methods) that takes into account the specifics of the problems under consideration, in which whole orbits take the place of individual stars in N-body methods. Accordingly, the stellar system is represented by a set of N orbits the changes in the spatial orientation and shape of which lead to a slow evolution of the system. We derive the equations governing the nonlinear dynamics of orbits separately for 2D (disk) and 3D systems. These equations have the form of Hamiltonian equations for canonically conjugate pairs of variables. In the 2D case, one pair of such equations will suffice: for the angular momentum L and for the angle of direction to the apocenter Ψ. In the 3D case, there are two such pairs. The first pair of equations is for the modulus of the angular momentum L and the angle of direction to the apocenter in the orbital plane Ψ, while the second pair is for L z (the component of the angular momentum vector L along the z axis) and the orientation angle of the line of nodes W. Together with the energy E, which is an adiabatic invariant, these two (or four) parameters completely define the orbit (in the 2D and 3D cases, respectively). The evolution of the system is traced by solving these equations within the framework of the suggested N-orbit approach. We have in mind two versions of this approach. In the first version, a separate orbit corresponds to each star along which the mass of this star is “smeared.” In this version, the number of orbits N orb is equal to the total number of stars N in the system under consideration. This version is a complete analogue of the N-body approach, except that the motion of each star is averaged over the orbit and we consider not the behavior of the star but the behavior of its orbit. In the second version, all stars from one small cell in the phase space of orbit parameters correspond to the orbit. In fact, this version of the N-orbit approach represents the method of solving the collisionless Boltzmann kinetic equation for the distribution function of orbit parameters. The number of orbits N orb in this approach is equal to the chosen number of cells. There exist two types of objects to the description of which N-orbit methods can be applied. First, these include the central regions of galaxies containing no large point masses. The stars in these regions move in symmetric (about the center) elliptical orbits that slowly precess due to the small deviation of the self-consistent potential from an exactly quadratic form (when all orbits are closed, so that the precession velocity is exactly equal to zero). Second, these include the star clusters around massive black holes at the centers of these clusters. The orbit of a star revolving around a central mass is a closed Keplerian ellipse and, consequently, has no precession. Slow precession appears when the relatively weak (compared to the attraction of the massive black hole) self-consistent gravitational field produced by cluster stars is taken into account. In this paper, to be specific, we will mainly deal precisely with the latter, near-Keplerian systems.

Glucose Measurement Using an Enzymatic Oscillatory Reaction

AbstractIn biological systems, oscillatory reactions are often found. These reactions, so‐called biological oscillators, have a characteristic oscillation period ranging from seconds to years [1]. For the oscillation in which an enzyme is involved, the reaction has been studied both experimentally [2–5] and theoretically [6–10]. In many cases, temperature control, stirring, or continuous flow of the reactant is necessary to observe continuous oscillation. No trial has been made yet to control the oscillation period or waveform. Here, we report an enzymatic oscillation reaction using catalase and glucose oxidase in which the oscillation period and waveform can be changed by the addition of glucose. We achieved good reproducibility with an oscillation period and waveform change that was sufficient to be applied to the glucose quantification. The effect of coexisting chemicals such as ascorbic acid, urea, or acetamidophenol on the oscillation is examined.

Coherent control of alkali cluster fragmentation dynamics

Metal clusters exhibit extraordinary chemical and catalytic properties, which sensitively depend upon their size. This behavior makes them interesting candidates for the real-time analysis of ultrafast photo-induced processes—ultimately leading to coherent control scenarii. We have performed transient multi-photon ionization experiments on small alkali clusters of different size in order to probe their wave packet dynamics, structural reorientations, charge transfers and dissociative events in different vibrationally excited electronic states including their ground state. The observed processes were highly dependent on the irradiated pulse parameters, like its phase, amplitude and duration; an emphasis to employ a feedback control system for generating the optimum pulse shapes. Their spectral and temporal behavior reflects interesting properties about the investigated system and the irradiated photochemical process. We present first the vibrational dynamics of bound, dissociated, and pre-dissociated electronically excited states of alkali dimers and trimers. The scheme for observing the wave packet dynamics in the electronic ground state using stimulated Raman-pumping is shown. Since the employed pulse parameters significantly influence the efficiency of the irradiated dynamic pathways photo-induced fragmentation experiments on bifurcating reaction channels were carried out. In these experiments different branching ionization and fragmentation pathways of electronically excited Na 2K were investigated. By employing an evolutionary algorithm for optimizing the phase and amplitude of the applied laser field, the yield of the resulting parent or fragment ions could significantly be influenced and interesting features could be concluded from the obtained optimum pulse shapes revealing the characteristic molecular oscillation period. Moreover, the influence on the optimal pulse shape due to fragmentation from larger clusters into NaK is obtained. The substructure of the optimal pulse shape thereby offers new insight into the fragmentation channel during the control process. Characteristic motions of the involved wave packets are proposed, in order to explain the optimized dynamic dissociation pathways.

The effect of high intensity laser propagation instabilities on channel formation in underdense plasmas

Experiments have been performed using high power laser pulses (up to 50 TW) focused into underdense helium plasmas (ne⩽5×1019 cm−3). Using shadowgraphy, it is observed that the laser pulse can produce irregular density channels, which exhibit features such as long wavelength hosing and “sausage-like” self-focusing instabilities. This phenomenon is a high intensity effect and the characteristic period of oscillation of these instabilities is typically found to correspond to the time required for ions to move radially out of the region of highest intensity.

Estimation of parameters and eigenmodes of multivariate autoregressive models

Dynamical characteristics of a complex system can often be inferred from analysis of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregressive (AR) models of first order. This paper describes the estimation of eigenmodes of AR models of arbitrary order. AR processes of any order can be decomposed into eigenmodes with characteristic oscillation periods, damping times, and excitations. Estimated eigenmodes and confidence intervals for the eigenmodes and their oscillation periods and damping times can be computed from estimated models parameters. As a computationally efficient method of estimating the parameters of AR models from high-dimensional data, a stepwise least squares algorithm is proposed. This algorithm computes models of successively decreasing order. Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients and eigenmodes are rough approximations of the confidence intervals inferred from the simulaitons.

Fourier‐Doppler Imaging of Line Profile Variations in ζ Ophiuchi

We present, for the first time, the Fourier-Doppler Imaging (FDI) analysis of periodic line profile variations in a ζ Oph-type star. For this purpose we obtained, in the period from 1996 May 3 to May 5, a total of 242 high-resolution, high signal-to-noise ratio spectra of the Be star ζ Oph itself. Using the FDI technique, we examine the variations in both time and wavelength and complement it with time series analysis. This kind of analysis is valid for both the nonradial pulsator model and the rotation modulation model, but we discuss the results in terms of the former model, considering it the more likely explanation for the observed line profile variability. Two distinct groups of modes are detected: medium (4 ≤ l ≈ |m| ≤ 8) and high-degree modes (which could be associated with 13 ≤ l ≈ |m| ≤ 17). It is shown that the high-frequency oscillations were strongly confined to an equatorial belt narrower than 20° and that the line profile variability was caused predominantly by sectoral modes, although tesseral modes |m| = l - 1 are not excluded in taking into account the effect of fast rotation. We discuss the modal nature of the waves with respect to the characteristic oscillation periods in the corotating frame and the high amplitude of the projected rotational velocity variations (≈20 km s-1).

Long-Range (Casimir) Interactions

Normally, nonrelativistic electromagnetic theory with two-particle Coulombic interactions adequately determines the interaction potential of systems A and B if the systems are composed of particles with characteristic velocities much less than the speed of light. If, however, the time it takes light to travel between A and B exceeds a characteristic oscillation period of A or B, the way in which the potential function depends on the separation of the systems can be altered. Called the Casimir effect, it has only recently been confirmed, and it arises in physics, chemistry, and biology. It is the clearest physical manifestation of the fact that, even in a vacuum, electromagnetic fields cannot all vanish.

Dependence of Turing pattern wavelength on diffusion rate

The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The diffusion coefficient D of NaCl is found to vary from 0.5×10−5 to 1.8×10−5 cm2/s for the gel conditions considered. The CIMA reactants are assumed to have diffusion coefficients that are directly proportional to that of NaCl. The wavelength λ of the observed hexagonal patterns (0.13–0.28 mm) varies in accord with the predicted relation for Turing patterns, λ∼D1/2. Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.

Molecular-dynamics study of binary soft-sphere glasses: Quench-rate effects and aging effects.

Molecular-dynamics simulations (MD) have been carried out on a soft-sphere model for binary alloys quenched into glassy states at different quench rates. The main purpose of the present work is to investigate slow relaxation phenomena of the quenched glassy states close to the glass transition by calculating both the static and dynamical structural changes upon aging (annealing) of them. For this purpose the MD simulations were performed for a time interval as long as an order of 2000\ensuremath{\tau}, where \ensuremath{\tau} is a microscopic time scale, equivalent to an order of the Einstein period, which is the characteristic period of oscillation of atoms. It is shown that the static properties exhibit neither significant changes during annealing of samples, nor changes for different samples. On the other hand, the dynamic properties show remarkable aging effects as well as sample-dependent behavior, meaning that the quenched glassy state cannot attain to an equilibrium state for the time scale of our simulations, due to dynamical slowing-down phenomena. The quenched sample is, however, shown to tend to a seemingly quasiequilibrium state after a sufficient annealing. Detailed discussions are made on both aging effects and sample-dependent behaviors of quenched glassy states, by paying particular attention to the behavior of the single-atom motion, mean-square displacement, and self-diffusion constant of the quenched glassy state. A non-Gaussian parameter is also calculated, which we propose as a good candidate to represent an order parameter of the glass transition.

Transient modelling of railgun plasma armatures

Simulations are performed with a one-dimensional, time-dependent model to investigate the dynamic behavior of railgun plasma armatures. Specifically, the model is applied to the analysis of three problems: (1) the simulation of the release of a projectile; (2) the simulation of the latter stages of the initiation of an armature, with the initial arc length 50% of its final equilibrium length; and (3) a second initiation simulation where the initial arc length is 10% of its final equilibrium length. For all three simulations, the armature length and projectile acceleration exhibit damped oscillations. After the first armature expansion, the period of oscillation of the armature length can be approximated by 3l/sub eq//a/sub 0/ where l/sub eq/ and a/sub 0/ are the armature length and acoustic propagation velocity, respectively, calculated for an equilibrium, isothermal plasma whose thermodynamic characteristics are obtained from a mass average of the properties in the nonisothermal simulation. This characteristic period of oscillation is consistent with the period observed in isothermal armature simulations. >