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The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T∗ is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T∗ is also tuned by a magnetic flux., Physical Review Letters, 130 (8), ISSN:0031-9007, ISSN:1079-7114

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

Chemical dynamics simulations are performed to study the dissociation of excited benzene-hexafluorobenzene (Bz-HFB) complex in N2 bath and the results are compared with the gas phase dynamics. Two N2 bath densities 20 and 750 kg/m3 are considered. Bz-HFB is excited with respect to the temperatures of 1000, 1500, and 2000 K at each bath density. The nature of the Bz-HFB* dissociation dynamics at the bath density of 20 kg/m3 is quite similar to gas phase one, but the same is drastically different at high bath density where energy transfer pathway dominates over dissociation and negligible direct dissociation of Bz-HFB* is reported.

We present a brief discussion of the phase-coherent dynamics of discrete breathers (intrinsic localized modes) in a system of two weakly coupled nonlinear chains and its comparison with periodic tunneling of quantum particles in a double-well potential and with macroscopic quantum tunneling of two weakly linked Bose–Einstein condensates. We consider the dynamics of relative phase of classically-tunneling discrete breathers in two weakly coupled nonlinear chains and show that the dynamics of the relative phase in the π/2 tunneling mode coincides with the experimentally observed dynamics of the relative phase of quantum particles, periodically tunneling in a double-well potential, both for noninteracting and strongly repulsively interacting particles. The observed coincidence demonstrates the correspondence between the dynamics of classical localized excitations in two weakly coupled nonlinear chains and tunneling dynamics of quantum object in the double-well potential. We show that in both π/2 and winding tunneling modes the relative phase experiences periodic jumps by π in the instants of complete depopulation of one of the weakly coupled chains or potential wells. The connection of the observed phase dynamics with the non-quantum uncertainty principle is discussed.

We consider networks of coupled phase oscillators of different complexity: Kuramoto–Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.

International audience; Protonated intermediates are postulated to be involved in the rate determining step of many sugar reactions. This paper presents a study of protonated sugar species, isolated in the gas phase, using a combination of infrared multiple photon dissociation (IRMPD) spectroscopy, classical ab initio molecular dynamics (AIMD) and quantum mechanical vibrational self-consistent field (VSCF) calculations. It provides a likely identification of the reactive intermediate oxocarbenium ion structure in a D-galactosyl system as well as the saccharide pyrolysis product anhydrogalactose (that suggests oxocarbenium ion stabilization), along with the spectrum of the protonated parent species: methyl D-galactopyranoside-H +. Its vibrational fingerprint indicates intramolecular proton sharing. Classical AIMD simulations for galactosyl oxocarbenium ions, conducted in the temperature range ~300-350 K (using B3LYP potentials on-the-fly) reveal efficient transitions on the picosecond timescale. Multiple conformers are likely to exist under the experimental conditions and along with static VSCF calculations, they have facilitated the identification of the individual structural motifs of the galactosyl oxocarbenium ion and protonated anhydrogalactose ion conformers that contribute to the observed experimental spectra. These results demonstrate the power of experimental IRMPD spectroscopy combined with dynamics simulations and with computational spectroscopy at the anharmonic level to unravel conformer structures of protonated saccharides, and to provide information on their lifetimes.

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed., Comment: 16 pages, 6 figures

The melting of an ultrathin lubricant film is studied at friction between atomically flat surfaces. We take into account fluctuations of lubricant temperature, which are defined by the Ornstein-Uhlenbeck process. Phase diagrams and portraits are calculated for second- and first-order transitions (the melting of an amorphous and that of a crystalline lubricants, respectively). It is shown that, in the former case, a stick-slip friction domain, separating the regions of dry and sliding friction, appears. In the latter case, three domains of stick-slip friction arise, which are characterized by the transitions between dry, metastable and stable sliding friction. The increase in the correlation time of lubricant temperature fluctuations leads to increasing in the rubbing-surface temperature needed for realization of sliding friction. The stationary states, corresponding to dry, stable and metastable sliding friction, are reached as a result of damped oscillations.

Driven mean-field threshold systems demonstrate complex observable space-time patterns of behavior that are difficult to understand or predict without knowledge of the underlying dynamics, which are typically unobservable. Here we describe a new method based on phase dynamics techniques to analyze and forecast the space-time patterns of activity in these systems. Application to earthquake data from a typical, seismically active region shows that the method holds considerable promise for forecasting the temporal occurrence of the largest future events. We demonstrate the power of our technique via an application to the difficult problem of earthquake forecasting in southern California.

Transient phase dynamics, synchronization and desynchronization which are stimulus-locked (i.e. tightly time-locked to a repetitively administered stimulus) are studied in two coupled phase oscillators in the presence of noise. The presented method makes it possible to detect such processes in numerical and experimental signals. The time resolution is enormous, since it is only restricted by the sampling rate. Stochastic stimulus locking of the phases or the n:m phase difference at a particular time t relative to stimulus onset is defined by the presence of one or more prominent peaks in the cross-trial distribution of the phases or the n:m phase difference at time t relative to stimulus onset in an ensemble of post-stimulus responses. Unlike the presented approach, both triggered averaging (where an ensemble of post-stimulus responses is simply averaged) and cross-trial cross correlation (CTCC) lead to severe misinterpretations: The oscillators' coupling may cause a transient anti-phase clustering of the post-stimulus responses. Triggered averaging cannot distinguish such a response decorrelation from a mean amplitude decrease of the single responses. CTCC not only depends on the oscillators' phase difference but also on their phases and, thus, inevitably displays "artificial" oscillations that are not related to synchronization or desynchronization.

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

The conventional view of conversion reaction is based on the reversibility, returning to an initial material structure through reverse reaction at each cycle in cycle life, which impedes the complete understanding on a working mechanism upon a progression of cycles in conversion-reaction-based battery electrodes. Herein, a series of tin-doped ferrites (Fe3- xSn xO4, x = 0-0.36) are prepared and applied to a lithium-ion battery anode. By achieving the ideal reoxidation into SnO2, the Fe2.76Sn0.24O4 composite anchored on reduced graphene oxide shows a high reversible capacity of 1428 mAh g-1 at 200 mA g-1 after 100 cycles, which is the best performance of Sn-based anode materials so far. Significantly, a newly formed γ-FeOOH phase after 100 cycles is identified from topological features through synchrotron X-ray absorption spectroscopy with electronic and atomic structural information, suggesting the phase transformation from magnetite to lepidocrocite upon cycling. Contrary to the conventional view, our work suggests a variable working mechanism in an iron-based composite with the dynamic phases from iron oxide to iron oxyhydroxide in the battery cycle life, based on the reactivity of metal nanoparticles formed during reaction toward the solid electrolyte interface layer.

A time dependent thermal model for a superconducting constriction based weak-link (WL) is discussed for investigating the deterministic dynamics of its temperature and phase. A new dynamic regime is found where a non-zero voltage exists across the WL and its temperature stabilizes between the bath temperature and superconductor's critical temperature. This regime exists over a limited bias current range and gives rise to a new hysteretic regime in current-voltage characteristics. We also discuss the effect of fluctuations on the current-voltage characteristics and experimental implications of this dynamic regime., Comment: 7 pages, 4 figures; revised on 25 Nov 2014

Collisions lead to the collapse and revival of the interference fringes between two atomic Bose–Einstein condensates. We study the collapses and revivals of the relative phase between the condensates for two different initial states. One state invokes Bose–broken symmetry allowing us to write the wavefunction as a superposition of total number (of both condensates) states whereas the other does not.

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references.

We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. The partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling., Comment: 6 pages, 5 figures, 27 references

We propose a natural two-speed model for the phase dynamics of Si(111) 7x7 phase transition to high-temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated results show that a 7x7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. Low-energy electron microscopy experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.

We have studied the phase properties of initially coherent light interacting with two identical two-level atoms using the Hermitian phase operator of Pegg and Barnett. The results show that, in a certain initial state of the atoms, the field would, to a certain extent, preserve its order in phase, even for a long interaction time with the two atoms.

Physico-chemical systems driven away from thermal equilibrium usually undergo various types of instabilities leading to the formation of spatio-temporal patterns on macroscopic time and space scales. In two-dimensional geometries, patterns of different symmetries may be simultaneously stable. We study here the phase stability of hexagonal planforms in the framework of amplitude equations and reduced dynamical models close to the instability points.

Hodgkin-Huxley model neurons coupled by weak excitatory interactions are studied by a phase reduction technique. All the information about the coupling between the neurons and their synchronization is then contained in an effective interaction between their phases. One shows analytically that an excitatory coupling can result in an effective inhibition between the neurons reducing their firing rates. Systems of two neurons exhibit bistability and out-of-phase locking. It is suggested that these features may have significant consequences for networks.

Based on the complex Ginzburg-Landau equation (CGLE), a new mapping model of oscillatory media is proposed. The present dynamics is fully determined by an effective phase field renormalized by amplitude. The model exhibits phase turbulence, amplitude turbulence, and a frozen state reported in the CGLE. In addition, we find a state in which the phase and amplitude have spiral structures with opposite rotational directions. This state is found to be observed also in the CGLE. Thus, one concludes that the behaviors observed in the CGLE can be described by only the phase dynamics appropriately constructed.

Chemical vapour deposition on a Cu substrate is becoming a very important approach to obtain high quality graphene samples. Previous studies of graphene growth on Cu mainly focus on surface processes. However, recent experiments suggest that gas-phase dynamics also plays an important role in graphene growth. In this article, gas-phase processes are systematically studied using computational fluid dynamics. Our simulations clearly show that graphene growth is limited by mass transport under ambient pressures while it is limited by surface reactions under low pressures. The carbon deposition rate at different positions in the tube furnace and the concentration of different gas phase species are calculated. Our results confirm that the previously realized graphene thickness control by changing the position of the Cu foil is a result of gas-phase methane decomposition reactions.

We investigate the dynamical properties of two mutually delay-coupled semiconductor lasers that are coupled via their optical fields. Because a semiconductor laser is an oscillator that features strong coupling between its amplitude and phase, this system serves as a prototype model of coupled amplitude-phase oscillators. Our main interest here is in the dynamics near and within the locking region where the two lasers emit light of the same frequency. We present experimental observations that give evidence for four qualitatively different dynamical regimes: stable continuous wave emission, oscillations at the laser's characteristic relaxation oscillation frequency, oscillation related to the frequency difference between the two lasers and more complicated dynamics. We characterize and identify these dynamical regimes and analyse them by means of a bifurcation analysis of the corresponding rate equation model with delay. Specifically, we present the underlying bifurcation structure, where the detuning and the pump current are the main bifurcation parameters. The combination of experiment and bifurcation analysis shows how changes in the dynamics arise from the presence of local and global bifurcations near the locking region. © 2009 IOP Publishing Ltd and London Mathematical Society.

We present a simple model for a patch antenna based on metamaterial concepts operating in the microwave region with a bandwidth of 1.9–2.6 GHz. The small size and the relatively large operational band make this device exploitable for electromagnetic energy harvesting in urban environments. Describing the antenna by an equivalent circuit composed of a transmission line having right/left hand properties with a RC load, we can properly account for the phase dynamics in correspondence of resonances characterized by a specific handedness. The model is validated measuring the response of the reflection scattering parameter S1,1 for a copper prototype fabricated on a FR4 printed circuit board.

Despite its simple mathematical structure, the Sprott E flow displays a chaotic dynamics whose complexity increases with the bifurcation parameter. This complexity shows up in the phase dynamics, which becomes highly incoherent. Such behavior is interpreted as the superposition of the dynamics of several different embedded standard maps.

Udgivelsesdato: OCT 22 2000 Low-energy and high-energy collision induced dissociation techniques are used to study the dissociation behavior of the gaseous Pt(CN)(6)(2-) and Pt(CN)(4)(2-) dianion complexes in order to probe the smallest stable dianion complex. Loss of neutral molecules from Pt(CN)(6)(2-) occurs resulting in Pt(CN)(5)(2-) and Pt(CN)(4)(2-), but no indication of the existence of Pt(CN)(3)(2-) was found. This indicates that the lifetime of Pt(CN)(3)(2-) is less than 4 mus (the flight time from the collision region to the detector). In contrast, all monoanion platinum-cyanide complexes were observed, i.e., Pt(CN)(n)(-) (n=1-6). The kinetic energy released in processes where monoanions are formed is much lower than the barrier height for the reverse reaction (>1.5 eV), which indicates that electron detachment is involved, e.g., Pt(CN)(3)(-) and CN- are not formed in the same dynamical process from Pt(CN)(4)(2-), or that the dynamics of the dissociation process is slow. For comparison, the Ru(bipy)(3)(2+)*--> [Ru(bipy)(2)-H](+)+bipyH(+) reaction is associated with a kinetic-energy release of similar to0.3 eV (bipy=2,2(')-bipyridine). (C) 2000 American Institute of Physics. [S0021-9606(00)00240-3].

We investigate the quantum-phase dynamics of a dissipative molecular system interacting with a single-mode amplitude-squeezed field (with a sub-Poissonian photon-number distribution) using the Monte Carlo wave-function method. As quantum dissipation, we consider molecular coherent (phase) and population relaxations, which are caused by nuclear vibration, and cavity relaxation (the dissipation of an internal single mode to outer mode). In this study, we elucidate the effects of these dissipations on the unique quantum dynamical behaviors of this coupled system, e.g., collapse-revival behavior of Rabi oscillations, using the quasiprobability (Q function) distribution of a single-mode field and the off-diagonal molecular density matrix. It is found that although the amplitude-squeezed field exhibits a distinct revival with larger amplitudes of molecular population in the presence of the molecular phase and population relaxations as compared to the coherent field, a very slight cavity relaxation suppresses the revival of molecular population and the increase in the magnitude of off-diagonal molecular density matrices during the quiescent region in the amplitude-squeezed field case more significantly than in the coherent field case. These features are shown to be closely related to the difference in the dynamics of Q function distributions between amplitude-squeezed and coherent fields.

The Kadomstev–Petviashvili (KP) equation is a well-known modulation equation normally derived by starting with the trivial state and an appropriate dispersion relation. In this paper, it is shown that the KP equation is also the relevant modulation equation for bifurcation from periodic travelling waves when the wave action flux has a critical point. Moreover, the emergent KP equation arises in a universal form, with the coefficients determined by the components of the conservation of wave action. The theory is derived for a general class of partial differential equations generated by a Lagrangian using phase modulation. The theory extends to any space dimension and time, but the emphasis in the paper is on the case of 3+1. Motivated by light bullets and quantum vortex dynamics, the theory is illustrated by showing how defocusing NLS in 3+1 bifurcates to KP in 3+1 at criticality. The generalization to N >3 is also discussed.

The effect of synchronization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in this paper is the saddle-node bifurcation of invariant curves that corresponds to the saddle-node bifurcation of two-dimensional tori in the complete system of differential equations for the dynamical system under study.

We investigate the dynamics of a three-state atomic/molecular model system interacting with a two-mode squeezed vacuum field in view of the correlation between the atomic/molecular density matrix and photon-phase distribution. It is found that two-mode squeezed vacuum field realizes the anomalous situation that the coherency between the atomic/molecular states concerning the two-photon process is preserved well during the dynamics though the coherency between other states completely vanish. This implies that the quantum and thermal features can coexist in the atomic/molecular system in the presence of two-mode squeezed vacuum field. Such phenomenon is found to originate in the feature of its initial photon-phase correlation of a two-mode squeezed vacuum. We also discuss how the present attractive features in off-diagonal density matrices affect the molecular non-linear polarization.

We investigate the quantum phase dynamics of an initially one-mode amplitude-squeezed photon field interacting with a two-state molecular system by using the numerically exact approach developed in a previous paper. As shown in previous studies, the collapses and revivals of Rabi oscillation of the molecular population are observed for the amplitude-squeezed field, while significant differences are detected in the amplitude of oscillation and the revival–collapse period between amplitude-squeezed and coherent fields. These features are found to be closely related to the differences in the dynamical behavior of the Pegg–Barnett phase and the quasiprobability ( Q function) distributions for these two photon fields.

We investigate the intermolecular-interaction (dipole–dipole interaction) effects on the quantum dynamics of dimer density matrices and photon-phase distributions using several dimer models with different intermolecular distances in the presence of a two-mode squeezed vacuum field. In this photon field, each mode is initially correlated and the reduced one-mode photon distribution is equivalent with that of a thermal field. For comparison, we perform parallel studies, in which the initial fields are two types of noncorrelated two-mode fields, i.e., a two-mode coherent field and a two-mode thermal field. It is found that although the two-mode squeezed vacuum field causes the random oscillations of dimer populations in the noninteracting dimer, the periodic oscillations like the collapse–revival behavior emerge as the intermolecular distance decreases (the intermolecular interaction increases). Similar and dissimilar features among quantum dynamics caused by these three types of fields are investigated by a...

Current-driven dynamics of superconducting phases of Josephson junction networks in magnetic fields are studied numerically. We here consider two-dimensional arrays (Josephson junction arrays, JJAs) with positional disorder. In the presence of strong disorder and driving bias currents, the nucleation of vortex–antivortex pairs causes the plastic flow and elastic flow of phases in JJAs. We focus on two threshold currents that characterize the boundaries of these flow regimes. We analyze the threshold currents on the basis of the scaling theory of pinning due to random potentials. It is found that the threshold currents show scaling behaviors characterized by scaling exponents in one dimension.

It is well-known that the interaction among atoms/molecules and quantized electromagnetic fields with a small number of photons provides a peculiar quantum nature, i.e., collapses and revivals in the Rabi oscillations. In this study, we investigate the intermolecular interaction (dipole–dipole interaction) effect on the collapse-revival behavior using several dimer models (composed of two kinds of two-state monomers with slightly different excitation energies) with different intermolecular distances in the presence of a two-mode squeezed coherent field, in which each mode is initially correlated. It is found that although the collapse-revival behavior is fairly overlapped and indistinct in the case of a noninteracting dimer under the present two-mode squeezed coherent field, the decrease in the intermolecular distance (the increase in the intermolecular interaction) resurrects relatively distinct collapse-revival behavior with longer collapse and revival times. By analyzing the quantum behavior from the v...

International audience; Benzophenone is a prototype molecule for photochemistry in the triplet state through its high triplet yield and reactivity. We have investigated its dynamics of triplet formation under the isolated gas phase conditions via femtosecond and nanosecond time resolved photoelectron spectroscopy. This represents the complete evolution from the excitation in S-2 to the final decay of T-1 to the ground state S-0. We have found that the triplet formation can be described almost as a direct process in preparing T1, the lowest reacting triplet state, from the S-1 state after S-2 -> S-1 internal conversion. The molecule was also deposited by a pick-up technique on cold argon clusters providing a soft relaxation medium without evaporation of the molecule and the mechanism was identical. This cluster technique is a model for medium influenced electronic relaxation and provides a continuous transition from the isolated gas phase to the relaxation dynamics in solution.

We derive a new nonlinear criterion for the occurrence of fast relaxation (crash) events at the edge of high-confinement-mode plasmas. These fast relaxation events called ELMs (edge-localized modes) evolve from ideal magnetohydrodynamics (MHD) instabilities, but the crash is not due only to linear physics. We show that for an ELM crash to occur, the coherence time of the relative phase between potential and pressure perturbations must be long enough to allow growth to large amplitude. This phase coherence time is determined by both linear and nonlinear dynamics. An ELM crash requires that the instability growth rate exceed a critical value, i.e., γ>γc, where γc is set by 1/τc and τc is the phase coherence time. For 0

The explicit expression of the phase of the Bose–Einstein condensates (BEC) is obtained with the expectation value of the quantum operator. With help of this explicit expression, the chemical potential of BEC and the phase diffusion induced by the nonlinear interaction (or two-body dipolar loss) are investigated. This result will helpful to understand the phase properties of the BEC.

A locally phase-shifted Sine–Gordon model well accounts for the phenomenology of unconventional Josephson junctions. The phase dynamics shows resonant modes similar to Fiske modes that appear both in the presence and in the absence of the external magnetic field in standard junctions. In the latter case, they are also in competition with zero field propagation of Sine–Gordon solitons, i.e., fluxons, which give rise to the so-called zero field steps in the current–voltage (I–V) of the junction. We numerically study the I–V characteristics and the resonances magnetic field patterns for some different faceting configurations, in various dissipative regimes, as a function of temperature. The simulated dynamics of the phase is analyzed for lower-order resonances. We give evidence of a nontrivial dynamics due to the interaction of propagating fluxons with localized semifluxons. Numerical results are compared with experimental outcomes obtained on high-quality high-Tc grain boundary YBCO junctions.

The high-velocity oxygen fuel (HVOF) thermal spray is used for a particulate deposition process in which micro-sized particles are propelled and heated in a supersonic combusting gas stream. It is characterized by high gas velocity and high density and is being used in an increasing variety of coating applications, such as ceramic and composite coatings, to improve wear and abrasion resistance. The particle temperature and velocity are two of the most important parameters in HVOF thermal spraying, which affect the quality of the coatings. To understand the particle dynamics, it is necessary to study, first, the thermal flow characteristics in the HVOF system. In this study, a numerical analysis is performed to predict the gas dynamic behaviors, and the effect of the geometrical parameter is studied to optimize the nozzle design.

We study the phase dynamics of turbulent Taylor vortex flow by applying a forced modulation to the upper boundary of a large-aspect-ratio system of concentric cylinders. The experiment shows that the axial phase variable of the turbulent Taylor vortex flow is a deterministic variable and its dynamics can be described by a simple diffusion model. The resultant diffusion coefficient of the turbulent Taylor vortex flow is about an order of magnitude larger than that of laminar/regular Taylor vortex flow. We argue that the approach of phase dynamics can also be applied to turbulent flows as long as there is, on sufficiently long-time scales, a coherent structure discernable in the system.

We investigate the Poincare transformation dynamics describing the stochastic motion of a relativistic electron in the regular electrostatic field of a wave packet. The conditions of local instability of the phase trajectories are determined: it is shown that the system is a structurally stable Y system with an attracting set of the hyperbolic type. The relationship between the dynamics at the strange attractor characterized by Lyapunov indices and its statistical structure described by the Kolmogorov entropy is discussed. The fractal dimension of the phase space of the system is determined. The results of a numerical simulation of the effect are presented and discussed.

Analytical and numerical methods were used to study the dynamics of the mapping that describes a determinate dynamic system consisting of a relativistic electron and a wave packet of potential waves. The mapping dynamics is shown to depend essentially on a parameter that characterizes the wave-packet intensity. The system behaves in different ways, depending on that parameter: it executes ergodic motion with displacement or motion with simultaneous regular and irregular trajectories. This mapping is shown to be typical and structurally stable.

In the presence of resonant Rabi oscillations and depending on the amplitude of the periodic drive, the dynamics of the phase of a two-state quantum system is either fractal (i.e. aperiodic according to a random process) or phase-locked (i.e. quasiperiodic).