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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.

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.

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.

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.

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.

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.

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.

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).

The phase dynamic equation of motion for a propagating periodic structure is derived in a euclidean invariant manner. The formulation is applied to the generalized Swift-Hohenberg model where the coefficients are complex numbers.

We show that the spontaneous formation of transverse spatial patterns due to diffraction in lasers can be described by a phase diffusion equation of the Kuramoto-Sivashinsky kind. Hence the origin of the pattern formation lies in spatial instabilities of the phase of the complex slowly varying laser field amplitude.

The application of the transient grating method to the understanding of gas-phase velocity distributions and collisional effects is presented. Theoretical models are discussed in view of the experimental data obtained from iodine vapor. Applications of the transient grating method to other gas-phase problems are also mentioned.

In the nature, the fish can control the wave propagation on the caudal fin using the sarcomere at the leading edge of the caudal fin. The control methods can be classified into three modes: Active Heave and Active Pitch (AHAP),Passive Heave and Active Pitch (PHAP), Active Heave and Passive Pitch (AHPP). Which mode can produce the largest thrust? Which mode can develop the most efficient swimming performance? So far, the research on these issues still cannot be found in the article. In this paper, we have studied the self-propulsion of the flexible plates driven by these three modes. It is expected that results can shed new light on understanding the locomotion mechanism of the fish and give a new idea for the design and control of the robot fish. The vibration of the flexible plate in the high velocity flow maybe unstable, and the velocity threshold of the flow are depending on the stiffness of the plate. The motion of the plate driven by AHAP is the most unstable, while AHPP is the most stable driving mode. The thrust on the flexible plate is mainly affected by the resonance effect, and the thrust in AHAP mode and AHPP mode are larger than that in PHAP mode. The propulsive efficiency is affected by both the resonance effect and the phase dynamics in the oscillator model. The phase dynamics is the dominant factor, and the resonance effect is the secondary factor.

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic. Phase synchronization has proven paradigmatic to study emergent collective behavior within a network. Defining the phase dynamics, however, is not a trivial task. The literature provides an arsenal of solutions, but results are scattered and their formulation is far from standardized. Here, we present, in a unified language, a catalogue of popular techniques for deriving the phase dynamics of coupled oscillators. Traditionally, approaches to phase reduction address the (weakly) perturbed dynamics of an oscillator. They fall into three classes. (i) Many phase reduction techniques start off with a Hopf normal form description, thereby providing mathematical rigor. There, the caveat is to first derive the proper normal form. We explicate several ways to do that, both analytically and (semi-)numerically. (ii) Other analytic techniques capitalize on time scale separation and/or averaging over cyclic variables. While appealing for their more intuitive implementation, they often lack accuracy. (iii) Direct numerical approaches help to identify oscillatory behavior but may limit an overarching view how the reduced phase dynamics depends on model parameters. After illustrating and reviewing the necessary mathematical details for single oscillators, we turn to networks of coupled oscillators as the central issue of this report. We show in detail how the concepts of phase reduction for single oscillators can be extended and applied to oscillator networks. Again, we distinguish between numerical and analytic phase reduction techniques. As the latter dwell on a network normal form, we also discuss associated reduction methods. To illustrate benefits and pitfalls of the different phase reduction techniques, we apply them point-by-point to two classic examples: networks of Brusselators and a more elaborate model of coupled Wilson–Cowan oscillators. The reduction of complex oscillatory systems is crucial for numerical analyses but more so for analytical estimates and model prediction. The most common reduction is towards phase oscillator networks that have proven successful in describing not only the transition between incoherence and global synchronization, but also in predicting the existence of less trivial network states. Many of these predictions have been confirmed in experiments. As we show, however, the phase dynamics depends to large extent on the employed phase reduction technique. In view of current and future trends, we also provide an overview of various methods for augmented phase reduction as well as for phase–amplitude reduction. Weindicate how these techniques can be extended to oscillator networks and, hence, may allow for an improved derivation of the phase dynamics of coupled oscillators.

Measurements of flame propagation velocities and extinction states in counterflow provide a valuable source of flame data that contain information about fundamental combustion physics. The approach to properly account for stretch effects in counterflow flame measurements through non-intrusive laser-based local velocity characterization was advanced in the mid-80s by Law and coworkers at atmospheric conditions with simple fuels. Subsequently, several research groups have extended the measurements to elevated pressures and complex fuels. However, counterflow flame data at subatmospheric pressures are limited. In the present study, a method is introduced for measuring laminar flame speeds and extinction strain rates in subatmospheric counterflow flames. A numerical study was performed to assess the dynamics of tracer particles used to facilitate measurements. It was found that the particle phase dynamics used in particle velocimetry measurements are not always representative of the underlying gas phase motion due to thermophoresis and insufficient drag, especially at low pressures. A numerical scheme was implemented whereby the computed particle phases were used for proper comparison with measurements and, based on the computed results, to infer the corresponding values of the gas phase. The method was applied to premixed methane/air and non-premixed methane–nitrogen/oxygen flames at pressures as low as 0.1 atm. Complimentary flame structure simulations were carried out which show that the kinetics of formyl radical prompt dissociation strongly impact the computed subatmospheric flames and may influence the validation of unimolecular and bimolecular reactions rate constants when tested against laminar flame data.

Thermoacoustic interactions in a circumferential network of lean-premixed combustors have a substantial impact on engine-level dynamics in a can-annular gas turbine combustion system. Previous experimental and numerical studies have focused on identifying the formation of large-scale interaction patterns and the modal dynamics of multiple eigenmodes. Since those investigations were primarily concerned with low-frequency interactions between adjacent combustors, there are currently no experimental observations that enable decisive discrimination between low- and high-frequency can-annular combustion instabilities. Here, we use pure hydrogen-air flame ensembles to trigger higher acoustic modes in four-coupled lean-premixed combustors, ultimately to understand the potential influence of self-excited instabilities on the spatiotemporal evolution of a can-annular system. The use of lean-premixed hydrogen-air flames enables measurements of previously unidentified phenomena, particularly in association with the excitation of high acoustic modes up to approximately 1.3 kHz. We demonstrate that self-excited standing azimuthal modes can be excited in the annular cross-talk section, particularly when the phase dynamics of the upstream flame tube sections are defined by alternating anti-phase oscillations. In this case, the temporal evolution of the can-annular system is governed by twofold degeneracy, incorporating an alternating push-pull mode in the longitudinal direction and a standing azimuthal mode in the circumferential direction at the same frequency. Based on experimental observations and Helmholtz simulations, we also show that a mixed state of synchronization and desynchronization can arise simultaneously as a result of symmetry breaking. The coexistence of coherent and incoherent motions is observed to be controlled by interactions between two closely spaced, but slightly misaligned, localized in-phase modes; this observation demonstrates experimentally the existence of a chiral state in can-annular thermoacoustics. The present results, for the first time, reveal a variety of phenomena involved in the response of a can-annular combustion system to higher frequency acoustic perturbations.

The crux of the technical issues facing the development of hydrogen gas turbine engines is the problem of how to enable low NOx, low dynamics combustor operations without detrimental flashback events in extremely fast lean-premixed hydrogen flames. While flashback mechanisms and nitrogen oxides emissions have been investigated extensively for high hydrogen content flames, the self-excited dynamics of lean-premixed pure hydrogen flame ensembles remain unclear. Here we use phase-resolved OH* chemiluminescence and OH PLIF imaging in a series of experiments in a multi-element injector configuration consisting of 293 small-scale injectors with an inner diameter of 3.0 mm. We collect a large experimental dataset to explore a variety of collective phenomena of the lean-premixed hydrogen-air flame ensemble, and perform systematic investigations of self-induced combustion instabilities. Our observations demonstrate that ultra-compact pure hydrogen flames generate high-amplitude pressure perturbations over a broad range of characteristic frequencies between 400 and 1800 Hz, corresponding to the third to tenth order eigenmodes. Low-frequency flame dynamics developed under relatively low equivalence ratio conditions involve a complex balance among several coexisting phenomena, including strong vortex interactions and periodic extinction-reignition processes, giving rise to large-scale asymmetric oscillations of the entire reaction zone. By contrast, the flame surface dynamics at an intermediate frequency of ~600 Hz exhibit prominent symmetric oscillations accompanied by merging and pinch-off of the constituent flames. Unexpectedly, high-frequency instabilities at approximately 1720 Hz (screech tones) are not influenced by such structurally complex flame dynamics, but by exceptionally simple, seemingly linear, flame surface motion without sudden flame area annihilation events like those observed for lower frequency cases. Despite the extremely low level of heat release rate fluctuations, on the order of less than 1%, the clustered premixed hydrogen flames are capable of producing disproportionately large pressure perturbations in excess of 12 kPa, originating from the synchronous phase dynamics of acoustic pressure and clustered flames’ heat release rate oscillations. These findings provide new insight into the driving mechanisms underlying high-frequency combustion dynamics of densely arranged pure hydrogen-air flames.

We report the first femtosecond time-resolved photoelectron spectroscopy study of 2-, 3- and 4-nitrobenzaldehyde (NBA) and nitrobenzene (NBE) in the gas phase upon excitation at 200 nm. In 3- and 4-NBA, the dynamics follow fast intersystem crossing within 1–2 picoseconds. In 2-NBA and NBE, the dynamics are faster ( ∼ 0.5 ps). 2-NBA undergoes hydrogen transfer similar to solution phase dynamics. NBE either releases NO 2 in the excited state or converts internally back to the ground state. We discuss why these channels are suppressed in the other nitrobenzaldehydes.

We study the current-voltage characteristics and phase dynamics of intrinsic Josephson junctions shunted by inductive and capacitive circuit elements. Here we investigate double and triple resonances that leads to charging of the superconducting layers in shunted stacks of junctions. We study numerically the dynamical response of the system to sweeping dc-bias currents, such as would typically be used in experiments. Our simulations reveal a series of features in the current-voltage characteristic of the system. In particular, we show that for larger numbers of junctions ( N ⪆ 15 ) the shunting causes charging to occur even along the outermost branch of the current-voltage characteristic. This charging on the outermost branch is associated with travelling wave solutions that become more stable than fully synchronous solutions in the shunted stacks with larger numbers of junctions. We observe a transformation of the travelling wave solution into a standing wave solution associated with a longitudinal plasma wave.

The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations.

Large-Eddy Simulations (LES) of an evaporating two-phase flow in an experimental burner are investigated. Two different numerical approaches for the simulation of the dispersed phase are coupled to the same gaseous solver: a mesoscopic Eulerian method and a Lagrangian particle tracking technique. The spray is represented by a single droplet size owing to the locally monodisperse formulation of the employed mesoscopic Eulerian approach. Both approaches use the same drag and evaporation models. They do not take into account the atomization process and a simplified injection model is applied instead. The presented methodology, referred as FIM-UR (Fuel Injection Method by Upstream Reconstruction) defines injection profiles for the monodisperse spray produced by a pressure-swirl atomizer. It is designed so as to ensure similar spray characteristics for both approaches and allows for a direct comparison between them. After a validation of the purely gaseous flow in the burner, liquid-phase dynamics and droplet dispersion are qualitatively and quantitatively evaluated for the Eulerian and Lagrangian simulations. Results obtained for both approaches are in very good agreement and compare reasonably with experiments, indicating that simplified injection methods are appropriate for the simulation of realistic combustor geometries.

The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes—termed anomalous behaviour—has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors.

Recently, there has been a great effort to extract the phase of chaotic attractors and complex oscillators. As a consequence many phases have been introduced, as example the standard phase θ based on the rotation of the vector position, and the phase φ based on the rotation of the tangent vector. Despite of the large interest in the phase dynamics of coupled oscillators there is still a lack of approaches that analyze whether these phase are equivalent and on what conditions these phases work. In this work, we show that the phase φ generalizes the standard phase θ , and it is equal to the length of the Gauss map, the generator of the curvature in differential geometry. Furthermore, we demonstrate, for a broad class of attractors, that the phase synchronization phenomenon between two coherent chaotic oscillators is invariant under the phase definition. Moreover, we discuss to which classes of oscillators the defined phases can be used to calculate quantities as the average frequency and the average period of oscillators. Finally, we generalize the phase φ which allows its use also to homoclinic attractors.

We present in this paper the development of a class of time-stepping algorithms for nonlinear elastodynamics that exhibits the controllable numerical dissipation in the high-frequency range required for the robust solution of the resulting numerically stiff systems. To motivate and illustrate better the developments in this general case, we present first the formulation and analysis of these methods for two simple model problems. Namely, we consider a nonlinear elastic spring/mass system and a simplified model of thin elastic beams. As it is discussed in detail in this paper, the conservation by the numerical algorithm of the momenta and corresponding relative equilibria of these characteristic Hamiltonian systems with symmetry is of the main importance. These conservation properties lead for a fixed and finite time step to a correct qualitative picture of the phase space where the discrete dynamics takes place, even in the presence of the desired and controlled numerical dissipation of the energy. This situation is contrasted with traditional “dissipative” numerical schemes, which are shown through rigorous analyses to not only lose their dissipative character in the general nonlinear range, but also the aforementioned conservation properties, thus leading to a qualitatively distorted approximation of the phase dynamics. The key for a successful algorithm in this context is the incorporation of the numerical dissipation in the internal modes of the motion while not affecting the group motions of the systems. The algorithms presented in this work accomplish these goals. The focus in this first part is given to first-order methods. Representative numerical simulations, ranging from applications in nonlinear structural dynamics to nonlinear continuum three-dimensional elastodynamics, are presented in the context of the finite element method to illustrate these ideas and results.

Biological communities are affected by perturbations that frequently occur in a more-or-less periodic fashion. In this communication we use the circle map to summarize the dynamics of one such community – the periodically forced Lotka–Volterra predator–prey system. As might be expected, we show that the latter system generates a classic devil's staircase and Arnold tongues, similar to that found from a qualitative analysis of the circle map. The circle map has other subtle features that make it useful for explaining the two qualitatively distinct forms of chaos recently noted in numerical studies of the forced Lotka–Volterra system. In the regions of overlapping tongues, coexisting attractors may be found in the Lotka–Volterra system, including at least one example of three alternative attractors, the separatrices of which are fractal and, in one specific case, Wada. The analysis is extended to a periodically forced tritrophic foodweb model that is chaotic. Interestingly, mode-locking Arnold tongue structures are observed in the model’s phase dynamics even though the foodweb equations are chaotic.

The mechanisms of the pulsed laser-induced ablation of strongly absorbing liquids and generation of acoustic transients are studied in the present work. Aqueous solutions of K CrO and pure water are irradiated by a KrF excimer laser l s 248 24 . . nm, FWHMs 24 ns and a CO laser l s 10.6 mm, variable pulse duration , respectively. The ablation process, including 2 the vapor cavity formation and the acoustic wave propagation, is visualized by laser flash photography. The measurement of acoustic transients is performed by a piezoelectric pressure transducer. Simultaneous detection of acoustic wave and optical transmission is also carried out to reveal the vapor-phase dynamics. The mechanisms of liquid ablation and acoustic pulse generation are examined on the basis of the thermoelastic behavior of the liquid medium and the evaporation dynamics. q 1998 Elsevier Science B.V.

A newly developed frequency and time resolved coherent anti-Stokes Raman scattering (CARS) technique is used to study properties of the A1g ring breathing mode of benzene in a dilution series of liquid mixtures with n-hexane. Recent advances in the interferometric use of incoherent light in CARS measurements (I(2)CARS) provide excellent precision in the recovered dephasing rate constants, vibrational frequencies, and the ratios of the resonant to non-resonant contributions to the signal. Using this technique we observe a more than two-fold decrease in the dephasing rate constant of the vibration, accompanied by a 0.54 cm−1 increase in the vibrational frequency in the limit of infinite dilution of benzene in n-hexane. These changes in the vibrational spectrum are discussed in terms of the condensed phase dynamics that are responsible. It is also seen how the non-resonant contributions to the signal manifest themselves quantitatively in these frequency and time resolved I(2)CARS measurements.

The phase and amplitude dynamics of a single-mode laser showing type-III intermittent pulsing are investigated experimentally. It is found that the subharmonic content of the intensity dynamics results from an asymmetrisation of the field attractor. Through a proper choice of the frequency reference for the field, it is found there is a clear correspondence between intensity- and phase dynamics.

Discrete variable representations (DVRs), constructed numerically from eigenstates of the one-dimensional adiabatic potential, provide the optimal quadrature for evaluating quasi-adiabatic propagator path integrals (QUAPI) for a system coupled to a harmonic bath. Calculations of partition functions and reaction rates for a multiple-minimum potential in a dissipative environment illustrate the convergence characteristics of this approach. The small number of quadrature points required, along with the rapid convergence of QUAPI methods, results in a powerful numerical scheme, complementary to Monte Carlo methods, for performing condensed phase dynamics calculations over the entire temperature range of interest in chemical physics.

In liquid-phase isomerization reactions, local departures from Maxwellian distributions appear to occur in different zones of the reaction coordinate chosen as dihedral angle connecting cis and trans forms. These deviations become appreciable for light masses and high barriers. The results partially reflect the fact that the reaction coordinate derived from isolated-molecule considerations is a poor representation of the solution-phase dynamics.