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In this paper we extendthe results of Frankel andKiemel ( SIAM J. Appl. Math ,5 3 (1993), pp. 1436-1446) to a network of slowly coupledoscillators. First, we use Malkin's theorem to derive a canonical phase model that describes synchronization properties of a slowly coupled network. Then, we illustrate the result using slowly coupledoscillators (1) near And ronov-Hopf bifurcations, (2) near saddle-node on invariant circle bifurcations, and (3) near relaxation oscillations. We compare andcontrast synchronization properties of slowly andweakly coupledoscillators.

The ultrafast optically-heterodyne-detected optical Kerr effect (OHD-OKE) is established as a relatively simple tool for recording the ultrafast dynamics of liquids with high temporal resolution and excellent signal-to-noise ratios. The principles and practice of the OHD-OKE method are outlined. Its application in recording the dynamics of several molecular liquids is described. The data are discussed in terms of the underlying microscopic molecular motions. Orientational motion--both librational and diffusive--is responsible for a significant fraction of the dynamics. Other potential contributions are discussed, but these are less readily assigned. The application of OHD-OKE measurements in interpreting ultrafast studies of the optical dynamics of solutions is discussed. Finally the extension of OHD-OKE methods to record the dynamics of more complex, heterogeneous, media is described.

Manganese oxides are often highly reactive and easily reduced, both abiotically, by a variety of inorganic chemical species, and biologically during anaerobic respiration by microbes. To evaluate the reaction mechanisms of these different reduction routes and their potential lasting products, we measured the sequence progression of microbial manganese(IV) oxide reduction mediated by chemical species (sulfide and ferrous iron) and the common metal-reducing microbe Shewanella oneidensis MR-1 under several endmember conditions, using synchrotron X-ray spectroscopic measurements complemented by X-ray diffraction and Raman spectroscopy on precipitates collected throughout the reaction. Crystalline or potentially long-lived phases produced in these experiments included manganese(II)-phosphate, manganese(II)-carbonate, and manganese(III)-oxyhydroxides. Major controls on the formation of these discrete phases were alkalinity production and solution conditions such as inorganic carbon and phosphate availability. The formation of a long-lived Mn(III) oxide appears to depend on aqueous Mn(2+) production and the relative proportion of electron donors and electron acceptors in the system. These real-time measurements identify mineralogical products during Mn(IV) oxide reduction, contribute to understanding the mechanism of various Mn(IV) oxide reduction pathways, and assist in interpreting the processes occurring actively in manganese-rich environments and recorded in the geologic record of manganese-rich strata.

Previous studies of the phase properties of optical linear amplifiers and attenuators have been restricted to situations where the effect on the phase of single-mode light is found to be diffusive. In this paper we give an analysis of phase-sensitive linear amplification and attenuation in the weak-field regime that clearly reveals a non-diffusive effect on the phase. Indeed we show that a weak field which has initially a uniform phase probability density can inherit non-random phase properties from both phase-sensitive attenuators and amplifiers. In contrast, we find that phase-insensitive amplifiers and attenuators have merely a diffusive effect on the phase of the light.

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.

Explosive volcanic eruptions are studied using a two-phase model of polydisperse suspensions of solid particles in gas. Eruption velocities depend on choking conditions in the volcanic conduit, which depend on acoustic wave propagation that is, in turn, influenced by the particle size distribution in the two-phase mixture. The acoustic wave spectrum is divided into three regions of superfast short waves moving at the pure gas sound speed, purely attenuated domain at intermediate wavelengths, and slower long waves for a dusty pseudogas. The addition of solid phases with differing particle sizes qualitatively preserves the features of two-phase acoustic wave dispersion, although it narrows the regions of short-fast and intermediate-blocked waves. Choking conditions, however, strongly depend on the number and size distribution of solid phases. Changes in particle sizes lead to variations in the choking conditions, which determine the eruption velocities and the resulting height of the erupting column. Smaller particles always exit the choking point faster than big particles, as expected. Even though particle-particle interaction is neglected, the particle distributions influence each other by momentum exchange through the gas. Therefore, the structure of the dispersion relation as well as the eruption or choking velocities and subsequent column height and particle deposition bear information on how eruption dynamics are controlled by size distribution and relative volume fractions of small and big particles. We suggest that unimodal distributions, with one dominant small particle size, favor development of vertical plinian eruptions, while bimodal distributions, with a comparable mean size, lead to pyroclastic lateral flows.

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.

The effect of pumping methods on the gain and phase dynamics of quantum-dot vertical cavity semiconductor optical amplifier is investigated. The gain and phase recovery time is considered at the ground state transition wavelength. By including the effect of the excited state and wetting layer on the refractive index change, it is shown that under electrical pumping, the better gain dynamics is achieved compared to the optical pumping scheme. However, the phase recovery time can be accelerated by optical pumping. These behaviors result from the different mechanisms of population inversion in these two pumping methods.

SummaryObjectives Female obesity is a state of relative hypogonadotrophic hypogonadism. The aim of this study is to examine gonadotrophin secretion and response to gonadotrophin-releasing hormone (GnRH) in the luteal phase of the menstrual cycle and to investigate the pharmacodynamics and pharmacokinetics of endogenous and exogenous luteinizing hormone (LH) in obese women. Design Participants underwent a luteal phase frequent blood sampling study. Endogenous LH pulsatility was observed, gonadotrophin-releasing hormone (GnRH) was given in two weight-based doses, and GnRH antagonist was administered followed by recombinant LH. Patients Regularly menstruating obese (n = 10) and normal weight (n = 10) women. Measurements Endogenous hypothalamic-pituitary function (as measured by LH pulsatility), pituitary sensitivity (GnRH-induced LH secretion), pharmacodynamics of endogenous LH and pharmacokinetics of exogenous LH were compared between the obese and normal weight groups. Results There were no statistically significant differences in endogenous LH pulsatility or pituitary responses to two weight-based doses of GnRH between the obese and normal weight women. There were no differences in the pharmacodynamics of endogenous LH or the pharmacokinetics of exogenous LH between the groups. FSH dynamics did not differ between the groups throughout the study. Conclusions The relative hypogonadotrophic hypogonadism of obesity cannot be explained by differences in LH and FSH luteal phase dynamics or differences in endogenous LH pharmacodynamics or exogenous LH pharmacokinetics.

Spore photoproduct lyase (SPL) catalyzes the repair of the UV lesion spore photoproduct (SP) in a reaction dependent on S-adenosyl-l-methionine (SAM). We have utilized H/D exchange to show that in the presence of SAM, a significant reduction in H/D exchange is observed upon binding SPTpT or undamaged oligonucleotide, indicating a shift of 20 or 10 amide protons, respectively, from a rapidly-exchangable state to a fully-protected conformation. In the absence of SAM, neither the oligonucleotide nor the SPTpT produce a significant perturbation in H/D exchange, indicating SAM is a requisite binding partner. Performing the same experiments in aerobic conditions reduced the magnitude of ligand-induced structural changes, consistent with the importance of the oxygen-sensitive iron–sulfur cluster for SAM and substrate binding.

The 8–15 Hz thalamocortical oscillations known as sleep spindles are a universal feature of mammalian non-REM sleep, during which they are presumed to shape activity-dependent plasticity in neocortical networks. The cortex is hypothesized to contribute to initiation and termination of spindles, but the mechanisms by which it implements these roles are unknown. We used dual-site local field potential and multiple single-unit recordings in the thalamic reticular nucleus (TRN) and medial prefrontal cortex (mPFC) of freely behaving rats at rest to investigate thalamocortical network dynamics during natural sleep spindles. During each spindle epoch, oscillatory activity in mPFC and TRN increased in frequency from onset to offset, accompanied by a consistent phase precession of TRN spike times relative to the cortical oscillation. In mPFC, the firing probability of putative pyramidal cells was highest at spindle initiation and termination times. We thus identified “early” and “late” cell subpopulations and found that they had distinct properties: early cells generally fired in synchrony with TRN spikes, whereas late cells fired in antiphase to TRN activity and also had higher firing rates than early cells. The accelerating and highly structured temporal pattern of thalamocortical network activity over the course of spindles therefore reflects the engagement of distinct subnetworks at specific times across spindle epochs. We propose that early cortical cells serve a synchronizing role in the initiation and propagation of spindle activity, whereas the subsequent recruitment of late cells actively antagonizes the thalamic spindle generator by providing asynchronous feedback.

Activation (in the following referred to as firing) of replication origins is a continuous and irreversible process regulated by availability of DNA replication molecules and cyclin-dependent kinase activities, which are often altered in human cancers. The temporal, progressive origin firing throughout S phase appears as a characteristic replication profile, and computational models have been developed to describe this process. Although evidence from yeast to human indicates that a range of replication fork rates is observed experimentally in order to complete a timely S phase, those models incorporate velocities that are uniform across the genome. Taking advantage of the availability of replication profiles, chromosomal position and replication timing, here we investigated how fork rate may affect origin firing in budding yeast. Our analysis suggested that patterns of origin firing can be observed from a modulation of the fork rate that strongly correlates with origin density. Replication profiles of chromosomes with a low origin density were fitted with a variable fork rate, whereas for the ones with a high origin density a constant fork rate was appropriate. This indeed supports the previously reported correlation between inter-origin distance and fork rate changes. Intriguingly, the calculated correlation between fork rate and timing of origin firing allowed the estimation of firing efficiencies for the replication origins. This approach correctly retrieved origin efficiencies previously determined for chromosome VI and provided testable prediction for other chromosomal origins. Our results gain deeper insights into the temporal coordination of genome duplication, indicating that control of the replication fork rate is required for the timely origin firing during S phase.

The ultrafast dynamics of gain and phase in bulk semiconductor optical amplifiers are numerically investigated over a broad band of about 200 nm based on the semiclassical method of density matrix equations. The gain dynamics and phase dynamics are compared in four different bands for 200 fs Gaussian pump pulse. It is predicted that the recovery time of phase may be longer or shorter than that of gain depending on probe wavelengths. Furthermore, phase recovery overshoot may appear at wavelengths shorter than the pump wavelength. These interesting features result from the competition between spectral-hole burning and carrier heating over the whole band.

We have studied a time response of electromagnetically induced transparency (EIT) in a rubidium vapor to a rapid variation of optical phase. We have observed a very fast growth of the absorption when the phase of the optical field has been abruptly changed, followed by a slow return to the level of steady-state absorption. The recovery time decreases with increasing optical power. A simple theoretical analysis shows that under our experimental conditions the low power limit of the recovery time is determined by the ground relaxation time. In our case it is defined by a time-of-flight of rubidium atoms through laser beam. The obtained value of the ground state relaxation time is in a good agreement with result of direct measurements by ‘relaxation in the dark’ method. Our technique based on phase dynamics in EIT can be used for investigation of the ground state relaxation and the fast control of EIT.

Light is the primary signal that calibrates circadian neural circuits and thus coordinates daily physiological and behavioral rhythms with solar entrainment cues. Drosophila and mammalian circadian circuits consist of diverse populations of cellular oscillators that exhibit a wide range of dynamic light responses, periods, phases, and degrees of synchrony. How heterogeneous circadian circuits can generate robust physiological rhythms while remaining flexible enough to respond to synchronizing stimuli has long remained enigmatic. Cryptochrome is a short-wavelength photoreceptor that is endogenously expressed in approximately half of Drosophila circadian neurons. In a previous study, physiological light response was measured using real-time bioluminescence recordings in Drosophila whole-brain explants, which remain intrinsically light-sensitive. Here we apply analysis of real-time bioluminescence experimental data to show detailed dynamic ensemble representations of whole circadian circuit light entrainment at single neuron resolution. Organotypic whole-brain explants were either maintained in constant darkness (DD) for 6 days or exposed to a phase-advancing light pulse on the second day. We find that stronger circadian oscillators support robust overall circuit rhythmicity in DD, whereas weaker oscillators can be pushed toward transient desynchrony and damped amplitude to facilitate a new state of phase-shifted network synchrony. Additionally, we use mathematical modeling to examine how a network composed of distinct oscillator types can give rise to complex dynamic signatures in DD conditions and in response to simulated light pulses. Simulations suggest that complementary coupling mechanisms and a combination of strong and weak oscillators may enable a robust yet flexible circadian network that promotes both synchrony and entrainment. A more complete understanding of how the properties of oscillators and their signaling mechanisms facilitate their distinct roles in light entrainment may allow us to direct and augment the circadian system to speed recovery from jet lag, shift work, and seasonal affective disorder.

It has long been considered that the Trans-Mexican Volcanic Belt (TMVB) is related to subduction along the Middle America trench. Within this view, it is expected that the tectonic dynamics of the Cocos plate can be reflected, to some extent, in the Popocatepetl's volcanic activity This work uses detrended fluctuation analysis, a method borrowed from statistical mechanics, to quantify the fractality and autocorrelations in the exhalation sequence of the Popocatepetl. It is found that the autocorrelations exhibit cyclic, non-periodic, dynamics with dominant periods of the order of 0.85 to 1.25 years. Interestingly, it is shown that the occurrence of slow-slip events in Southern (Guerrero and Oaxaca) Mexico coincides with peaks of the autocorrelation cycle of the exhalation sequence. The result suggests the use of the volcano exhalation sequence as a proxy of aseismic events in the Cocos-North American plate boundary. That is, by monitoring the autocorrelation dynamics of the exhalation sequence in the Popocatepetl, one could be able to suspect the occurrence of a slow-slip event in Southern Mexico.

The phase dynamics that occur in bulk InGaAsP-InP semiconductor optical amplifiers (SOAs) in response to picosecond pulse excitations at 10 and 40 GHz are studied experimentally and numerically for various amplifier lengths. The time dependencies of the phase changes and of the absolute gain of the amplifier are measured simultaneously. The total phase shifts induced by 1.5-ps pulses at 10 GHz are higher than /spl pi/ in SOAs with active region lengths between 0.5 and 2 mm and exceed 2/spl pi/ in a 1.5-mm-long amplifier. Phase shifts above /spl pi/ are measured at 40 GHz in 1.5- and 2-mm-long SOAs. The dependence of the total phase shift on the amplifier bias current and length and on pump pulse energy is investigated. Numerical simulations based on a comprehensive time-domain SOA model allow us to confirm the experimental results for a wide range of amplifier parameters. In particular, SOAs with lengths up to 5 mm have been modeled, and the calculations suggest that the maximum phase shifts occur in amplifiers of approximately 2-mm length. The phase dynamics measurements are illustrated at the example of an optical time division multiplexing add-drop multiplexer, based on a SLALOM switch, gated by 10- or 40-GHz control pulses. We find that simultaneous good dropping and clearing is possible if the length and the operating conditions of the SOA in the switch are chosen such as to induce a full /spl pi/ phase shift.

Volcanic eruptions involve high-speed turbulent flows of gas and magma mixtures in which peak gas velocities often approach 600 m s−1. Such speeds are well in excess of the slow mixture sound speeds of approximately 150 m s−1 predicted by pseudo-gas theory, in which the gas and magma phases are assumed to be locked to each other; eruptions thus appear to be highly super-sonic. Indeed, flow in the volcanic conduit will choke when it reaches the sound speed and to attain supersonic velocities one must invoke special conduit nozzle shapes. However, the pseudo-gas approximation is a long-wavelength assumption, while choking and acoustic shocks are a short-wavelength effect; thus, the approximation is likely inapplicable for the choking phenomenon. To allow for non-pseudo-gas effects, such as phase separation, in the short-wavelength limit requires a more complete treatment of two-phase eruptions. We therefore develop and explore a model for two-phase, high Reynolds number flow of a compacting suspension of magma particles in a compressible gas. Flow properties, such as mixture density, are controlled both by gas content as well as gas compressibility, both of which vary according to different processes of compaction and compression, respectively. The two phases of the mixture separate because of their different densities, and the interaction forces (turbulent drag and inertial exchange) can be complex. The model is used to examine acoustic-porosity wave propagation and the development of shocks or choking structures in a volcanic conduit. Sound waves in separable mixtures are highly dispersive with fast waves propagating at the pure gas sound speed at small wavelengths, slow waves travelling at the pseudo-gas speed at long wavelengths, and pure attenuation and sound blocking at intermediate wavelengths. As shock fronts in gas density develop they become increasingly short wavelength features and thus will only cause choking if the maximum speed in the flow reaches the pure gas sound speed. Non-linear, finite-amplitude steady-state models of eruptions in a volcanic conduit show that compaction occurs over the magma particle gravitational deceleration height, and either suppresses gas expansion for fast eruptions, or isopycnally collapses the gas volume near the base of the erupting column for slow eruptions. Once compaction ceases, the gas expands toward a shock structure or choking point, which is coincident with a rapid gas acceleration and a high-speed vent eruption. Increased turbulent drag between the gas and particles suppresses compaction effects but greatly sharpens the shock front at the choking point. Although the standard pseudo-gas models predict such choking to occur at low velocities, the full two-phase theory always has choking occur when the gas reaches the pure gas sound speed, in keeping with the sound-speed dispersion analysis. Therefore, the full two-phase theory predicts choking to occur at the pure gas sound speed, which (for water vapour at the relevant high temperatures) is about 700 m s−1. Eruption velocities of 600 m s−1 are therefore fully consistent with the limit imposed by this choking condition, and no special conditions to obtain supersonic eruptions, such as nozzled conduit geometries, are necessary.

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.

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference Δφ between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02–0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index γ = 〈sinΔφ〉2 + 〈cosΔφ〉2that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index γ has two distinct peaks, one at 0.11 Hz [γ = 0.59 ± 0.09] and another at 0.33 Hz (γ = 0.55 ± 0.17). In the very low-frequency range (0.02–0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 ± 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1–0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.

SUMMARY Aim A major question with regard to the ecology of temperate rain forests in south-central Chile is how pioneer and shade-tolerant tree species coexist in old- growth forests. We explored the correspondence between tree regeneration dynamics and life-history traits to explain the coexistence of these two functional types in stands apparently representing a non-equilibrium mixture. Location This study was conducted in northern ChiloeIsland, Chile (41.6� S, 73.9� W) in a temperate coastal rain forest with no evidence of stand disruption by human impact. Methods We assessed stand structure by sampling all stems within two 50 · 20 m and four 5 · 100 m plots. A 600-m long transect, with 20 uniformly spaced sampling points, was used to quantify seedling and sapling densities, obtain increment cores, and randomly select 10 tree-fall gaps. We used tree-ring analysis to assess establishment periods and to relate the influences of disturbances to the regeneration dynamics of the main canopy species. Results Canopy emergent tree species were the long-lived pioneer Eucryphia cordifolia and the shade-tolerant Aextoxicon punctatum. Shade-tolerant species such as Laureliopsis philippiana and several species of Myrtaceae occupied the main canopy. The stem diameter distribution for E. cordifolia was distinctly unimodal, while for A. punctatum it was multi-modal, with all age classes represented. Myrtaceae accounted for most of the small trees. Most tree seedlings and saplings occurred beneath canopy gaps. Based on tree-ring counts, the largest individuals of A. punctatum and E. cordifolia had minimum ages estimated to be > 350 years and > 286 years, respectively. Shade-tolerant Myrtaceae species and L. philippiana had shorter life spans (< 200 years). Most growth releases, regardless of tree species, were moderate and have occurred continuously since 1750. Main conclusions We suggest that this coastal forest has remained largely free of stand-disrupting disturbances for at least 450 years, without substantial changes in canopy composition. Release patterns are consistent with this hypothesis and suggest that the disturbance regime is dominated by individual tree-fall gaps, with sporadic multiple tree falls. Long life spans, maximum height and differences in shade tolerance provide a basis for understanding the long- term coexistence of pioneer and shade-tolerant tree species in this coastal, old- growth rain forest, despite the rarity of major disturbances.

Femtosecond electron diffraction (FED) is a new technique within the still-developing field of ultrafast diffraction. This paper presents an outline of the basic features of FED, including a brief history of its development in terms of the technical challenges of working with femtosecond electron pulses and the ultrathin samples required. Application of FED to melting in aluminium and gold excited by intense femtosecond laser pulses will be discussed. The interplay of experiment and theory will be explored, particularly with respect to molecular dynamics simulations of the same processes we experimentally observe. Homogeneous nucleation emerges as an important melting mechanism under the strongly-driving conditions that we employ. Future applications of FED will be discussed in terms of progress to date.

The plastic crystal phase forming N-methyl-N-propylpyrrolidinium tetrafluoroborate organic salt (P13BF4) was combined with 2, 5 and 10 wt.% poly(vinyl pyrrolidone) (PVP). The ternary 2 wt.% PVP/2 wt.% LiBF4/P13BF4 was also investigated. Thermal analysis, conductivity, optical thermomicroscopy, and Nuclear Magnetic Resonance (11B, 19F, 1H, 7Li) were used to probe the fundamental transport processes. Both the onset of phase I and the final melting temperature were reduced with increasing additions of PVP. Conductivity in phase I was 2.6 × 10− 4 S cm− 1 5.2 × 10− 4 S cm− 1 1.1 × 10− 4 S cm− 1 and 3.9 × 10− 5 S cm− 1 for 0, 2, 5 and 10 wt.%PVP/P13BF4, respectively. Doping with 2 wt.% LiBF4 increased the conductivity by up to an order of magnitude in phase II. Further additions of 2 wt.% PVP slightly reduced the conductivity, although it remained higher than for pure P13BF4.

We describe the phase dynamics of a timing extraction system based on direct optical injection locking of a multifrequency oscillator employing an InGaAs/InP heterojunction bipolar phototransistor. We present a general model for the locking range, jitter transfer function, and output phase noise. The model is confirmed by a series of locking experiments. We consider first fundamental timing extraction, that is, a 10-GHz oscillator extracting the clock from a 10-Gbit/s data stream. Second, we address superharmonic timing extraction where 40-Gbit/s data lock the fourth harmonic of the 10-GHz oscillator. In the superharmonic timing extraction case, a clock is extracted at 40 GHz as well as its subharmonics at 10, 20, and 30 GHz.

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker–driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.

We investigate the long-time dynamics of two-component dilute gas Bose–Einstein condensates with relatively different two-body interactions and Josephson couplings between the two components. Although in certain parameter regimes the quantum state of the system is known to evolve into macroscopic superposition, i.e., Schrodinger cat state, of two states with relative atom number differences between the two components, the Schrodinger cat state is also found to repeat the collapse and revival behavior in the long-time region. The dynamical behavior of the Pegg–Barnett phase difference between the two components is shown to be closely connected with the dynamics of the relative atom number difference for different parameters. The variation in the relative magnitude between the Josephson coupling and intra- and inter-component two-body interaction difference turns out to significantly change not only the size of the Schrodinger cat state but also its collapse–revival period, i.e., the lifetime of the Schrodinger cat state.