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Asymptotic AFM amplitude-phase dynamics is a powerful modeling tool for the development of AFM control systems and applications. We explain the model and demonstrate simple practical examples that can be easily programmed and analyzed using simulation tools such as Control and Simulation Loop (National Instruments) or Simulink (Mathworks). We first introduce asymptotic AFM models, then formulate their mathematical properties relevant to AFM, and provide examples of simulation for Hertz and Lennard-Jones tip-sample interaction forces. Material of this paper can be used to study and practice AFM dynamics in simulation, as well as for design of AFM model-based control modes and applications.

The advent of high flux femtosecond electron sources provides a new window for observing atomic motions during structural transitions. Studies of ultrafast melting of metals reveal microscopic mechanisms and the full potential of the approach.

SUMMARY Since thr recent experimental observation of Dose-Einstein condensation in dilutc atomic gases, much interest has been raised about the coherence properties of the condensates Considerable attention has ben devoted to the matter uf the relativr phasp bctween two condensates: hm this phase manifests itself in an interference experiment [I], haw it cm be estnbliihed by measurement, and how it evolves in prespnee of atomic interactionsl2). Rerrritl) it was predicted that the relative phase betwm two condensates should display collopscs and revivals in time due to atomir inierxtioiis. For condcnsates with a rclatwely small number of atoms. of the ordcr of some hundreds, the revirds of thr 7ihar;e cm occur on the 10.'~ time Scale and niight in principle be observed. Howerer up to non a theoretical analysis of irifluence of partrcie lams 011 Lhr pha? dpnmirr B~F missing. Such loss proccs~s. due for example to collisions of rondmsed atonic With the buckgiuund gas or to three-bod! colliaionr. arp nnaruidiiblu in a real experiment and might spoil the cnherenrr prevmring the ubrurvtion of the revivals. IVe dewlop B model to dearrihe thP phase dynamici of the condensates m presence r the asaurnption that the fraction of lost parLicles in II, wc obtain analytical results for thP time depcrldcnce abservables for two nm overlapping and mutually non sueb as tlir nwm beating intensity of the condensates .epresented by the quantity (0'6) (a.herp o (a') and b (6') are the creation iannihilat,ion) operator^ of a particle in the condmsatr A ui B respectively). and the relacive phase probability distrihul ion. We find that. besides the collapses and revirals due to thr Hakiltonian evolution, the rrlvtive phase dependent observable (0'6) expericncps im esponmttal deea)- in time with a rate X given hr the mean total tiumber of luss ewnts per unit oft derohereuce betaren tw condensatcs, is therefore apprommatel inverse lifetiiiiu of a particle in the condensates (whew :T is the total number of atomr). Neverthclcs \ye show that losses do nnt prevent the ObsQrvatiOn of the rrlatise phase rsyivals in condensates with small number of atoms. Finally; se giw a suggestive interimtation of the dramatic cffect of the losses on the rflatii-e phase based on the h1oel.e Carlo wa\p function approach the condensates relative phase in a single !dome Carlo reaiization is shifted br a random amount on tbe order of 7 cosarquently to each mch loss event occurring in the condensates. A few loss prorcsses in a given time interd are then sufficient to smear out the relative phase completely when the average over the stochastic realizacion is taker

Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

Summary form only given. Nonlinear delay dynamical systems have found several fundamental and applied issues in Optics, since delays from time of flight of the light becomes easily important, even with a few cm of fibers, compared to fast or even ultra-fast photonic response times. Fiber pigtailed modern Telecom devices can thus provide easy system design strategies to build well-controlled high complexity nonlinear delay dynamics. Recently in that context, electro-optic phase modulation, combined with an imbalanced Mach-Zehnder DPSK demodulator providing a temporally nonlocal nonlinear phase-to-intensity conversion, together with a delayed optoelectronic feedback loop, was proposed as an efficient optical chaos generator for demonstrating 10 Gb/s optical chaos communications.

In this paper, a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model), is proposed for the simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. Bulk regions of the two phases are governed by a non-ideal equation of state (for example, the van der Waals equation of state), whereas an artificial near-critical equation of state is applied in the interfacial region. The interfacial equation of state is described by a double well density dependence of the free energy. The continuity of chemical potential is enforced at the interface boundaries. Using the AILB model, large density and viscosity ratios of the two phases can be simulated. The model is able to quantitatively capture the coexistence curve for the van der Waals equation of state for different temperatures. Moreover, spatially varying viscosities can be simulated by choosing the relaxation time as a function of local density.

Ultrafast spectroscopy of quantum dot semiconductor optical amplifiers (SOAs) provides valuable information about the potential of these devices for emerging applications such as multi-wavelength regeneration while giving insight on their unique carrier dynamics. Pump-probe spectroscopy was used to analyse the carrier dynamics in InAs/GaAs quantum dot amplifiers. We have developed a ldquotwo-colourrdquo experimental configuration that allows us to pump and probe different parts of the amplified spontaneous emission spectrum and develop a detailed picture of the relevant carrier processes in both absorption and gain regimes of QD-SOAs. The study has revealed that hole recovery and intradot electron relaxation occur on a picosecond timescale, while the electron capture time is on the order of 10 ps. The relaxation of the wetting layer carrier density was shown to have a strong effect on the phase dynamics of both ground and excited state transients, while having a much weaker effect on the gain dynamics. Such behaviour is strongly encouraging for reduced pattern effect operation in high speed optical networks.

Optical chaos communications met intensive research efforts during the last 10 years [1,2], resulting in 2004 in a field experiment in the metropolitan optical network of Athens [3]. Current efforts are now concentrating on device oriented architectures, in order to improve reliability, efficiency, and security. Among the few competitive approaches developed in the literature, the electro-optic one showed first its strong potential in terms of bit rate and decoding quality [4]. However, it was suffering from a few drawbacks in terms of technological complexity, due to the intensity superposition condition required by the mixing between the binary intensity message and the chaotic optical intensity carrier.

Summary form only given. Experimental and theoretical studies of intensity and phase dynamics of spatially coupled lasers have produced interesting results. The investigation of these particular nonlinear oscillators in various well-controlled spatial arrangements gives closer insight into the relations between symmetry and dynamics. The experimental systems we consider consist of two or three coupled lasers in one semi-monolithic Nd:YVO/sub 4/ microchip resonator, generated by pump beams delivered through a 2D arrangement of single-mode optical fibers.

Already several years ago [3], it was suggested that a laser with optical injection can respond to external perturbations by emitting spikes if the perturbation overcomes a certain threshold, all the spikes being identical to each other, in complete analogy with the behaviour of the simple theta-model neuron [1]. The underlying explanation of this phenomenon lies in the isomorphism between a model of neuron [1] and that of an over-damped oscillator with periodic forcing (often called the Adler equation [2]). The control of these spikes was only achieved recently [5], while their observation goes back to [4]. Although there is an excellent agreement between these observations and the predictions of the reduction to pure phase dynamics of a laser model [3], it was soon noticed that whenever the pure phase dynamics reduction ceases to be valid, more complex dynamical phenomena can take place, leading to multipulse excitability [6]. This has led to the investigation of the behaviour of a semiconductor laser locked to an external forcing in response to external perturbations beyond the simple case of the Adler-like mode. We observe resonator features of the neuron-like system and multi-spike responses. Beyond improving the understanding of the neuron-like excitable dynamics of the laser with injected signal, our aim is to leverage the multipulse excitability and the resonator features of the optical neuron analogue for optical data processing and to provide possible insight about complex solitons interactions in forced oscillatory media [7, 8].

We used a method based on the modelling of phase dynamics to quantify the coupling strength between EEG channels. A distinction between the characteristics of coupling strength for the cases of limb movement and background activity is observed.

A phased-array two-dimensional CPLL array is introduced. The phase dynamics are analyzed and an approximate solution are obtained using the method of continuum phase. By detuning the free-running frequencies of edge elements, linear phase distribution can be achieved among the array. An experimental CPLL array circuit is also shown and tested, proceedings.

This paper provides stability analysis for phase shifting active combustion control system where modulation of the fuel flow is used to suppress thermo-acoustic instability. The analysis is based on Krylov-Bogolubov averaged model for the oscillations with the external periodic forcing. The amplitude dynamics and phase dynamics are described by nonlinear first order models. The control inputs are the amplitude and phase of forcing (fuel modulation). The analysis demonstrates that phase dynamics and amplitude dynamics are each unstable in the desired target regime. Practical stabilizing control approaches and their limitations in the presence of feedback delays are discussed and analyzed. The analysis in this paper is verified in detailed simulations and validated in experiments with a jet engine scale combustor rig.

In this paper, set of equations for the oscillator amplitude and phase dynamics are presented by describing the coupled series-resonant oscillator array in term of Z-parameters, and they are simplified for nearest-neighbor coupling topologies. For beam-scanning using, equations of phase dynamics are analyzed under the phase model; the free-running frequencies of oscillators are controlled for certain relations. The usefulness is illustrated through simulations.

The introduction of the unencrypted global positioning system (GPS) L2 civil (L2C) signal has the potential to improve measurements made with the L2 frequency, an important observable in GPS-based ionospheric research and monitoring. Recent work has shown significant differences between the legacy L2P(Y) and L2C-derived total electron content rate of change index (ROTI). This difference is observed between L2P(Y) and L2C-derived ROTI with certain receiver models and between zero-baseline receiver pairs. We discuss the likely cause for these differences: L1-aided tracking used to track both the L2P(Y) and L2C signals. We also present L2C data that are confirmed to be from tracking independent of L1. Using the ionospheric-free linear combination, we show that the independently tracked carrier phase dynamics are significantly more accurate than the L1-aided observables. This result is confirmed by comparing the behavior of the L2C and L2P(Y) carrier phase observables upon a sudden antenna rotation.

In this work, experimental study of chaotic synchronization of a semiconductor lasers is presented. An external optical feedback (OF) is used to reach the anti-phase chaotic synchronization among the orthogonal polarization modes of vertical cavity surface emitting laser (VCSEL). The high levels of (OF) achieve good anti-phase synchronization dynamic of the chaotic signal with zero time delay between the polarization dynamic of the VCSEL. For the (OF) levels of 101 μW and 150 μW we have observed good matching signal of the anti-phase dynamics among VCSEL's polarization modes. While low (OF) levels play less important role in this phenomenon. No synchronization among the orthogonal polarization signals obtained for the range of 1 μW to 53μW of (OF). Such property makes VCSELs attractive for applications; such as chaos based secure optical communications and random number generation.

Synchronization properties of model systems containing large numbers of phase oscillators have many potential biophysical and other applications. Biophysical examples include networks of pacemaker cells in the heart and suprachiasmatic nucleus of the brain. In physical systems the phase dynamics of high-Tc superconducting materials continue to attract attention, since systems of intrinsic Josephson junctions form natural arrays of coupled phase oscillators. As such, they have the potential to act as systems in which various exotic synchronization effects, such as the relatively recently discovered chimera states, may be naturally observed. In this study we make a detailed exploration of the wider parameter space containing regions of chaos synchronization in the CCJJ+DC model of intrinsic Josephson junctions. Extensive regions of phase synchronization - corresponding to the Shapiro steps with zero charge density in the S-layers - are found through numerical simulation. By computing the Lyapunov exponent spectra, we see that chaos synchronization occurs only within certain sub-regions that overlap with 'uncharged' steps in the IV-characteristics. Such chaos synchronization may be useful in applications requiring more powerful, high-frequency, chaotic signals.

Ionospheric scintillation is the name given to the disturbance caused by electron density irregularities along the propagation path of electromagnetic waves through the ionosphere. These non-nominal propagation conditions mainly cause carrier phase variations and amplitude fades. It is important to point out that both degradations are correlated, and thus deep amplitude fades and rapid phase variations (the so-called canonical fades) occur in a simultaneous and random manner. Regarding the carrier synchronization problem under harsh propagation conditions, such as high dynamics, multipath effects or ionospheric scintillation, canonical fades make the latter the most challenging scenario, which can be considered as a benchmark on the performance of robust carrier tracking techniques. This phenomenon particularly affects satellite-based positioning systems in the equatorial regions and at high latitudes. In this work, both amplitude and phase variations due to scintillation are first modeled using an autoregressive (AR) model, and then included into the system state-space formulation. Therefore, a Kalman filter (KF) based solution can be aware of both dynamics and scintillation phase evolutions. This arises as the natural solution to mitigate those undesired propagation effects. Moreover, in order to counteract the main drawbacks of standard KF-based tracking solutions, an extended KF (EKF) architecture is considered, tracking both the phase dynamics, scintillation phase and amplitude. This implies directly operating with the baseband received signal's complex samples, avoiding the use discriminators and thus its saturation and the loss of Gaussianity. Simulation results are provided to support the theoretical discussion and to show the performance improvements of such new approach.

The nonlinear dynamics of semiconductor optical amplifiers (SOAs) are investigated. We focus on the nonlinear gain, phase and chirp dynamics that can be used for high speed all-optical switching. Ultrafast component in the phase dynamics is observed. We explain this phenomenon by using a numerical model that includes the impact of sub-picosecond intra-band effects in the SOA. In addition, we also investigate the chirp properties, and analyze the influences of chirp dynamics upon the detuned-filtering-based optical switches that can realize more than 160 Gbit/s operating speed. The results are useful for SOA-based high speed all-optical switching in photonic networks.

In this paper we analyze the stability and two-phase dynamics of the equilibrium water distributions inside the porous media of a polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL), which is described with first and second-order parabolic partial differential equations (PDE). A Lyapunov function-based stability criterion is implemented for the liquid mass continuity PDE, while physics and math-based arguments are used to demonstrate a key range of liquid distribution that cannot attain equilibrium. The quantity of water within the fuel cell directly affects performance, efficiency, and durability. High membrane humidity is desirable for proton conductivity, yet excess liquid water in the anode has been experimentally shown to be a cause of output voltage degradation. We identify the unstable state(s) representing unbounded growth of liquid water and show that stabilization of channel water mass is sufficient for a stable liquid distribution.

A new method of beam scanning via coupled phase locked loops (PLLs) is presented. The steady-state of phase dynamics equation and phase noise of coupled PLLs are analyzed. By detuning the free-running frequency of the edge oscillators, linear phase distributions across the one-dimensional PLLs array can be achieved. This coupled PLLs phase array can be used for phase-shifterless beam scanning. A S-band one- dimensional experimental array is presented, giving a measured phase progression among the array.

We demonstrated recently both numerically and experimentally that two such signal pulses can form a stable bound state at a certain close spacing on the order of the pulse width, provided they are in antiphase. This bound state has been called a soliton molecule, and may allow denser packing of signals and thus an increase of the data-carrying capacity of fibers. As we set out to systematically characterize the range of existence and the stability properties of the soliton molecule, it became evident that the phase dynamics inside the pulse is responsible for the binding mechanism. We therefore adopted a FROG variant called VAMPIRE (very advanced method of phase and intensity retrieval of E-fields), in which the pulse to be measured is correlated with a reference pulse as in blind-FROG.

This paper presents the first experimental demonstration of optical orbital angular momentum exchange between different field polarizations and the quantification of azimuthal optical flow resulting from the nonlinear interaction. This investigation establishes the connections between inhomogeneously polarized beams and helical phase fronts, as well as the nonequilibrium phase dynamics that underlie multiple filamentation.

Van der Pol oscillator can be used to model microwave negative oscillator, and injection locked oscillator can be looked as forced Van der Pol oscillator. The article studies the amplitude and phase dynamics of the forced Van der Pol oscillator, and gets conditions under which injection locking phenomena can occur. Injection locked Van der Pol oscillator is also realized with a simple modern semiconductor circuit in the article. At last OrCAD PSpice is used to simulate the circuit and testify the conclusions got by theory analyzing.

Semiconductor lasers with time-delayed feedback display fluctuations that range from stochastic to deterministic and provide examples of complex, high-dimensional temporal dynamics. This study describes the measurement of Hurst exponents to characterize the scaling behavior of the phase dynamics for such systems. This work also discusses the evolution of patterns in liquid crystal light modulators with electronic feedback and study the response of these systems to drive signals that demonstrate the phenomenon of generalized synchronization for spatio-temporal systems.

Spatiotemporal phase dynamics of response of brain waves to periodic flicker stimuli are investigated to compare the response properties of the alpha waves with those of steady-state visually evoked potentials (SSVEPs). Under flicker stimuli the frequency of which is outside the range 8 - 13 Hz (outside the range of the alpha wave), the response of the brain wave, namely, the SSVEPs, constitutes the phase reversal between the frontal and occipital lobes as well as the spontaneous alpha wave for most of subjects. Under the flicker stimuli the frequency of which is in the range 8 - 13 Hz, the response of the brain wave, including the entrainment of the alpha wave as well as the SSVEPs, also shows the phase reversal. Spatial phase gradient of the SSVEPs is almost uniform from the frontal to occipital regions, which is also seen in the spontaneous alpha wave although the phase difference between the frontal and occipital lobes is varied complicatedly with time. These results suggest that the spatiotemporal dynamics of the SSVEPs and alpha wave are closely related to each other under the flicker stimuli. The underlying mechanism of the SSVEPs may be considered in the context of the entrainment of nonlinear oscillators.

We study a multimode semiconductor laser subject to a moderate optical feedback. The steady state is destabilized by either a simple Hopf bifurcation leading to in phase dynamics or by a degenerate Hopf bifurcation leading to antiphase dynamics. The degenerate bifurcation is also a source of multiple coexisting attractors. We show that a simple interpretation of the low frequency fluctuations in the multimode regime is provided by a chaotic itinerancy among the many coexisting unstable attractors produced by the degenerate Hopf bifurcation., info:eu-repo/semantics/published

The authors describe results from an experiment where the number of ripple periods in the slow wave structure of a backward wave oscillator (BWO) is increased. Both microwave power and frequency measurements are made for each shot. For a given cathode voltage and beam current, the microwave peak power and frequency are plotted as a function of BWO length. In previous investigations, the observation of two power maxima as a function of length was explained by the interaction of the electron beam with the forward traveling wave and reflections at the transition from the slow wave structure into the output waveguide. However, recent numerical calculations using the phase dynamics of electron beam and electromagnetic modes suggest that the power maxima are due to the phase relationship between the electron beam density wave and the backward wave. Experiments were performed on the Sinus-6, a relativistic electron beam accelerator. By adjusting the pressure in the Sinus-6 spark gap switch, cathode voltages between 400 kV to 650 kV can be obtained. The experiment was repeated for different sets of beam parameters. In all cases, the magnetic field used for beam transport was longer than the length of the slow wave structure. The experimentalmore » results are compared with phase model calculations and PIC code simulations using KARAT and TWOQUICK.« less

Recent experimental progress in high power modelocked semiconductor lasers together with the discovery of subpicosecond time scale gain and index dynamics in semiconductor amplifiers has underscored the need for an improved theory of amplification in these devices that correctly accounts for TeraHertz bandwidths and high intensities. The authors present an improved and more general version of their theoretical model for femtosecond pulse amplification in a SLA that includes the influence of finite intraband relaxations time. Comparison of calculation with a sequence of experiments on an angle stripe geometry SLA show excellent agreement and give parameter values that are all reasonable and also give information on the underlying physics. The propagation of the pulse in the SLA is described by a nonlinear equation for the time domain pulse envelope which includes both intensity and phase shaping effects as well the rapid gain and phase dynamics which have been observed through pump-probe experiments. >

A simple method to evaluate the phase noise properties of the coupled oscillators for arbitrary coupling and injection-locking topologies is presented. The method is based on the phase dynamics equation and the concept of noise admittance to represent the noise source. The PM noise of the coupled oscillators can be easily analyzed by solving the coupling matrix related to the coupling topologies, after neglecting amplitude noise and AM-to-PM conversion. An 8.5 GHz prototype array was constructed to verify the phase noise reduction of the total PM noise and the array injection locked by the external low phase noise source.

Lienard-Wiechert (LW) fields, which are exact solutions of the Wave Equation for a point charge in free space, are employed to formulate a self-consistent treatment of the electron beam dynamics and the evolution of the generated radiation in long undulators. In a relativistic electron beam the internal forces leading to the interaction of the electrons with each other can be computed by means of retarded LW fields. The resulting electron beam dynamics enables us to obtain three dimensional radiation fields starting from an initial incoherent spontaneous emission, without introducing a seed wave at start-up. In this paper, we present electromagnetic radiation studies, including multi-bucket electron phase dynamics and angular distribution of radiation in the time and frequency domain produced by a relativistic short electron beam bunch interacting with a circularly polarized magnetic undulator.