Temporal dynamics of high repetition rate pulsed single longitudinal mode dye laser

Theoretical and experimental studies of temporal dynamics of grazing incidence grating (GIG) cavity, single-mode dye laser pumped by high repetition rate copper vapour laser (CVL) are presented. Spectral chirp of the dye laser as they evolve in the cavity due to transient phase dynamics of the amplifier gain medium is studied. Effect of grating efficiency, focal spot size, pump power and other cavity parameters on the temporal behaviour of narrow band dye laser such as build-up time, pulse shape and pulse width is studied using the four level dye laser rate equation and photon evolution equation. These results are compared with experimental observations of GIG single-mode dye laser cavity. The effect of pulse stretching of CVL pump pulse on the temporal dynamics of the dye laser is studied.     

大气压氩气介质阻挡辉光放电的一维仿真研究

为了研究氩气(Ar)中介质阻挡大气压辉光放电(APGD)的放电机理, 通过建立一个一维的多粒子自洽耦合流体模型, 采用有限元方法进行数值计算, 得到了气体间隙压降、介质表面电荷密度、放电电流密度随时间的周期变化波形, 以及电子、离子、亚稳态粒子密度和空间电场强度的时空分布. 仿真计算结果表明：介质表面积聚的电荷对于放电的过程的起始及熄灭具有重要作用;当增大外施电压时, 放电击穿时刻提前, 放电电流密度和介质表面电荷密度峰值增大, 表明放电过程更加剧烈;随着阻挡介质相对介电常数的增大, 放电电流密度也随之增大. 各粒子密度及电场的时空分布表明放电过程在外施电压半个周期中只有一次放电, 且存在明显的阴极位降区、负辉区、等离子体正柱区等辉光放电的典型区域, 为大气压辉光放电(APGD).     

Radially ingoing and outgoing dispersive and dissipative structures in electron‐ion plasmas in the presence of electron trapping

In this article, non‐linear propagation of ingoing and outgoing electrostatic waves on the ion time scale in an unmagnetized, non‐relativistic electron‐ion (ei) plasma in the presence of warm ions, ion kinematic viscosity, and trapped Maxwellian electrons was examined in a non‐planar geometry. In the weak non‐linearity limit, modified soliton and shock equations were derived with the inclusion of electron trapping in cylindrical and spherical geometries. The finite difference method was used to solve all these equations in the non‐planar geometries using the planar versions of these equations as an initial input. The results were compared with their counterparts with quadratic non‐linearity and the main differences were expounded. It was shown that the spatio‐temporal scales over which the shocks form for the non‐planar trapped Burgers equation are much shorter by comparison with the shocks admitted by the non‐planar trapped Korteweg de Vries Burgers equation. It was also found that unlike their non‐linear shock counterparts, the solitary structures admitted by the non‐planar trapped Korteweg de Vries equation exhibit a phase shift.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

利用一维原子链模型研究薄膜瞬态结构变化

对于晶格结构响应的仿真与实验有助于我们理解激光激发引起的动态过程.利用一维原子链模型研究了激光加热后由于温度分布不均匀性产生的热应力对晶格的影响,该模型的计算结果与使用超快X射线衍射获得的实验结果相符合.该模型为研究光激发金属以及半导体等材料的超快晶格动力学提供了理论分析基础.     

Numerical modeling of transient progression of plasma formation in biological tissues induced by short laser pulses

A theoretical model based on the rate equation for free electron density is proposed to investigate transient progression of plasma formation in soft biological tissues during laser shock processing. The laser focusing region around the focus point is considered to be one-dimensional along the direction of the incident beam, and is discretized into numerous thin control volumes. In simulation of the transient plasma progression, the laser intensity distribution and the temporal evolution of the free electron density are calculated sequentially for each control volume using a fourth-order Runge–Kutta method with adaptive time step control. The rate-equation formalism is first validated with previously published theoretical and experimental results. Simulation of the dynamics of plasma formation is then performed. The results include temporal evolution and spatial distribution of the free electron density as well as the growth of the plasma. It is shown that the threshold laser intensity for optical breakdown in water and the maximum length of the resulting plasma obtained from the present model are in good agreement with existing experimental data. PACS 42.65.-k; 52.38.-r; 87.80.-y     

Application of High Current and Current Zero Simulations of High‐Voltage Circuit Breakers

This paper reports on the use of computational fluid dynamic (CFD) simulations to predict the interruption behaviour of high‐voltage circuit breakers (HV‐CB) using the self‐blast principle. Two different levels of accuracy of the arc model are proven to be sufficiently accurate for simulating the high‐current phase and the period around current zero (CZ). For the high‐current phase, a simplified equivalent model of the arc is implemented to predict the pressure build‐up, and even more important to accurately trace the hot gas from the arcing zone into the exhausts and the heating volume. A detailed analysis of the gas mixing in the heating volume for different arcing times and current amplitudes showed the optimum geometrical design of the heating volume. For the CZ phase, a more detailed arc model is needed including the effects of ohmic heating, radiative energy transfer, and turbulent cooling fully resolved in space and time. The validation with experiments was done and shows good agreement which justifies the use of the implemented model. With it, scaling laws varying only one parameter at a time (pressure and applied current slope) were derived and confirm previously found empirical laws. This is of particular interest, as it is very difficult to derive such scaling laws from experiments where the scatter is always very large and where it is impossible to vary only one parameter at a time. The influence of the most important geometrical parameters of the nozzle on the interruption performance is shown. In addition to previous experimental indications of this, the simulation reveals that turbulent cooling on the arc edge is the main reason for the difference in interruption performance. Moreover, the exact spatio‐temporal build‐up of arc resistance and with it the detailed understanding of the arc interruption process is possible and shown here for the first time. These simulations enable us to predict HV‐CB performance and to minimise the number of development tests and are routinely used in new development projects. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Markov Properties of Electrical Discharge Current Fluctuations in Plasma

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal’s coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal’s coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal’s coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.     

Using the traditional model to evaluate the active force of the human lateral rectus muscle

The information on the force of extraocular muscles(EOMs)is beneficial for strabismus diagnosis and surgical planning,and a direct and simple method is important for surgeons to obtain these forces.Based on the traditional model,a numerical simulation method was proposed to achieve this aim,and then the active force of the lateral rectus(LR)muscle was successfully simulated when the eye rotated every angle from 0°to 30°in the horizontal plane from the nasal to the temporal side.In order to verify these simulations,the results were compared with the previous experimental data.The comparison shows that the simulation results diverged much more than the experimental data in the range of 0°–10°.The errors were corrected to make the simulation results closer to the experimental data.Finally,a general empirical equation was proposed to evaluate the active force of the LR muscle by fitting these data,which represent the relationship between the simulation forces and the contractive amounts of the LR muscle.     

Reaction kinetics and solubility in water‐organic binary solutions are governed by similar solvation equilibria

The solvation effects observed in water‐organic solutions were studied by combining data for reaction kinetics and dissolution equilibria by means of a linear free‐energy (similarity) analysis. Kinetic data for the pH‐independent hydrolysis of (4‐methoxyphenyl)‐2,2‐dichloroacetate measured in this work and solubility data for naphthalene, and other substrates of low polarity, in aqueous binary mixtures of methanol, ethanol, acetonitrile, dimethyl sulfoxide (DMSO), and 1,4‐dioxane were used. Linear similarity relationships were discovered for these data over the full range of solvent compositions studied. To gain insight into the similarities observed between these different phenomena, molecular dynamics simulations were carried out for naphthalene and an ester in water–acetonitrile solutions. The results revealed considerable preferential solvation of these substrates by the co‐solvent. Linear relationships between the experimental data and the mole fractions of acetonitrile in the solvation shells of substrates were found. Surprisingly, a linear relationship was found between the mole fractions of acetonitrile in the solvation shells of the ester and naphthalene. This linearity indicated that a similar solvation mechanism governs even such different phenomena as dissolution and reaction kinetics. The relationships between the experimental data and the results of the molecular dynamics calculations found in this work explained the solvent effect observed in water‐organic solutions on the molecular level. Copyright © 2015 John Wiley & Sons, Ltd.     

Software for the data analysis of the arrival‐timing monitor at SACLA

X‐ray free‐electron laser (XFEL) pulses from SPring‐8 Ångstrom Compact free‐electron LAser (SACLA) with a temporal duration of <10 fs have provided a variety of benefits in scientific research. In a previous study, an arrival‐timing monitor was developed to improve the temporal resolution in pump–probe experiments at beamline 3 by rearranging data in the order of the arrival‐timing jitter between the XFEL and the synchronized optical laser pulses. This paper presents Timing Monitor Analyzer (TMA), a software package by which users can conveniently obtain arrival‐timing data in the analysis environment at SACLA. The package is composed of offline tools that pull stored data from cache storage, and online tools that pull data from a data‐handling server in semi‐real time during beam time. Users can select the most suitable tool for their purpose, and share the results through a network connection between the offline and online analysis environments.     

Lasing action assisted by long‐range surface plasmons

It is shown that lasing action at subwavelength scales can be achieved in realistic plasmonic systems supporting long‐range surface plasmons (LRSPPs). To this end, a general numerical framework has been developed that is able to accurately account for the full spatio‐temporal lasing dynamics and the vastly different length‐ and time‐scales featured by this class of systems. Starting from a loss compensation regime for propagating LRSPPs, it is shown how the introduction of an optical feedback mechanism induces the formation of a self‐sustained laser oscillation at moderate pump intensities. The simplicity of the proposed subwavelength scale laser offers significant potential as a novel class of planar light sources in complex plasmonic circuits.     

Effect of Mass and Charge of Ionic Species on Spatio‐Temporal Evolution of Transient Electric Field in CCP Discharges

The formation of capacitive sheath and existence of the transition electric field between sheath edge and bulk plasma in RF‐CCP discharge is predicted (PRL 89, 265006 2002); such structures are sensitive to the plasma composition. On the basis of semi‐infinite particle‐in‐cell (PIC) simulation the effect of charge and mass of ionic species on the spatio‐temporal evolution of the transient electric field and phase mixing phenomena in linear and weakly nonlinear regime has been explored. As an important feature, the simulation results predict that the maximum amplitude of the transient electric field decreases with increasing ionic mass and charge; further the sheath width increases with increasing ionic mass while follow opposite trend with increasing ionic charge. The excitation of wave like structures in the transition region and efficient energy transport to the bulk region of CCP discharges in a nonlinear regime has also been predicted. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐paraxial polarization spatio‐temporal coupling in ultrafast laser material processing

Two hundred years after Malus' discovery of optical anisotropy, the study of polarization‐driven optical effects is as active as ever, generating interest in new phenomena and potential applications. However, in ultrafast optics, the influence of polarization is frequently overlooked being considered as either detrimental or negligible. Here we demonstrate that spatio‐temporal couplings, which are inherent for ultrafast laser systems with chirped‐pulse amplification, accumulate in multi‐pulse irradiation and lead to a strongly anisotropic light‐matter interaction. Our results identify angular dispersion in the focus as the origin for the polarization dependence in modification, yielding an increase in modification strength. With tight focusing (NA ≥ ∼0.4), this non‐paraxial effect leads to a manifestation of spatio‐temporal couplings in photo‐induced modification. We devise a practical way to control the polarization dependence and exploit it as a new degree of freedom in tailoring laser‐induced modification in transparent material. A near‐focus, non‐paraxial field structure analysis of an optical beam provides insight on the origin of the polarization dependent modification. However, single pulse non‐paraxial corrected calculations are not sufficient to explain the phenomena confirming the experimental observations and exemplifying the need for multi‐pulse analysis.

     

Methodology for the solutions of some reduced Fokker‐Planck equations in high dimensions

In this paper, a new methodology is formulated for solving the reduced Fokker‐Planck (FP) equations in high dimensions based on the idea that the state space of large‐scale nonlinear stochastic dynamic system is split into two subspaces. The FP equation relevant to the nonlinear stochastic dynamic system is then integrated over one of the subspaces. The FP equation for the joint probability density function of the state variables in another subspace is formulated with some techniques. Therefore, the FP equation in high‐dimensional state space is reduced to some FP equations in low‐dimensional state spaces, which are solvable with exponential polynomial closure method. Numerical results are presented and compared with the results from Monte Carlo simulation and those from equivalent linearization to show the effectiveness of the presented solution procedure. It attempts to provide an analytical tool for the probabilistic solutions of the nonlinear stochastic dynamics systems arising from statistical mechanics and other areas of science and engineering.     

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato–Lefever equation, we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion. Both of them can induce the temporal drift and frequency shift. Based on the moment analysis method, we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation. Finally, the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted. Our results pave the way for further understanding the soliton dynamics and spectral characteristics, and providing an effective route to manipulate frequency comb.     

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.     

Approaching complexity by stochastic methods: From biological systems to turbulence

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.     

First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

In this paper strong evidence is provided for significant far from equilibrium phase transition processes in the Earth’s magnetosphere as revealed by the nonlinear analysis of in situ observations. These results constitute the solid base for the solution of the durable controversy about the chaotic or non-chaotic character of the magnetospheric dynamics. During the last two decades the concept of low dimensional chaos was supported by theoretical and experimental methods by our group in Thrace and others scientists, as an explicative paradigm of the magnetospheric dynamics including substorm processes. In parallel, the concept of self-organized criticality (SOC) and space-time intermittency was introduced as new and opposing to low dimensional chaos concepts for modeling the magnetospheric dynamics. Novel results concerning the nonlinear analysis of in situ space plasma data (magnetic-electric field, energetic particles and bulk plasma flow time series) obtained by the Geotail spacecraft presented in this paper for the first time reveal the following: (a) Coexistence of SOC and chaos states in the magnetospheric system and global phase transition from one state to the other during substorms. (b) Strong intermittent turbulent character of the magnetospheric system at the SOC or the low dimensional chaos states. (c) Clear indications for non-extensivity and q-Gaussian statistics during periods of low dimensional and chaotic dynamics of the magnetosphere. (d) Low dimensional and nonlinear space plasma dynamics in the day side magnetopause and bow shock dynamics. The dual character of the magnetospheric dynamics including low dimensional chaotic (coherent) and high dimensional turbulent states, as supported in this paper, is in agreement and verifies previous theoretical and experimental studies.