Time Scale Parameter Research Articles

Calibration and Optimization of the Ångström–Prescott Coefficients for Calculating ET0 within a Year in China: The Best Corrected Data Time Scale and Optimization Parameters

This study used meteorological data from official data sets to correct Ångström–Prescott formula parameters for China’s agricultural zones for which existing research encountered the problem of spatio-temporal scale disunity. The data, collected from 124 stations, were used to correct the as and bs coefficients of the Ångström–Prescott formula, by area, at 5–50 year-scales, the former taking into account China’s comprehensive agricultural zones. We focused on how the as and bs obtained from the different time scales corrected data affected the calculating solar radiation (Rs_c) precision, determined the optimal time scale for the corrected data, and compared and selected the as and bs with the minimum estimation error as the recommended values. The results show that our corrected as and bs coefficient values significantly reduce the range of the relative error of Rs_c, with 10 years being the best time scale for the corrected data. Further, the Rs_c precisions estimated by as and bs coefficients based on the Food and Agriculture Organization of the United Nations (FAO) and the regression result of the best time scale corrected data are inconsistent in different months by area. The best choice in practice is combining the two coefficients and optimizing their use. This study provides a research-based process for standardizing the correction of Ångström–Prescott formula parameters and selecting the corrected data time scale in China. It would be helpful in improving the calculation accuracy for reference crop evapotranspiration (ET0).

A model-based state-of-charge estimation method for series-connected lithium-ion battery pack considering fast-varying cell temperature

Accurately estimating the state-of-charge (SOC) of lithium-ion batteries under complicated temperature conditions is crucial in all-climate battery management systems. This paper proposes a model-based SOC estimation method for series-connected battery pack with time-varying cell temperature. Systematic battery experiments are conducted to investigate the influences of changing temperature on both cell characteristics and cell-to-cell inconsistencies. A normalized open-circuit voltage (OCV) model is developed and applied in cell Thevenin model to describe the temperature-dependent OCV-SOC characteristic. The battery pack SOC is analyzed considering the effect of passive balance control. Then, a lumped parameter battery pack model is established by connecting cell models in series. To reduce computational complexity, a dual time-scale parameter identification framework is proposed which is supported by an online filtering process of selecting variable reference cell (VRC). An adaptive co-estimator is presented to update pack parameters in dual time-scale using an optimized recursive least squares algorithm, and to estimate the battery pack SOC using an extended Kalman filter. Experimental verifications are conducted under time-varying environmental temperature ranging from −40 °C to 40 °C. Results indicate the established model can well describe the dynamic behavior of battery pack, and the proposed method can estimate the battery pack SOC with considerably high precision.

Chromospheric activity behavior of an eclipsing binary system KOI 68AB

AbstractWe present the results obtained from KOI 68AB's light variation, which exhibits a sinusoidal light variation due to the stellar spots. Two active regions longitudinally separated by about 180° between the latitudes of +70° and +110° were found. A total of 313 flares were determined, and flare parameters were calculated. The One Phase Exponential Association model was derived using these parameters. The energy saturation parameter Plateau value was found to be 1.219 ± 0.088 s, and its time scale parameter half‐life value was found to be 1,190 s. The flare number per hour, known as N1 frequency, was found to be 0.02406 h−1, while the flare‐equivalent duration emitted per hour, known as N2, was found to be 0.000008. Considering new spectral observations, the target seems to be an eclipsing binary system. Because of this, the light curve is analyzed under an assumption that the target is an eclipsing binary. In these analyses, the sum of the fractional radii is found to be 0.1908, and the fractional radii ratio is 1.8973.

Most probable transition pathways and maximal likely trajectories in a genetic regulatory system

We study the most probable transition pathways and maximal likely trajectories in a genetic regulation model of the transcription factor activator’s concentration evolution, with Gaussian noise and non-Gaussian stable Lévy noise in the synthesis reaction rate taking into account, respectively. We compute the most probable transition pathways by the Onsager–Machlup least action principle, and calculate the maximal likely trajectories by spatially maximizing the probability density of the system path, i.e., the solution of the associated nonlocal Fokker–Planck equation. We have observed the rare most probable transition pathways in the case of Gaussian noise, for certain noise intensity, evolution time scale and system parameters. We have especially studied the maximal likely trajectories starting at the low concentration metastable state, and examined whether they evolve to or near the high concentration metastable state (i.e., the likely transcription regime) for certain parameters, in order to gain insights into the transcription processes and the tipping time for the transcription likely to occur. This enables us: (i) to visualize the progress of concentration evolution (i.e., observe whether the system enters the transcription regime within a given time period); (ii) to predict or avoid certain transcriptions via selecting specific noise parameters in particular regions in the parameter space. Moreover, we have found some peculiar or counter-intuitive phenomena in this gene model system, including: (a) A smaller noise intensity may trigger the transcription process, while a larger noise intensity cannot, under the same asymmetric Lévy noise. This phenomenon does not occur in the case of symmetric Lévy noise; (b) The symmetric Lévy motion always induces transition to high concentration, but certain asymmetric Lévy motions do not trigger the switch to transcription.These findings provide insights for further experimental research, in order to achieve or to avoid specific gene transcriptions, with possible relevance for medical advances.

Using Radar Data to Calibrate a Stochastic Parametrization of Organized Convection

AbstractStochastic parameterizations are increasingly becoming skillful in representing unresolved atmospheric processes for global climate models. The stochastic multicloud model, used to simulate the life cycle of the three most common cloud types (cumulus congestus, deep convective, and stratiform) in tropical convective systems, is one example. In this model, these clouds interact with each other and with their environment according to intuitive‐probabilistic rules determined by a set of predictors, depending on the large‐scale atmospheric state and a set of transition time scale parameters. Here we use a Bayesian statistical method to infer these parameters from radar data. The Bayesian approach is applied to precipitation data collected by the Shared Mobile Atmospheric Research and Teaching Radar truck‐mounted C‐band radar located in the Maldives archipelago, while the corresponding large‐scale predictors were derived from meteorological soundings taken during the Dynamics of the Madden‐Julian Oscillation field campaign. The transition time scales were inferred from three different phases of the Madden‐Julian Oscillation (suppressed, initiation, and active) and compared with previous studies. The performance of the stochastic multicloud model is also assessed, in a stand‐alone mode, where the cloud model is forced directly by the observed predictors without feedback into the environmental variables. The results showed a wide spread in the inferred parameter values due in part to the lack of the desired sensitivity of the model to the predictors and the shortness of the training periods that did not include both active and suppressed convection phases simultaneously. Nonetheless, the resemblance of the stand‐alone simulated cloud fraction time series to the radar data is encouraging.

Spectral analysis of temporal variability of nonlinear and nonstationary rainfall-runoff processes

This study deals with the time-dependent nonlinear response of catchments to the variations in rainfall. Both the rainfall and runoff discharge fields are treated to be nonstationary in time. A functional series representation, a generalization of the linear convolution integral, is employed to quantify the nonlinear relation between the input and output. The Fourier-Stieltjes representation approach is used to evaluate the variance of runoff discharge in the spectral frequency domain. The analysis based on the spectral solution for the runoff discharge variance clearly demonstrates that larger values of rainfall characteristic time scale or catchment size parameter lead to larger variability of the runoff discharge, while a larger catchment scale parameter leads to smaller variability of the runoff discharge.

Kinetics of sol-to-gel transition in irreversible particulate systems

A comprehensive theory encompassing the kinetics of the sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation systems, we show that this transition has three distinct regimes with kinetic exponent z∈1,2 corresponding to aggregation of sol clusters proceeding to the ideal gel point (IGP); z∈2,5.7 for gelation of sol clusters beyond IGP; and z∈2,3.5 for a hitherto unidentified regime involving aggregation of gels when monomer-dense. We further establish universal power-law scaling relationships that connect the kinetics of these three regimes. Improved parameterizations are performed on the characteristic timescale parameters that define each regime.

Quantum to classical transition in an information ratchet.

Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare and hence quantifying possible quantum supremacy in information ratchets has been elusive. We propose a step towards filling this void between quantum and classical ratchets by introducing a model with continuous variables: a quantum particle in a box coupled to a stream of qubits. The dynamics is solved exactly and we analyze the quantum to classical transition in terms of a natural timescale parameter for the model.

BP Gulf of Mexico Neogene Astronomically-tuned Time Scale (BP GNATTS)

AbstractThis paper introduces an integrated Neogene microfossil biostratigraphic chart developed within post-merger BP for the Gulf of Mexico Basin and is the first published industrial framework “fully-tuned” to orbital periodicities. Astronomical-tuning was accomplished through a 15-year research program on the Ocean Drilling Program’s (ODP) Leg 154 sediments (offshore NE Brazil) with sampling resolution for calcareous nannofossils and planktonic foraminifera ∼20 k.y. and 40 k.y. (thousand year), respectively. This framework extends from the Late Oligocene (25.05 Ma) to Recent at an average Chart Horizon resolution for the Neogene of 144 k.y., approximately double that of published Gulf of Mexico biostratigraphic charts and a fivefold increase over the highest resolution global calcareous microfossil biozonation. Such resolution approximates that of fourth to fifth order parasequences and is a critical component in the verification of seismic correlations between mini-basins in the deep-water Gulf of Mexico. Its utility in global time-scale construction and correlation has been proven, in part, by application of the scheme in full to internal research for the Oligocene–Miocene boundary interval on the global boundary stratotype section and point (GSSP) in northern Italy and offshore wells in the eastern Mediterranean Sea. This step change in Neogene resolution, now at the level of cyclostratigraphy (the orbital periodicity of eccentricity) and the magnetostratigraphic chron, demonstrates the potential for calcareous microfossil biostratigraphy to more consistently reinforce correlations of these time scale parameters. The integration of microfossil disciplines, consistent taxonomies, and rigorous analytical methodologies are all critical to obtaining and reproducing this new level of biostratigraphic resolution.

Evolutionary dynamics of the prisoner's dilemma with expellers

Expulsion refers to the widespread behavior of expelling intruders from the owners’ territories, which has not been considered in current models on the evolutionary dynamics of cooperation so far. In the context of prisoner’s dilemma, we present a simple game-theoretical model of expulsion in which punishing cooperators (i.e. expellers) are able to banish defectors from their own neighborhoods. In the mean-field limit, our theoretical analysis of prisoner’s dilemma with expellers shows that the increment of either vacant sites ratio or time scale parameter between pairwise interaction process and strategy updating process can slow down evolutionary speed though defection is the only stable fixed point anyway. In more realistic spatial settings, we provide both analytical and numerical results for the limiting case where pairwise interaction dynamics proceeds much faster than strategy updating dynamics. Using the extended pair approximation methods and Monte Carlo simulations, we show that the introduction of expellers not only promotes coevolution of expulsion and cooperation by means of both direct and indirect domain competition but also opens the gate to rich dynamical behaviors even if expulsion is costly. Phase diagrams reveal the occurrence of frozen as well as dynamical stationary states, between which continuous or discontinuous phase transition may happen. For intermediate ranges, we investigate numerically the coupled interplay between pairwise interaction dynamics and strategy updating dynamics, and show that the validity of main results for the limiting case can be extended to this general case. Interestingly, there exists an optimal value of time scale parameter that results in the maximum fraction of altruistic players, which resembles the coherence resonance phenomenon in dynamical systems. Our results may provide insights into understanding coevolutionary dynamics of expulsive and cooperative behavior in social dilemma situations.

Efficient Quantification and Simulation of Modal Dynamics in Multimode Fiber Links

Sudden environmental effects, such as mechanical vibration, wind, and lightning, impart microsecond-timescale changes to the transmission matrix of multimode optical fibers. We introduce a timescale parameter to characterize the rate of channel changes in mode-division-multiplexed (MDM) links. We show how to efficiently generate continuous unitary matrices that form the basis for a simplified, yet general, dynamic channel model incorporating the effects of modal dispersion, mode-dependent loss, and time-varying mode coupling. We show that fast environmental perturbations can be modeled by deriving the unitary matrices from a linear ramp model, where the ramp slopes depend on the timescale parameter. We discuss the implications of channel dynamics on adaptive multiple-input-multiple-output (MIMO) equalization at the receiver in long-haul MDM links using coherent detection and in short-reach MDM links using direct detection. We show that the channel timescale and the rotation rate of the generalized Stokes vector on the generalized Poincare sphere are both predictive of adaptive MIMO equalizer misadjustment. Our simplified channel model can be applied to optimize adaptive MIMO equalization algorithms for tracking modal dynamics.

Aging in Metropolis dynamics of the REM: a proof

We consider Metropolis dynamics of the Random Energy Model. We prove that the classical two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. To do this we link the two-time correlation function to a certain continuous-time clock process which, after proper rescaling, is proven to converge to a stable subordinator almost surely in the random environment and in the fine $$J_1$$ -topology of Skorohod. This fine topology then enables us to deduce from the arcsine law for stable subordinators the asymptotic behavior of the two-time correlation function that characterizes aging.

Inferring demographic parameters in bacterial genomic data using Bayesian and hybrid phylogenetic methods

BackgroundRecent developments in sequencing technologies make it possible to obtain genome sequences from a large number of isolates in a very short time. Bayesian phylogenetic approaches can take advantage of these data by simultaneously inferring the phylogenetic tree, evolutionary timescale, and demographic parameters (such as population growth rates), while naturally integrating uncertainty in all parameters. Despite their desirable properties, Bayesian approaches can be computationally intensive, hindering their use for outbreak investigations involving genome data for a large numbers of pathogen isolates. An alternative to using full Bayesian inference is to use a hybrid approach, where the phylogenetic tree and evolutionary timescale are estimated first using maximum likelihood. Under this hybrid approach, demographic parameters are inferred from estimated trees instead of the sequence data, using maximum likelihood, Bayesian inference, or approximate Bayesian computation. This can vastly reduce the computational burden, but has the disadvantage of ignoring the uncertainty in the phylogenetic tree and evolutionary timescale.ResultsWe compared the performance of a fully Bayesian and a hybrid method by analysing six whole-genome SNP data sets from a range of bacteria and simulations. The estimates from the two methods were very similar, suggesting that the hybrid method is a valid alternative for very large datasets. However, we also found that congruence between these methods is contingent on the presence of strong temporal structure in the data (i.e. clocklike behaviour), which is typically verified using a date-randomisation test in a Bayesian framework. To reduce the computational burden of this Bayesian test we implemented a date-randomisation test using a rapid maximum likelihood method, which has similar performance to its Bayesian counterpart.ConclusionsHybrid approaches can produce reliable inferences of evolutionary timescales and phylodynamic parameters in a fraction of the time required for fully Bayesian analyses. As such, they are a valuable alternative in outbreak studies involving a large number of isolates.

Impulsive effects on competitive neural networks with mixed delays: Existence and exponential stability analysis

In the proposed research work, the problem of dynamic analysis for a class of existence and global exponential stability of impulsive competitive neural networks (ICNNs) with multiple delays and effects of time scale parameter is investigated. Here the mixed delays include infinite distributed delay and discrete time multiple delays. Firstly, by means of non-linear Lipschitz measure (NLM) and some matrix inequality techniques, the existence and uniqueness of the network equilibrium point is proved, while by fabricating a suitable Lyapunov functional, some new brand of algebraic sufficient conditions is ensured to be globally exponentially stable in voice of linear matrix inequality (LMI). Finally, a numerical example with simulations are shown to illustrate the essence and merits of our obtained analytical results with some existing ones in the available literature.

Stochastic differential equations driven by deterministic chaotic maps: analytic solutions of the Perron–Frobenius equation

We consider discrete-time dynamical systems with a linear relaxation dynamics that are driven by deterministic chaotic forces. By perturbative expansion in a small time scale parameter, we derive from the Perron–Frobenius equation the corrections to ordinary Fokker–Planck equations in leading order of the time scale separation parameter. We present analytic solutions to the equations for the example of driving forces generated by Nth order Chebychev maps. The leading order corrections are universal for but different for N = 2 and N = 3. We also study diffusively coupled Chebychev maps as driving forces, where strong correlations may prevent convergence to Gaussian limit behavior.

Parameterizing Generalized Laguerre Functions to Compute the Inverse Laplace Transform of Fractional Order Transfer Functions

This article concentrates on using generalized Laguerre functions to compute the inverse Laplace transform of fractional order transfer functions. A novel method for selecting the timescale parameter of generalized Laguerre functions in the operator space is introduced and demonstrated on two systems with fractional order transfer functions.

Optimal switching under a hybrid diffusion model and applications to stock trading

This paper is concerned with the optimal switching problem under a hybrid diffusion (or, regime switching) model in an infinite horizon. The state of the system consists of a number of diffusions coupled by a finite-state continuous-time Markov chain. Based on the dynamic programming principle, the value function of our optimal switching problem is proved to be the unique viscosity solution to the associated system of variational inequalities. The optimal switching strategy, indicating when and where it is optimal to switch, is given in terms of the switching and continuation regions. In many applications, the underlying Markov chain has a large state space and exhibits two-time-scale structure. In this case, a singular perturbation approach is employed to reduce the computational complexity involved. It is shown that as the time-scale parameter ε goes to zero, the value function of the original problem converges to that of a limit problem. The limit problem is much easier to solve, and its optimal switching solution leads to an approximate solution to the original problem. Finally, as an application of our theoretical results, an example concerning the stock trading problem in a regime switching market is provided. It is emphasized that, this paper is the first time to introduce the optimal switching as a general framework to study the stock trading problem, in view of their inherent connection. Both optimal trading rule and convergence result are numerically demonstrated in this example.

Weak order in averaging principle for stochastic differential equations with jumps

In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is of order 1. This reveals that the rate of weak convergence is essentially twice that of strong convergence.

Recursively Convolutional CFS-PML in 3-D Laguerre-FDTD Scheme for Arbitrary Media

Weighted Laguerre finite-difference time-domain (Laguerre-FDTD) method is an efficient and unconditionally stable time-domain numerical method. The complex frequency-shifted perfectly matched layer (CFS-PML) is the main absorbing boundary condition in the Laguerre-FDTD method. The implementations of CFS-PML in the Laguerre-FDTD method, which have been reported, include the use of auxiliary variables and auxiliary differential equations. These implementations make CFS-PML sensitive to its parameters and timescale parameter s of weighted Laguerre polynomials and result in potential instability and poor absorption issues in numerical simulations. In this paper, we proposed an efficient and stable implementation of CFS-PML based on recursive convolution in the Laguerre-FDTD method. The accuracy of the proposed implementation is theoretically validated. Its numerical dispersion is theoretically derived for choosing the key parameters of CFS-PML in the Laguerre-FDTD scheme. The numerical dispersion demonstrates that the timescale factor s needs to match the simulated signal frequency and the CFS-PML parameter $\alpha $ is chosen as $0.5s\varepsilon _{0}$ to obtain the minimum dispersive error. Numerical examples validate the theoretical predictions and verify that the proposed implementation of CFS-PML is robust and retains the advantages of CFS-PML in classical FDTD method, such as effectively absorbing evanescent as well as guided waves. It requires nonsplits of electromagnetic field components, no auxiliary variables, and no modifications when applying it to inhomogeneous, lossy, and dispersive media. The CFS-PML formulas can directly be converted into computer codes of the Laguerre-FDTD method.

An improved preference method for the FAST TCP protocol parameter

Aiming at the weaknesses of FAST TCP in choosing protocol parameter for static mapping. A slow time-scale iterative search preference parameter method based on the difference between each path traffic service intensity and its transmission bandwidth is proposed. The stochastic model and its fluid model was derived, in which each path TCP connection followed Poisson process and the size of transport files obeyed the exponential distribution. A Lyapunov function including TCP connection’s mean waiting time was constructed to prove that, for those links which are in heavy traffic, if each path’s traffic service intensity was equal to its transmission bandwidth, the number of each path’s active TCP connection would stay stable, and the average waiting time will reach the minimum. Thereby the proposed method is theoretically feasible. Moreover, NS-2 simulations are presented to verify this effective method.