A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Closed-form steady-state solutions for forced vibration of second-order axially moving systems

Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

Deep learning for determining pure isotropic proton spectra from solidstate spectra

Recently,an article on ^(1)H solid-state NMR spectra was published,in which the authors proposed a deep learning approach to infer the pure isotropic proton NMR spectra obtained at an infinite magic angle spinning(MAS)rate.This approach even allowed to obtain,by far,the best resolved ^(1)H spectra of molecular solids[1](https://doi.org/10.1002/anie.202216607).Deep learning based artificial intelligence is developing rapidly,and its application is deepening.Currently,there are many applications of deep learning in the field of magnetic resonance,such as the reconstruction of the under-sampled multidimensional spectra[2-4],the deconvolution of two-dimensional NMR spectra[5]and noise suppression and weak peak retrial[6],etc.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.

Doppler spectral analysis for time-evolving sea surfaces using second-order small slope approximation

The second-order small slope approximation （SSA2） method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the numerical method for both vertical and horizontal polarizations, meaning that SSA2 gives a satisfactory prediction of the spectral difference between two po- larizations; while such discrepancy cannot be captured using the lowest-order SSA （SSA1） model. In particular, the Doppler shifts and spectral widths for different incident angles, wind directions and polarizations are analyzed, demonstrating correct variations with respect to such parameters. Those observations prove that the SSA2 provides an efficient and relatively fast tool for sea surface Doppler spectral analysis.

Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Core level excitation spectra of La and Mn ions in LaMnO3

Manganese-based perovskite is popular for research on ferromagnetic materials,and its spectroscopic studies are essential for understanding its electronic structure,dielectric,electrical,and magnetic properties.In this paper,the M-edge spectra of La ions and the M-edge,L-edge,and K-edge spectra of Mn ions in LaMnO3 are calculated by considering both the free-ion multiplet calculation and the crystal field effects.We analyze spectral shapes,identify peak origins,and estimate the oxidation states of La and Mn ions in LaMnO3 theoretically.It is concluded that La ions in LaMnO3 predominantly exist in the trivalent state,while Mn ions exist primarily in the trivalent state with a minor presence of tetravalent ions.Furthermore,the calculated spectra are in better conformity with the experimental spectra when the proportion of Mn3+is 90%and Mn4+is 10%.This article enhances our comprehension of the oxidation states of La and Mn within the crystal and also provides a valuable guidance for spectroscopic investigations of other manganates.

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

Second-Order Correlation Function for Asymmetric-to-Symmetric Transitions due to Spectrally Indistinguishable Biexciton Cascade Emission

We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.

Second-order phase correction of NMR spectra acquired using linear frequency-sweeps

NMR spectra acquired with experiments using frequency-sweeps such as the wide-band uniform-rate smooth truncation(WURST)spin-echo and Carr-Purcell-Meiboom-Gill(CPMG)sequences cannot be absorptively phased by using only conventional zerothand first-order phase correction.Implementation of phase correction up to the secondorder is described for obtaining absorptive spectra,which have more desirable line shapes and noise properties than magnitude spectra.The relationship of the second-order phase to the parameters of frequency sweeps is derived.The second-order phasing in the frequency-domain is equivalent to a point spread in the time-domain signal.The application of second-order phase correction is demonstrated with a wideline 35Cl CPMG spikelet spectrum.

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES

In[20],a semi-implicit spectral deferred correction(SDC)method was proposed,which is efficient for highly nonlinear partial differential equations(PDEs).The semi-implicit SDC method in[20]is based on first-order time integration methods,which are corrected iteratively,with the order of accuracy increased by one for each additional iteration.In this paper,we will develop a class of semi-implicit SDC methods,which are based on second-order time integration methods and the order of accuracy are increased by two for each additional iteration.For spatial discretization,we employ the local discontinuous Galerkin(LDG)method to arrive at fully-discrete schemes,which are high-order accurate in both space and time.Numerical experiments are presented to demonstrate the accuracy,efficiency and robustness of the proposed semi-implicit SDC methods for solving complex nonlinear PDEs.

LEGENDRE-GAUSS-RADAU SPECTRAL COLLOCATION METHOD FOR NONLINEAR SECOND-ORDER INITIAL VALUE PROBLEMS WITH APPLICATIONS TO WAVE EQUATIONS

We propose and analyze a single-interval Legendre-Gauss-Radau(LGR)spectral collocation method for nonlinear second-order initial value problems of ordinary differential equations.We design an efficient iterative algorithm and prove spectral convergence for the single-interval LGR collocation method.For more effective implementation,we propose a multi-interval LGR spectral collocation scheme,which provides us great flexibility with respect to the local time steps and local approximation degrees.Moreover,we combine the multi-interval LGR collocation method in time with the Legendre-Gauss-Lobatto collocation method in space to obtain a space-time spectral collocation approximation for nonlinear second-order evolution equations.Numerical results show that the proposed methods have high accuracy and excellent long-time stability.Numerical comparison between our methods and several commonly used methods are also provided.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.