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.

A simple semiempirical model for the static polarizability of ions

A concise analytical model for the static dipole polarizability of ionized atoms and molecules is created for the first time.As input,it requires,alongside the polarizability of neutral counterpart of a given ion,only the charge and elemental composition.This physically motivated semiempirical model is based on a number of established regularities in polarizability of charged monatomic and polyatomic compounds.In order to adjust it,the results of quantum chemistry calculations and gas-phase measurements available for a broad range of ionized multielectron species are employed.To counteract the appreciable bias in the literature data toward polarizability of monoatomic ions,for some molecular ions of general concern the results of the authors'own density functional theory calculations are additionally invoked.A total of 541 data points are used to optimize the model.It is demonstrated that the model we suggested has reasonable(given the substantial uncertainties of the reference data)accuracy in predicting the static isotropic polarizability of arbitrarily charged ions of any size and atomic composition.The resulting polarizability estimates are found to achieve a coefficient of determination of 0.93 for the assembled data set.The created analytic tool is universally applicable and might be advantageous for some applications where there is an urgent need for rapid low-cost evaluation of the static gas-phase polarizability of ionized atoms and molecules.This is especially relevant to constructing the complex models of nonequilibrium chemical kinetics aimed at precisely describing the observable refractive index(dielectric permittivity)of plasma flows.The data sets that support the findings of this study are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.07526.

A simple semiempirical model for the static polarizability of electronically excited atoms and molecules

We present a semiempirical analytical model for the static polarizability of electronically excited atoms and molecules,which requires very few readily accessible input data,including the ground-state polarizability,elemental composition,ionization potential,and spin multiplicities of excited and ground states.This very simple model formulated in a semiclassical framework is based on a number of observed trends in polarizability of electronically excited compounds.To adjust the model,both accurate theoretical predictions and reliable measurements previously reported elsewhere for a broad range of multielectron species in the gas phase are utilized.For some representative compounds of general concern that have not yet attracted sufficient research interest,the results of our multireference second-order perturbation theory calculations are additionally engaged.We show that the model we developed has reasonable(given the considerable uncertainties in the reference data)accuracy in predicting the static polarizability of electronically excited species of arbitrary size and excitation energy.These findings can be useful for many applications,where there is a need for inexpensive and quick assessments of the static gas-phase polarizability of excited electronic states,in particular,when building the complex nonequilibrium kinetic models to describe the observed optical refractivity(dielectric permittivity)of nonthermal reacting gas flows.

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.

TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn_3O_3 II-VI Semiconductor Clusters

The geometrical structure of semiconductor clusters including Zn3O3 was optimized by the DFT B3LYP method. With the same basis sets, dipole moments, polarizabilities and secondorder hyperpolarizabilities have been calculated and compared with the results obtained by TDDFT B3LYP method combined with sum-over-state （SOS） formula. The calculation results indicate that the dipole moments of the ground state depend on the atom radius and electronegative differences between elements and are their balance point as well. The polarizabilities of the clusters accord with the rule of the corresponding energy transformation from ground to excited state. The results predict an increase of second-order hyperpolarizabilities with increasing the distances between atoms in the clusters as well as a decrease of the polarizabilities and second-order hyperpolarizabilities in the same serial of semiconductor clusters with increasing the dipole moments of the ground states. The changes of dipole moments in ground states are inconsistent with transition moments. Spatial structure, charge transfer and other factors play an important role in composing the transition moments.

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.

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).

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.

Static electric dipole polarizability of lithium atoms in Debye plasmas

The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium. The plasma screening of the Coulomb interaction is described by the Debye-Hiickel potential and the interaction between the valence electron and the atomic core is described by a model potential. The electron energies and wave functions for both the bound and continuum states are calculated by solving the SchrSdinger equation numerically using the symplectic integrator. The oscillator strengths, partial-wave, and total static dipole polarizabilities of the ground state and n ≤ 3 excited states of the lithium atom are calculated. Comparison of present results with those of other authors, when available, is made. The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions, especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a0, which is associated with the Cooper minima.

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.

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method （ATMM） is applied to calculating the critical radius τc and the dipole polarizability αd in two confined systems： the hydrogen atom and the Hulthēén potential. We find that there exists a linear relation between τe^1/2 and the quantum number nτ for a fixed angular quantum number l, moreover, the three bounds of αd（αd^K,αd^B,αd^U） satisfy an inequality：αd^K≤αd^B≤αd^U,A comparison betwen the ATMM,the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

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.

NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.

Optical Basicity and Polarizability of Nd³⁺-Doped Bismuth Borate Glasses

This paper reports on different physical and optical properties of Nd3+-doped bismuth borate glasses. The glasses containing Nd3+ in (25 - x)Bi2O3:20Li2O:20ZnO:35B2O3:xNd2O3 (where x = 1, 1.5, 2 mol%) have been prepared by melt-quenching method. The amorphous nature of the glasses was confirmed by X-ray diffraction studies. The physical parameters like dielectric constant, refractive index, ionic concentration, oxygen-packing density, inter ionic distance, polaronradius, reflection loss, energy gap, molar refractivity, molar polarizability, electronic polarizability, optical basicity and field strength are computed. On the basis of the measured values of the density and refractive index, the Nd3+ ion concentration in glasses, the polarizability of oxide ions and optical basicity were theoretically determined. The theoretical value of average electronic polarizability and oxide ion polarizability were calculated by using Lorentz-Lorenz formula. Theoretical optical basicity of the glasses is evaluated based on equation proposed by Duffy and Ingram. The metallization criterion has also been calculated on the basis of refractive index and energy gap. The large value of metallization criterion indicates that the glass materials are insulators. The results obtained predict the nature of bonding in the present glasses and provide basis for developing new nonlinear optical material.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.