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.

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.

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.

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.

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.

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.

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.

Simultaneous determination of metronidazole and tinidazole in plasma by using HPLC-DAD coupled with second-order calibration

A method using HPLC-DAD coupled with second-order calibration was developed to simultaneously determine metronidazole and tinidazole in plasma samples in this paper. The second-order calibration method based on APTLD （alternating penalty trilinear decomposition） algorithm was proposed to analyze the three-way HPLC-DAD data from both standard and prediction samples, which makes it possible that calibration can be performed even in the presence of unknown interferences with a simple and green chromatographic condition and short analysis time. The results showed that good recoveries were obtained although the chromatographic and spectral profiles of the analytes of interest as well as background were partially overlapped with each other in plasma samples.

Second-order consensus in networks of dynamic agents with communication time-delays

This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.

Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.

Second-order random interfacial wave solutions for two-layer fluid with a free surface

A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.

Consensus of Second-order Multi-agent Systems with Nonsymmetric Interconnection and Heterogeneous Delays

In this paper, a consensus algorithm of multi-agent second-order dynamical systems with nonsymmetric interconnection and heterogeneous delays is studied. With the hypothesis of directed weighted topology graph with a globally reachable node, decentralized consensus condition is obtained by applying generalized Nyquist criterion. For the systems with both communication and input delays, it is shown that the consensus condition is dependent on input delays but independent of communication delays.