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.

Industrial utilization of arsenic-containing gold dressing tailings as pellet prepared by straight grate process

The utilization of arsenic-containing gold dressing tailings is an urgent issue faced by gold production companies worldwide.The thermodynamic analysis results indicate that ferrous arsenate(FeAsO_(4)),pyrite(FeS_(2))and sodium cyanide(NaCN)in the arsenic-containing gold metallurgical tailings can be effectively removed using straight grate process,and the removal of pyrite and sodium cyanide is basically completed during the preheating stage,while the removal of ferrous arsenate requires the roasting stage.The pellets undergo a transformation from magnetite to hematite during the preheating process,and are solidified through micro-crystalline bonding and high-temperature recrystallization of hematite(Fe_(2)O_(3))during the roasting process.Ultimately,pellets with removal rates of 80.77% for arsenic,88.78% for sulfur,and 99.88% for cyanide are obtained,as well as the iron content is 61.1% and the compressive strength is 3071 N,meeting the requirements for blast furnace burden.This study provides an industrially feasible method for treating arsenic-containing gold smelting tailings,benefiting gold production enterprises.

Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

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.

Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings

Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.

975 nm multimode semiconductor lasers with high-order Bragg diffraction gratings

The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calcu-lated using the 2D finite difference time domain(FDTD)algorithm and the scattering matrix method(SMM).The periods and etch depth of the grating parameters have been optimized.A board area laser diode(BA-LD)with high-order diffraction grat-ings has been designed and fabricated.At output powers up to 10.5 W,the measured spectral width of full width at half maxi-mum(FWHM)is less than 0.5 nm.The results demonstrate that the designed high-order surface gratings can effectively nar-row the spectral width of multimode semiconductor lasers at high output power.

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).

Monitoring shear deformation of sliding zone via fiber Bragg grating and particle image velocimetry

Monitoring shear deformation of sliding zones is of great significance for understanding the landslide evolution mechanism,in which fiber optic strain sensing has shown great potential.However,the cor-relation between strain measurements of quasi-distributed fiber Bragg grating(FBG)sensing arrays and shear displacements of surrounding soil remains elusive.In this study,a direct shear model test was conducted to simulate the shear deformation of sliding zones,in which the soil internal deformation was captured using FBG strain sensors and the soil surface deformation was measured by particle image velocimetry(PIV).The test results show that there were two main slip surfaces and two secondary ones,developing a spindle-shaped shear band in the soil.The formation of the shear band was successfully captured by FBG sensors.A sinusoidal model was proposed to describe the fiber optic cable deformation behavior.On this basis,the shear displacements and shear band widths were calculated by using strain measurements.This work provides important insight into the deduction of soil shear deformation using soil-embedded FBG strain sensors.

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Intelligent Integrated Control of Underactuated Mechanical Systems with Second-order Nonholonomic Constraints

This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sliding-mode control and a model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. Then the fuzzy sliding-mode controller is employed to control the movement that the acrobot enters the balance area from the swing-up area. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model, is used to balance the acrobot. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities.

Waveguide Bragg Grating for Fault Localization in PON

Femtosecond laser direct inscription is a technique especially useful for prototyping purposes due to its distinctive advantages such as high fabrication accuracy,true 3D processing flexibility,and no need for mold or photomask.In this paper,we demonstrate the design and fabrication of a planar lightwave circuit(PLC)power splitter encoded with waveguide Bragg gratings(WBG)using a femtosecond laser inscription technique for passive optical network(PON)fault localization application.Both the reflected wavelengths and intervals of WBGs can be conveniently tuned.In the experiment,we succeeded in directly inscribing WBGs in 1×4 PLC splitter chips with a wavelength interval of about 4 nm and an adjustable reflectivity of up to 70% in the C-band.The proposed method is suitable for the prototyping of a PLC splitter encoded with WBG for PON fault localization applications.

Strain-Insensitive Fiber Bragg Grating Composite Structure for Wide-Range Temperature Sensing

This paper reports on the design,fabrication,and temperature strain sensing performance of a fiber Bragg grating composite structure for surface mounted temperature measurements over a wide temperature range,with highly reduced strain cross-sensitivity.The fiber Bragg grating sensor is encapsulated in a polyimide tube filled with epoxy resin,forming an arc-shaped cavity.This assembly is then placed between two layers of glass fiber prepreg with a flexible pad in between and cured into shape.Experimental results,supported by finite element simulations,demonstrate an enhanced temperature sensitivity is 26.3 pm/°C over a wide temperature range of–30°C to 70°C,and high strain transfer isolation of about 99.65%.

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.