Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

The application on order analysis for the rotating machinery with LabVIEW

Order analysis is regarded as one of the most significant method for monitoring and analyzing rotational machinery for the phenomenon of " frequency smear".However,the order analysis based on resampling is a signal processingwhich converts the constant time interval sampling into constant angle interval sampling,while with the variety of the rotational speed.The superiority of the order analysis is investigatedon implement of order analysis.Andthrough comparing the advantage and disadvantage between spectrum and order analysis,the paper will discuss the order analysis form a deep perspective.

Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization

Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.

Modeling and Dynamic Analysis of Fractional-Order Buck Converter in Continuous Conduction Mode

According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities

This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.

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.

Literature Review, Meta-Analysis, and Mega-Analysis in Ecological and Agricultural Sciences

Literature review is an important component in any scientific research. In ecological and agricultural sciences, many studies have been conducted over years. With accumulation of scientific studies and published papers, it is critical to summarize and evaluate these previous research findings. Different literature review methods have been applied, including traditional qualitative literature review, quantitative meta-analysis, and more recently, mega-analysis, or meta-meta-analysis. Here we briefly describe these different approaches and draw attention to the recent development of data synthesis. Several case studies were used to illustrate the application of these methods in the ecological and agricultural sciences.

SAR tomography imaging via higher-order spectrum analysis

To deal with the non-Caussian noise in standard 2-D SAR images, the deramped signal in imaging plane, and the possible symmetric distribution of complex noise, the fourth-order cumulant of complex process is introduced into SAR tomography. With the estimated AR parameters of ARMA model of noise through Yule-Walker equation, the signal series of height is pre-filtered. Then, through ESPRIT, the spectrum is obtained and the aperture in height direction is synthesized. Finally, the SAR tomography imaging of scene is achieved. The results of processing on signal with non-Gaussian noise demonstrate the robustness of the proposed method. The tomography imaging of the scenes shows that the higher-order spectrum analysis is feasible in the application.

First order sensitivity analysis of magnetorheological fluid damper based on the output damping force

With many features,the magnetorheological fluid( MRF) damper is widely applied in the semiactive vibration control system. And sensitivity analysis is an important method to study the influence weight of various parameters on damping force characteristics. A mathematical model of the output damping force on the MRF damper is established by the mechanism modeling method,a first order output sensitivity equation is deduced and the expression of the first order output sensitivity function is obtained. The first-order sensitivity functions of ten design parameters are solved,and the influence degree of system parameters change on the output force of MRF damper is analyzed by comparing the sensitivity index of the parameters. Two sensitivities of vibration velocity and control current are obtained through experiment to prove the other parameters sensitivity analysis conclusion by analogy verification,which provides guidance for the structure optimization design of MRF damper.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Analysis on Sixth-Order Compact Approximations with Richardson Extrapolation for 2D Poisson Equation

By using Richardson extrapolation and fourth-order compact finite difference scheme on different scale grids, a sixth-order solution is computed on the coarse grid. Other three techniques are applied to obtain a sixth-order solution on the fine grid, and thus give out three kinds of Richardson extrapolation-based sixth order compact computation methods. By carefully analyzing the truncation errors respectively on 2D Poisson equation, we compare the accuracy of these three sixth order methods theoretically. Numerical results for two test problems are discussed.

Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

PainlevéAnalysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients

There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.

Spatial-temporal Evolution Analysis on Land Use Multifunctionality in the China-Vietnam Border Area

Exploring the spatial and temporal evolution characteristics of the border land use multifunctionality(LUMF)provides insights for taking advantage of border land use and optimizing border land use policies.Based on the improved Technique for Order Preference by Similarity to an Ideal Solution(TOPSIS)mode,this study identifies and evaluates the LUMFs in the China-Vietnam border area between 2000 and 2018 from the perspectives of agricultural production,social security,ecological service,landscape recreation,and national security.The results show that:1)The comprehensive land use functions in most counties and cities continued to be improved.2)The comprehensive land use function exhibits remarkable spatial divergence and aggregation characteristics.The high-value area of the agricultural production function and social security function evolves from the east to the west.In addition,the spatial evolution of ecological service function is complicated,without an obvious spatial divergence and aggregation pattern.The landscape recreation function shows different spatial differentiation characteristics in the early and middle stage,and forms a large cluster in the later stage.Finally,the spatial evolution pattern of the national security function is significant.3)Designing differentiated border land policies,improving border land use security,and establishing a long-term mechanism for ecological protection and ecological compensation can aid in optimizing the LUMF level in the border area.

MODIFIED HIGHER ORDER SPECTRAL ANALYSIS BASED TDE ALGORITHM FOR CFAR SIGNAL DETECTION PROBLEM

With the conditions of small data size and low Signal-to-Noise Ratio (SNR), the application of Higher Order Statistics (HOS) is restrained not only by its high estimation variance,but also by its low estimation precision. Therefore, a modified HOS based Time Delay Estimation (TDE) algorithm is proposed to overcome these problems. Comparing with the conventional TDE algorithms, the estimation variance is improved greatly. A typical simulation example is completed in order to test the performance of the algorithm proposed, which shows that the proposed algorithm has advantages over the traditional ones in both detection performance and computation efficiency.

Visual function and higher order aberration after implantation of aspheric and spherical multifocal intraocular lenses:a meta-analysis

AIMTo assess the visual outcomes of aspheric multifocal intraocular lenses (IOLs) compared with spherical multifocal IOL after cataract surgery.

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.

AN ANALYSIS OF EFFECTS OF FETAL ORDER AND PARENTAL AGE ON RETINOBLASTOMA

Seventy-eight cases of retinoblastoma (Rb) diagnosed at the Eye ENT Hospital, Shanghai Medical University from 1953 to 1985 were studied. The results of multiple logistic regression analysis and conditional probability model showed that high fetal order had a moderate risk (OR=1.28, P<0.05) of developing unilateral Rb. Both unilateral and bilateral cases were independent of parental ages, and no interaction could be found between fetal order and paternal of maternal age; also, the effect of fetal order was not confounded by parental ages.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.