Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

A one-dimensional polynomial chaos method in CFD–Based uncertainty quantification for ship hydrodynamic performance

A one-dimensional non-intrusive Polynomial Chaos （PC） method is applied in Uncertainty Quantification （UQ） studies for CFD-based ship performances simulations. The uncertainty properties of Expected Value （EV） and Standard Deviation （SD） are evaluated by solving the PC coefficients from a linear system of algebraic equations. The one-dimensional PC with the Legendre polynomials is applied to： （1） stochastic input domain and （2） Cumulative Distribution Function （CDF） image domain, allowing for more flexibility. The PC method is validated with the Monte-Carlo benchmark results in several high-fidelity, CFD-based, ship UQ problems, evaluating the geometrical, operational and environmental uncertainties for the Delft Catamaran 372. Convergence is studied versus PC order P for both EV and SD, showing that high order PC is not necessary for present applications. Comparison is carried out for PC with/without the least square minimization when solving the PC coefficients. The least square minimization, using larger number of CFD samples, is recommended for current test cases. The study shows the potentials of PC method in Robust Design Optimization （RDO） and Reliability-Based Design Optimization （RBDO） of ship hydrodynamic performances.

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.

A polynomial chaos expansion method for the uncertain acoustic field in shallow water

To obtain a universal model solving the uncertain acoustic field in shallow water, a non-intrusive model coupled polynomial chaos expansion （PCE） method with Helmholtz equa- tion is established, in which the polynomial coefficients are solved by probabilistic collocation method （PCM）. For the cases of Pekeris waveguide which have uncertainties in depth of water column, in both sound speed profile and depth of water column, and for the case of thermocline with lower limit depth uncertain, probability density functions （PDF） of transmission loss （TL） are calculated. The results show that the proposed model is universal for the acoustic propa- gation codes with high computational efficiency and accuracy, and can be applied to study the uncertainty of acoustic propagation in the shallow water en^-ironment with multiple parameters uncertain.

A Survey of Newtonian Core-Shell Systems with Pseudo High Order Symplectic Integrator and Fast Lyapunov Indicator

Newtonian core-shell systems, as limiting cases of relativistic core-shell models under the two conditions of weak field and slow motion, could account for massive circumstellar dust shells and rings around certain types of star remnants. Because this kind of systems have Hamiltonians that can be split into a main part and a small perturbing part, a good choice of the numerical tool is the pseudo 8th order symplectic integrator of Laskar ＆ Robutel, and, to match the symplectic calculations, a good choice of chaos indicator is the fast Lyapunov indicator （FLI） with two nearby trajectories proposed by Wu, Huang ＆ Zhang. Numerical results show that the FLI is very powerful when describing not only the transition from regular motion to chaos but also the global structure of the phase space of the system.

On the Calculation of Lyapunov Indicators with Post-stabilization in a Weyl Field

We present details of a work aiming at the overestimation of Lyapunov exponents defined by the geodesic deviation equations in the previous work. The geodesic deviation vector with post-stabilization is used to compute the fast Lyapunov indicator, considered to be a very sensitive tool for discrimination between ordered or weakly chaotic motions. We make a detailed study of the dynamics in the superposed Weyl field between a black hole and shell of octopoles by using the fast Lyapunov indicator with the Poincare surface of section. In particular, we examine the effects on the dynamics around the fixed points, of varying one of the three parameters （specific energy E, specific angular momentum L and octopolar moment 0）, while keeping the other two fixed, and identify the intervals of the varying parameter where the motion is regular or chaotic.