Derivations of Vector Area and Volume Elements in Curved Coordinate Systems for Flux Vector Fields Helping Eye Disease

Our aim in this paper is to interest retinal eye specialists in preventing dry macula degeneration by a special flurry vector field through open or closed curved surfaces. The flux of vector fields through surfaces is based on vector element area and volume element. Therefore, we explain a few geometrical derivations of area and volume elements in curved orthogonal coordinate systems. We hope that by derivation of a spatial vector field flurry against drusen through open or closed surfaces due to the Gauss theorem might select drusen under eye retina cells without destroying the cells and prevent macula degeneration. A changed flurry of a magnetic or electric vector field through a closed line causes an electric or magnetic vector field on the surface closed by the line. We also hope that derivation by Stokes’ and Greens’ theorems, with the help of iron, might help eye cells to get in life.

Construction analysis on integral lifting of steel structure by the vector form intrinsic finite element

A newnumerical method based on vector form intrinsic finite element（VFIFE） is proposed to simulate the integral lifting process of steel structures. First, in order to verify the validity of the VFIFE method, taking the steel gallery between the integrated building and the attached building of Nanjing M obile Communication Buildings for example, the static analysis was carried out and the corresponding results were compared with the results achieved by the traditional finite element method. Then, according to the characteristics of dynamic construction of steel structure integral lifting, the tension cable element was employed to simulate the behavior of dynamic construction. The VFIFE method avoids the iterative solution of the stiffness matrix and the singularity problems. Therefore, it is simple to simulate the complete process of steel structure lifting construction.Finally, by using the VFIFE, the displacement and internal force time history curves of the steel structures under different lifting speeds are obtained. The results show that the lifting speed has influence on the lifting force, the internal force, and the displacement of the structure. In the case of normal lifting speed, the dynamic magnification factor of 1. 5 is safe and reasonable for practical application.

Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element(VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method(FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

THE CLOSED-FORM SOLUTION OF VECTOR FINITE ELEMENT INTEGRAL EQUATIONS FOR THREE DIMENSIONAL ELECTROMAGNETIC ANALYSIS

In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing the open region problems,the first-order Absorbing Boundary Condition(ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form.Based on the formulas,the hybrid Expanded Cholesky Method(ECM) and MultiFrontal algorithm(MF) is applied to solve finite element equations.Using the closed-form solution,the elec-tromagnetic field of three dimensional targets can be studied sententiously and accurately.Simulation results show that the presented formulas are successfully and concise,which can be easily used to analyze three dimensional electromagnetic problems.

A method for generating double-ring-shaped vector beams

We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam–Berry phase（PBP） optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases.

Three-dimensional arbitrarily anisotropic modeling for time-domain airborne electromagnetic surveys

Electrically anisotropic strata are abundant in nature, so their study can help our data interpretation and our understanding of the processes of geodynamics. However, current data processing generally assumes isotropic conditions when surveying anisotropic structures, which may cause discrepancies between reality and electromagnetic data interpretation. Moreover, the anisotropic interpretation of the time-domain airborne electromagnetic （TDAEM） method is still confined to one dimensional （1D） cases, and the corresponding three-dimensional （3D） numerical simulations are still in development. In this study, we expanded the 3D TDAEM modeling of arbitrarily anisotropic media. First, through coordinate rotation of isotropic conductivity, we obtained the conductivity tensor of an arbitrary anisotropic rock. Next, we incorporated this into Maxwell＇s equations, using a regular hexahedral grid of vector finite elements to subdivide the solution area. A direct solver software package provided the solution for the sparse linear equations that resulted. Analytical solutions were used to verify the accuracy and feasibility of the algorithm. The proven model was then applied to analyze the effects of arbitrary anisotropy in 3D TDAEM via the distribution of responses and amplitude changes, which revealed that different anisotropy situations strongly affected the responses of TDAEM.

Optimization of highly nonlinear dispersion-flattened photonic crystal fiber for supercontinuum generation

A simple type of photonic crystal fiber （PCF） for supercontinuum generation is proposed for the first time. The proposed PCF is composed of a solid silica core and a cladding with square lattice uniform elliptical air holes, which offers not only a large nonlinear coefficient but also a high birefringence and low leakage losses. The PCF with nonlinear coefficient as large as 46 W-1 · km-1 at the wavelength of 1.55 um and a total dispersion as low as ±2.5 ps. nm-1 · km -1 over an ultra-broad waveband range of the S-C-L band （wavelength from 1.46 um to 1.625 um） is optimized by adjusting its structure parameter, such as the lattice constant A, the air-filling fraction f, and the air-hole ellipticity η. The novel PCF with ultra-flattened dispersion, highly nonlinear coefficient, and nearly zero negative dispersion slope will offer a possibility of efficient super-continuum generation in telecommunication windows using a few ps pulses.

Stress and modal birefringence of single-mode specialty optical fibers with three-stress regions

Stress-induced birefringence and modal birefringence of single-mode specialty optical fibers with three stress regions are numerically analyzed by the vector finite element method. Stress distribution and stress-induced birefringence distribution of three kinds of optical fibers with different cross structures are presented and compared, and the influence on the stress- induced birefringence by temperature change are analyzed as well. The results show that the fibers with three-stress regions have a lower linear birefringence, which is very important for the fabrication of the circular polaxization-maintalning fiber with high performance drawn from the same fiber preform by using the spinning method.

Experimental and Numerical Analysis of Surface Magneto-Hydrodynamic Propulsion Induced by NdFeB Magnets

The so-called surface Magneto-hydro-dynamic(MHD)propulsion relies on the Lorentz force induced in weak electrolyte solutions(such as seawater or plasma)by NdFeB Magnets.The Lorentz force plays an important role in such dynamics as it directly affects the structures of flow boundary layers.Previous studies have mainly focused on the development of such boundary layers and related fluid-dynamic aspects.The main focus of the present study is the determination of electromagnetic field distributions around the propulsion units.In particular dedicated experiments and numerical simulations(based on the finite volume method)are conducted considering a NACA0012 airfoil immersed in seawater.The results show that,along the propulsion unit,the field strength undergoes a rapid attenuation in the direction perpendicular to the wall.

FLOW AROUND A CIRCULAR CYLINDER USING A FINITE-VOLUME TVD SCHEME BASED ON A VECTOR TRANSFORMATION APPROACH

Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solving the Unsteady Reynolds-Averaged Navier-Stokes（URANS） equations.An Elemental Velocity Vector Transformation（EVVT） approach is proposed for the local normal and tangential velocity transformation at the interfaces of main and satellite elements.The presented method is validated by comparing with the available experimental data and numerical results.It is shown that the two-dimensional TVD finite volume method with the Renormalization Group（RNG） turbulence model can be used to determine hydrodynamic forces and captures vortex shedding characteristics very well.

Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method

Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method(IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters. Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève(K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.