STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

Model Simplification and Parameter Modification for Offshore Platforms Using Experiment Data

In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of freedom. The simplified model can be obtained with modal reduction. Then the design sensitivity analysis of the eigenvalues and eigenvectors has been carried out using the modal frequency and modal shape of the test. A two-story frame structure and a jacket model structure have been calculated. Meanwhile, the modified coefficient, the FEM computational and experimental values have been given. It has been shown that the FEM model modified using the test modal value is efficient.

Horizontal Slow Oscillation of a Moored Tanker and Numerical Method of Hopf-Bifurcation

In this paper, a six-order nonlinear dynamic model with three degrees of freedom is presented for the study of the 'fishtail' motion of a Single Point Mooring System. The effect of parameter variations on the equilibrium state of the system is analyzed. In order to study the stability of the equilibrium state, the mooring-line length l is chosen as a bifurcation parameter, so that all eigenvalues of the Jacobian matrix under different parameters can be worked out, and then the Hopf-bifurcation point can be found. Finally, the Hopf-bifurcation periodic solution of the system is computed.

UNSTEADY TRANSONIC AERODYNAMIC LOADINGS ON THE AIRFOIL CAUSED BY HEAVING, PITCHING OSCILLATIONS AND CONTROL SURFACE

An implicit upwind finite volume solver for the Euler equations using the improved flux - splitting method is established and used to calculate the transonic flow past the airfoils with heaving, pitching oscillations and the control surface. Results are given for the NACA64A - 10 airfoil which is in harmonic heaving and pitching oscillation and with the control surface in the transonic flow field. Some computational results are compared with the experiment data and the good agreements are shown in the paper.

Model Simulation and Eigen-Analysis for Polarimetric Scattering from Tree Canopy in SAR Imagery

In this paper, a theoretical model of multi-level, non-spherical scatterers is developed for fully polarimetric scattering from tree canopy in SAR imaging at C band. The amplitude functions of non-spherical particles with randomly spatial orientation are derived by the generalized Rayleigh-Gans (GRG) approximation. The non-diagonal extinction matrix and the Mueller matrix solution are constructed. Numerical solutions of polarimetric scattering of four Stokes parameters from random, non-spherical scatterers are obtained. To physically identify polarimetric scattering of the Mueller matrix solution, the coherency matrix and its eigen-analysis are discussed. Functional dependence of the coherency matrix and entropy upon various parameters are obtained. As an application, the analysis of AirSAR images at P, L, C bands is discussed.

ON THE COMPUTATION OF THE MAIN EIGEN-PAIRS OF THE CONTINUOUS-TIME LINEAR QUADRATIC CONTROL PROBLEM

The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has been reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae = eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.

MATRIX INVESTIGATION ON ISAICHEV ORIENTATION RELATIONSHIP

By means of TEM technique the orientation relationships of cementite, precipitated from islands of granular bainite during tempering, with ferrite have been observed. By calculating the eigenvalues and eigenvectors of transformation matrix, Isaichev relationship has been analyzed. The results indicate that Isaichev relationship is indeed the sum of Kurdjumov-Sachs relationship and Pitsch relationship, so the viewpoint that the cementite with Isaichev relationship precipitates from austenite, instead of ferrite, was confirmed. Moreover, the matrix calculation shows that three reported orientation relationships among austenite, ferrite and cementite in pearlitic transformation cannot be simultaneously valid. (Edited author abstract) 4 Refs.

LARGE AMPLITUDE VIBRATION OF THIN ANNULAR PLATES

A pure analytic solution of the axisymmetric large amplitude free vibration of thin annualar plates is presented in this paper: By using the modified iteration method, we derive an analytic relation for the amplitudes vs. frequencies of vibrations. The present paper shows the great potentiality of this method to tackle the large amplitude vibration problems of plates.

New WKB method in supersymmetry quantum mechanics

In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersymmetric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.

MATRIX PERTURBATION METHOD FOR THE VIBRATION PROBLEM OF STRUCTURES WITH INTERVAL PARAMETERS

When the parameters of structures are uncertain, the structural natural frequencies become uncertain. The interval parameters description, i.e. the unknown-but bounded parameters description is one of the methods to study the uncertainty. In this paper, the vibration problem of structure with interval parameters was studied, and the eigenvalue problem of the structures with interval parameters was transferred into two different eigenvalue problems. The perturbation method was applied to the vibration problem of the structures with interval parameters. The numerical results show that the proposed method is sufficiently accurate and needs less computational efforts.

On time independent Schr?dinger equations in quantum mechanics by the homotopy analysis method

A general analytic approach,namely the homotopy analysis method(HAM),is applied to solve the time independent Schrodinger equations.Unlike perturbation method,the HAM-based approach does not depend on any small physical parameters,corresponding to small disturbances.Especially,it provides a convenient way to gain the convergent series solution of quantum mechanics.This study illustrates the advantages of this HAM-based approach over the traditional perturbative approach,and its general validity for the Schrodinger equations.Note that perturbation methods are widely used in quantum mechanics,but perturbation results are hardly convergent.This study suggests that the HAM might provide us a new,powerful alternative to gain convergent series solution for some complicated problems in quantum mechanics,including many-body problems,which can be directly compared with the experiment data to improve the accuracy of the experimental findings and/or physical theories.

ATTENUATION AND GROUP VELOCITY OF NORMAL MODE IN AN ISO-VELOCITY SHALLOW WATER

Proceeding from the eigenvalue equation of the normal mode in homogeneous shallow water, we derive several formulae calculating the mode attenuation and group velocity, and compare their accuracy by means of numerical results. The paper especially discusses the attenuation and the group velocity of critical mode in a Pekeris channel and shows that in general, the attenuation and the group velocity of the critical mode respectively are less than the absorption and the sound speed in the bot -torn . Therefore, the Kornhauser, Raney, Weston Tindle ' s conclusions are modified that the attenuation and the group velocity of the critical mode are exactly equal to the absorption and the sound speed in the bottom, respectively.

STABILITY EIGENFUNCTIONS OF A BOUNDARY-LAYER FLOW OVER VISCOELASTIC COMPLIANT WALL

The eigenfunctions in a stability problem of boundary-layer flow over a viscoelastic compliant wall were studied. Two categories of modes, TSI and CIFI, exist in the eigenvalue solutions. The eigenfunctions of flow-based TSI were investigated together with those in the flow over rigid wall, whereas the eigenfunctions of wall-based CIFI were compared with the wall functions in an individual wall without fluid constraint. The physical characteristics of the eigenmodes were discussed based on their eigenfunctions.

TEMPORAL EIGENVALUE SPECTRA OF BOUNDARY-LAYER FLOW OVER RIGID WALL AND COMPLIANT WALL

The temporal eigenvalue spectra of the equation system for the boundary-layer flows over both rigid wall compliant and viscoelastic compliant wall are numerically studied. In a rigid-wall case only the fluid-based eigenmodes, the Tollmien-Schlichting instability (TSI) mode, exist. In a compliant-wall case, both the TSI and wall-based compliance-induced instability flow instability (CIFI) modes occur. The variations of the two categories of eigenvalues at various wall material stiffness and damping are also displayed.

Nonlinear dynamics study of an open resonant Λ-type system

A way resulting in lasing without inversion （LWI） in an open resonant A-type system from a nonlinear dynamics viewpoint is investigated. The destabilization of the non-lasing solution can occur not only through pitchfork bifurcation, giving rise to continuous wave LWI, but also through Hopf bifurcation, giving rise to self-pulsing LWI. This is much different from that of the corresponding closed resonant A-type system in which the destabilization of the non-lasing solution can occur only through pitchfork bifurcation. The effects of the unsaturated gain coefficient, cavity loss coefficient, atomic injection and exit rates on the two bifurcations are discussed.

Coupling of two defect modes in photonic crystal fibers

The coupling characteristics of two defect modes in photonic crystal fibers are investigated theoretically by the finite-difference time-domain (FDTD) method. The transmission spectrum and eigenmodes of optical wave are found to be very sensitive to the geometrical and physical parameters of the structure, as well as to the relative position of the two defects.

Supermode analysis of seven-core photonic quasi-crystal fibers

We design custom-shaped modes for a sixfold symmetric photonic quasi-crystal fiber （PQF）, an optical fiber with a sixfold symmetric quasi-periodic array of air holes in the cladding region. The supermodes of the PQF are calculated by the finite element method, and the coupling of an in-phase supermode for the quasi-periodic optical fiber is numerically optimized to obtain identical values. The optimization is guaranteed by the selection of appropriate PQF design parameters. The eigenvalue equation associated with a seven-core PQF is derived from a coupled mode equation. We realize mode shaping and provide the far-field distribution mode of PQFs. The results are beneficial for the structural design and uniform distribution of the in-phase supermodes of PQFs.

Guided-mode resonances in multimode planar periodic waveguides

Using the effective medium theory and the waveguide eigenvalue equation,we design a multimode planar periodic waveguide.When a plane wave illuminates the grating at the designed angle and wavelength, more than one leaky modes are excited coincidentally.Then the reflection efficiency around this designed angle and wavelength is investigated using a rigorous coupled wave analysis formulation and a gap of reflection peaks is found.Electric field distributions reveal that this high reflectivity gap is due to the coupling between these two coincidentally excited leaky modes.