Nonsymmetrical System Research Articles

Propagation of elliptical Gaussian beams modulated by an elliptical annular aperture

An analytical propagation expression for a generalized astigmatic elliptical Gaussian beam (EGB) modulated by an elliptical annular aperture and passing through an axially nonsymmetrical optical system is obtained by the use of vector integration. The derived analytical results provide more convenience for studying the propagation and transformation of EGBs than the usual method of using the diffraction integral directly, and the efficiency of the numerical calculation is significantly improved. Some numerical simulations are illustrated for the propagation properties of EGBs passing through a free space with an elliptical annular aperture, an elliptical screen, or an elliptical aperture. Further extensions are also pointed out.

Propagation and transformation of flat-topped multi-Gaussian beams in a general nonsymmetrical apertured double-lens system

On the basis of expanding a hard-edged aperture function as a finite sum of complex Gaussian functions, an approximate analytical expression for the propagation of an input complex amplitude distribution passing through a general nonsymmetrical apertured double-lens system is derived. Then, the propagation result for two-dimensional flat-topped multi-Gaussian beams is given. It is shown that the apertured Lohmann's symmetrical double-lens system for fractional Fourier transform is a special case of the general apertured double-lens system. The numerical calculation, graphical illustration, and some discussions for the transformation of the two-dimensional flat-topped multi-Gaussian beam in apertured Lohmann's symmetrical double-lens systems are also presented.

Off-axial elliptical Hermite-cosh-Gaussian beams

A new kind of light beams named the off-axial elliptical Hermite-cosh-Gaussian beams (EHChGBs) is introduced in this paper by use of tensor method. An analytical propagation expression for an off-axial EHChGB passing through an axially nonsymmetrical optical ABCD system is derived by use of vector integration. The derived formula can be easily reduced to the propagation formulas of off-axial elliptical cosh-Gaussian beams and elliptical Hermite-cosh-Gaussian beams. Some numerical simulations are illustrated for the propagation properties of off-axial EHChGBs passing through a free space and a focusing optical system, and further extensions are suggested.

Propagation of decentered elliptical Gaussian beams in apertured and nonsymmetrical optical systems

A hard-edged elliptical aperture is described approximately by a tensor form, which can be expanded as a finite sum of complex Gaussian functions. An analytical propagation expression for a decentered elliptical Gaussian beam (DEGB) through an axially nonsymmetrical optical system with an elliptical aperture is derived by using vector integration. The approximate analytical results are compared with numerically integral ones, and it is shown that this method can significantly improve the efficiency of numerical calculation. Some numerical simulations are illustrated for the propagation properties of DEGBs through apertured and nonsymmetrical optical transforming systems.

Decentered controllable elliptical dark-hollow beams

A new kind of laser beam, named a decentered controllable elliptical dark-hollow beam (DCEDHB), is defined by a tensor method. The propagation formula for a DCEDHB through an axially nonsymmetrical optical system is derived by vector integration. The derived propagation formula could be reduced to the formula for a controllable elliptical dark-hollow beam (CEDHB) and a controllable dark-hollow beam (CDHB) under certain conditions. As an application example of the derived formula, the propagation characteristics of a DCEDHB in free space are calculated and discussed. As another example we study the propagation properties of coherent and incoherent beam combinations with radial array for DCEDHB.

First-and second-order sensitivities of beams with respect to cross-sectional cracks

This paper deals with a variational formulation for the sensitivity problem of beam systems in the context of deformable solids with cracks. Natural frequencies are defined as state variables involved in the energy functional of the system, while the crack's length and position are treated as system parameters. The hierarchical equation system is formed and solved for the first and second derivatives of the natural frequency functions with respect to the crack's length and position. An analytical procedure for calculations of the second-order sensitivities of natural frequencies is proposed for the non-symmetrical equation system operator. Numerical algorithms are worked out and implemented computationally. Analytical and numerical aspects of the problem are discussed in detail through a number of illustrative results.

Transient dynamics in electric power system with DC transmission: fractal growth in stability boundary

The paper is concerned with transient dynamics and stability of an electric power system with DC transmission. Nowadays, DC transmission systems are widely applied to conventional electric power systems. However, the transient dynamics of AC/DC power systems, affected by the active power that flows into DC transmissions, is not entirely understood. The paper derives a non-symmetrical swing equation system to analyse the transient dynamics of an AC/DC power system. The non-symmetry implies a unidirectional component of an external forcing that corresponds to both DC power and exciting power swing. The paper discusses a stability boundary and its qualitative change in the non-symmetrical swing equation system. An understanding of the stability boundary gives an important clue to the transient dynamics of AC/DC power systems. Fractal structure growth in the stability boundary caused by the change of DC power flow is described. The existence of a fractal boundary implies that the system behaviour becomes chaotic and unpredictable, depending on the operation of the DC transmission.

Decentered elliptical flattened Gaussian beam

A decentered flattened Gaussian beam (DEFGB), is defined by a tensor method. The propagation formula for a DEFGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a generalized decentered elliptical flattened Gaussian beam under certain condition. As an example application of the derived formula, the propagation characteristics of a DEFGB in free space are calculated and discussed. As another example we have studied the properties of superposition with radial array consisted by DEFGB.

Decentered elliptical Hermite-Gaussian beam.

A new kind of laser beam called the decentered elliptical Hermite-Gaussian beam (DEHGB) is defined by use of a tensor method. The propagation formula of the DEHGB passing through a nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be easily reduced to the propagation formula of an aligned elliptical Hermite-Gaussian beam and that of a decentered elliptical Gaussian beam under certain conditions. By use of this formula, the propagation characteristics of the DEHGB through free space are presented graphically. As application examples, we construct a generalized laser array using the DEHGB as the fundamental mode. We also obtain the decentered elliptical flattened Gaussian beam by expressing it as superposition of a series of DEHGBs by using polynomial expansion.

A Trefftz approach to computational mechanics

AbstractThis paper presents a Trefftz method for solving structural elasticity problems and flow problems of incompressible viscous fluids. The problem of unilateral contact is also dealt with. For each type of problem, Trefftz polynomials and associated variational formulations are given. Complex structures are studied by a sub‐structuring technique. This method requires the resolution of a non‐symmetrical linear system. It is shown that it is possible to take advantage of this Trefftz approximation in two ways: (i) the approach presented can be considered as a simplified method which enables a solution to be evaluated quickly; (ii) this approach also makes it possible to obtain a good quality solution associated with high degree polynomial bases. This method is adapted to optimization processes because the discretization of the structure requires only very few sub‐domains to build a good approximation and offers a great flexibility in use. Copyright © 2003 John Wiley & Sons, Ltd.

Decentered elliptical Gaussian beam.

A new kind of laser beam, called a decentered elliptical Gaussian beam (DEGB), is defined by a tensor method. The propagation formula for a DEGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a fundamental elliptical Gaussian beam and a decentered Gaussian beam under certain conditions. As an example application of the derived formula, the propagation characteristics of a DEGB in free space are calculated and discussed. As another example we study the properties of a generalized laser beam array constructed by use of a DEGB as the fundamental mode.

Measurement of Nonsymmetrical Electric Field Vector Distribution in Nitrobenzene Using Electrooptic Method

The three-dimensional nonuniform electric field vector distribution was measured in a nonsymmetrical electrode system using the Kerr electrooptic effect with the reconstruction technique modified by computed tomography (CT). The intensity of the light transmitted through a dielectric liquid in nonuniform field was detected at many points on one plane. It was found that the nonuniform electric field in the liquid can be measured three-dimensionally and visualized.

Group theoretical formulation of nonsymmetrical systems by the group supermatrix procedure

The group supermatrix procedure, developed by Zloković for systems with symmetry properties described by groups, can be also applied to systems without symmetry. Transformation of a nonsymmetrical system into a system with symmetry properties is accomplished by symmetrization of support conditions, by adding fictitious structural parts and by removing existing ones. The generalized displacements and forces in the above symmetrized system coincide with corresponding values in the nonsymmetrical system. The group supermatrix procedure performs the analysis for each G-invariant subspace separately, using only a part of the structure. This provides, in comparison with conventional methods, a drastic reduction in the amount of data input, computation and necessary memory space of the computer.

Fading statistics for intersatellite optical communication

The narrow beam widths associated with intersatellite optical communication links make such links susceptible to signal fading because of pointing jitter. Such fading can be aggravated by stationary offsets in pointing. We calculated the fade rates for the case of two spaceborne telescopes having Gaussian beam profiles, a pointing offset, and pointing jitter that can be described by Gaussian statistics. An integral solution is derived for the general case of a nonsymmetrical system, with and without pointing bias, and closed-form solutions are presented for the case of a symmetrical system (identical platforms and optics). These results show that, for a system with 3-dB margin, the rms pointing jitter must be held to less than 7% of the full beam width to keep the fade rate below once per year.

The Relation between Colloid Stability and Wetting

Surface forces acting between colloidal particles and in wetting films are considered. Wetting films, as distinct from colloids, represent a nonsymmetrical system bounded by a solid and a gas phase. The electrical potentials of solid-liquid and liquid-air interfaces can be different not only in value, but sometimes also in the sign causing the forces of electrostatic attraction. Particular attention has been given to the effect of structural forces. They play a dominant role in the region of contact angles at θ < 20° (hydrophilic repulsion forces) and at θ > 40° (hydrophobic attraction forces). The intermediate region corresponds to the field of application of the DLVO theory. The short-range hydrophobic forces in wetting films of water seem to be the same as in water interlayers between two hydrophobic surfaces. This may be explained by considering unstable wetting films to he disposed between two hydrophobic surfaces: the hydrophobic solid substrate and the hydrophobic water-air interface. It is suggested that lyophobic attraction forces can also exist in other polar liquids bounded by two low-energy nonwetting surfaces.

An error-free Levison algorithm to solve integer Toeplitz system

This paper presents an error-free form of Levison algorithm to solve integer nonsymmetrical Toeplitz system. It removes roundoff errors. Their accumulation can, when using classic algorithms, deteriorate or destroy the solution. It retains the speed of original Levison algorithms. Its modular form can be easily implemented for parallel computer.

Application Of Anamorphic Systems To Directional Pseudocolor Encoding

An optical nonsymmetrical imaging system composed of two anamorphic spectrum analyzers in cascade is implemented. This system can provide an undistorted final image in spite of the geometrical distortion effects in the intermediate Fourier plane. The introduction of chromatic sector filters in this plane provides a real-time technique to pseudocolor encode the spatial frequency information of a black-and-white transparency. In this way, greater discrimination is achieved in the angular orientation of object details that generate the same spatial frequencies. Experimental pseudocolored images, obtained with a symmetrical system and a nonsymmetrical system, of a black-and-white transparency are shown.

片ロッド油圧シリンダを有する電気油圧サーボ機構の高精度連続軌跡制御

This paper deals with the "Continuous Path" control method of a servomechanism with an electro-hydraulic servo valve and a nonsymmetrical cylinder. The nonsymmetrical cylinders have nonlinear characteristics such as piston displacement drift and a difference in speeds of the reciprocating motion due to their nonsymmetrical structure. Therefore, the application of an optimal servo system to a nonsymmetrical cylinder is difficult by reason of its linear theory. We have eliminated the nonlinearities from this cylinder system by utilizing the velocity feedback method. Experimental results suggest that the characteristics of the nonsymmetrical cylinder system compensated by velocity feedback are identical with the characteristics of the symmetrical cylinder system regarding the static and dynamic characteristics. In order to realize accurate CP control, an error system is applied to this compensated system. Therefore, it is verified from experimental results that the adoption of this optimal servomechanism serves to eliminate the position deviation, velocity deviation and acceleration deviation together in the steady state. Furthermore, as the parameters of the performance criterion can be denoted by physical coefficients, the relation between these coefficients and the characteristics of this optimal servo on the basis of computer simulations is indicated by using figures. Consequently, the characteristics of this optimal system can be clearly recOgnized, and designed simply.

Image forces and electron spectrum at the surface of liquid helium

On the basis of the longitudinal field Green function, in a three-layer non-symmetrical system of media with spatial dispersion the image-force potential is calculated for surfaces of the semi-infinite helium bath and a liquid helium film, and also for a surface of the phase-separated 3He 4He mixture. The dependence of the surface electron spectrum on the film thickness and on the pressing electric field strength is analyzed.

Electromagnetic Processes in AC/DC Power Converters: Part III---Nonsymmetrical Transient, Processes

The following problems of nonsymmetrical transient processes are discussed in the article: 1) Processes in a nonsymmetrical ac system (one-phase and two-phase faults, nonsymmetry of the firing angles, etc.). 2) Misfiring of the converter valve. 3) Arc-back process.