Diffraction of gaussian beams by plane apertures: A different approach

Abstract

We first develop an integral equation formalism to solve the boundary value problems of the paraxial scalar wave equation when data, of the Dirichlet or Neumann type, are given on a closed surface S, in particular when S is a plane. Then, we show how this formalism can be used to analyse the scattering by perfectly conducting planes of paraxial waves, specially of Gaussian beams, and how it may be applied to paraxial wave diffraction by plane apertures. Finally, the diffraction of Gaussian beams by slits, rectangular and circular apertures is investigated.     

A class of partially coherent beams carrying optical vortices

A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.     

A class of polytropic flows in plane non-steady magneto-gasdynamics

The equations governing a certain class of non-steady isentropic conducting flows are reduced to an associated time-independent system. Adopting a complex-variable notation, solutions are then obtained in which the orthogonal trajectories to the fluid streamlines are ellipses or hyperbolae and the magnetic field lines are rectilinear. Further, flows are also derived in which the magnetic lines are parabolae having a common axis, while the orthogonal trajectories to the velocity streamlines are concentric ellipses.     

A class of parallel multiple‐front algorithms on subdomains

A class of parallel multiple‐front solution algorithms is developed for solving linear systems arising from discretization of boundary value problems and evolution problems. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill‐conditioning may occur due to differing material properties or the use of high degree finite elements (p methods). Next, the method is implemented on distributed‐memory multiprocessor systems with the final reduced (small) Schur complement problem solved on a single processor. A novel algorithm that implements a recursive partitioning approach on the subdomain interfaces is then developed. Both algorithms are implemented and compared in a least‐squares finite‐element scheme for viscous incompressible flow computation using h‐ and p‐finite element schemes. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical technique for solving truss and plane problems for a new class of elastic bodies

It is customary to use a displacement-based formulation to seek solutions to boundary value problemsfor its computational efficacy. In displacement-based formulations, it is convenient to prescribe the constitutiverelation for stress as an explicit function of displacement gradient. However, from a general theoretical pointof view, the stress and displacement gradient could be related by an implicit function. This study developstechniques to solve boundary value problems when linearized strain and stress are related by an implicitfunction. Here both the stresses and the displacement are taken as unknowns. The stress field is constructed suchthat it satisfies the equilibrium equations identically within the element and the traction continuity requirementsbetween the elements. A continuously differentiable displacement field is constructed, and the linearized strainis computed from this displacement field. Then, the unknown parameters in the stress and displacement fieldare estimated such that the constitutive relation holds in weak integral sense. Though in this procedure thenumber of unknowns has increased in comparison with the displacement formulation, both the strength andserviceability condition can be checked directly without any post-processing. Also, in this procedure, both theequilibrium equations and continuity of displacement are met exactly. The equation that is not satisfied exactlyis the constitutive relation, which is an approximation anyway. The efficacy and accuracy of this method arebenchmarked by studying some standard problems. Planar and three-dimensional truss elements have beendeveloped and benchmarked. Then, a rectangular plane element is implemented and its performance recorded.     

A natural partitioning scheme for parallel simulation of multibody systems

A parallel partitioning scheme based on physical-co-ordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent co-ordinates. Key features of the present scheme include an explicit determination of the independent co-ordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two-stage staggered solution procedure and a Schur complement based parallel preconditioned conjugate gradient numerical algorithm.     

A new method of shear stiffness prediction of periodic Timoshenko beams

This article interprets the new implementation of an asymptotic homogenization method for effective bending stiffness of heterogeneous beam structures with periodic microstructure along its axial direction in an intuitionistic way. With this interpretation, the authors then develop a new method of evaluating effective shear stiffness for their Timoshenko beam model. This method can be easily implemented numerically in commercial software. Different kinds of elements and modeling techniques available in commercial software can be applied to model the unit cell. Several examples are given to demonstrate the effectiveness of this new method.     

Dynamic elasto-plastic response of beams — A new model

A new approximate model to analyze the dynamic elasto-plastic large deformation response of beams is presented. The model beam is composed of two rigid parts interconnected by a gap of zero width which is built of fibers having an imaginary length. The imaginary length governs the strains and stresses in the beam, for equal deflections in the real and model beams, and is found to be almost constant in the elastic and elasto-plastic domains. The deflected shape is triangular because interest is focused on midspan deflection, while advanced existing models [13] can be used to determine the deflected shape. Comparison of predicted final deflections with test results show very good correspondence. Apart from the final deflection, which may easily be measured in tests, the model also calculates the time dependence of the dynamic reactions, bending moment and membrane force, displacement, velocity and acceleration as well as stress and strain distributions at selected times. Calculation of a complete response time history requires only a few seconds. The proposed model is extendable to various boundary conditions and load distributions and might be generalized to include strain hardening and rate effects.     

A class of plane self-similar motions of a non-newtonian fluid with nonlinear thermophysical properties

The plane self-similar solution of a set of complete equations for the dynamics of a nonlinearly viscous fluid aad the energy equation is obtained analytically with the temperature dependence of the transfer coefficients taken into account.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 1, pp. 129–136, January, 1985.     

A new boundary integral equation for notch problem of plane elasticity

A new boundary integral equation for the notch problem of plane elasticity is formulated in this paper. In the formulation, the distributed dislocation density is taken to be the unknown function and the resultant force function to be the right-hand term in the resulting integral equation. As a result the integral equation derived contains a logarithmic kernel. The equation is compact in form and convenient for computation. The accuracy of the method is demonstrated through a number of numerical examples.     

A new formulation of the plastic design problem for plane frames

Using a parametrie representation, it was proved in 1959¹ that the static and kinematic approaches to the plastic collapse problem are dual linear programming problems. In this paper, the generalized parameters used previously are given physical meaning and shown to be readily programmed for computer application. One important advantage of the method is that the equations can be written in general terms such that no assumptions regarding the structural from need to be built into the program. The application is extended to the more general problem of automatic plastic design and it is shown that the inclusion of a serviceability constraint (e.g. no plastic hinges at a given load factor) is trivial in this formulation. The difficult problem of several loading cases is shown to be readily, treated by designing for a given load factor for shakedown rather than plastic collapse. Thought this latter facility, by its dependence on elastic behavior, requires iteration of the stiffness of the structure, repaid convergence appears to be generally obtained. Finally a method is suggested whereby an adequate allowance for frame instability may be made without destroying the linearity of the equations. Thought the equations, as developed, have application to steel framed structures in mind, the extension to the limit design of reinforced concrete structures appears to present no addition complications.     

A promising new class of plasticine: Metallic plasticine

Soft, malleable, and non-dry on exposure in air are the typical features for plain plasticine, which lead plasticine to be widely used in many industrial fields and our daily life. As a kind of clay, poorly electric conductivity and thermal conductivity of plain plasticine seriously limit its applications. Therefore,synthesizing a kind of plasticine having metallic bond is of importance for extending its applications in some special cases, such as thermal-cooling medium, anti-static electricity, electromagnetic shielding,etc. Here, we report a novel GaInSnCdZn_2 alloy, which exhibits similar behavior as compared to those of plasticine at near room temperature(30–40℃), and a good electrical conductivity due to its nature of metal. This new GaInSnCdZn_2 alloy can be called as metallic plasticine that contains the near-eutectic structure with low melting point and the other relatively high melting point phases. In this metallic plasticine, the near-eutectic structure with low melting point plays the same role as the oily ingredient in plain plasticine, dominating the plastic deformation, while the other relatively high melting point phases act as the stuffing like the CaCO3 in plain plasticine. The creation of metallic plasticine offers a general strategy for designing/preparing a new class of plasticine which possesses both the nature of metal and plasticine.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

参数曲面与平面求交的一种新方法

本文提出了一种新的参数曲面与平面求交算法，基于平面的半空间性质，通过参数域平面的二向线性插值，将求交问题转化为一系列简单的离散、判断、比较、排序等运算，能较好的解决曲面片内的交线不连续和交线丢失问题，算法简便，可靠性好，计算精度高，在ＮＣ自动编程中具有广泛的应用场合。     

A variational approach to magneto-elastic buckling problems for systems of ferromagnetic or superconducting beams

Based upon a variational principle derived in a preceding paper, expressions for the magneto-elastic buckling values for ferromagnetic or superconducting systems are given. These relations are evaluated for systems of slender beams. Explicit buckling values are calculated for a single ferromagnetic or superconducting beam of arbitrary cross-section, and for systems of two parallel ferromagnetic or superconducting rods. In the analysis needed for the calculation of the intermediate (i.e., rigid-body) and the perturbed magnetic fields, an intensive use of methods inherent in the theory of complex functions is made. In conclusion our results for a set of two superconducting rods are compared with the results of a mathematically less complicated, but also less rigorous, theory.     

A new approach to the finite element modelling of beams with warping effect

As a first step toward developing a finite element formulation that can model coupling among extensional, bending and torsional behaviour of beams, a new method is proposed to properly represent the warping of arbitrary cross-sections. The basic approach is to introduce a small warping displacement superimposed over flat cross-sections of a shear-flexible beam in a deformed configuration. Numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach. The present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation.     

A new type of attractor in autonomous systems

We have studied the dynamic regimes of an autonomous chaotic system (a modified oscillator with inertial nonlinearity) and found a chaotic attractor of a new type. The autocorrelation function, power spectrum, and Lyapunov exponents of this attractor have been calculated. Some of these characteristics resemble the behavior of a strange nonchaotic attractor.     

Bulk metallic glasses: A new class of engineering materials

Bulk glass-forming alloys have emerged over the past fifteen years with attractive properties and technological promise. A number of alloy systems based on lanthanum, magnesium, zirconium, palladium, iron, cobalt and nickel have been discovered. Glass-forming ability depends on various factors like enthalpy of mixing, atomic size and multicomponent alloying. A number of processes is available to synthesise bulk metallic glasses. The crystallisation behaviour and mechanical properties of these alloys pose interesting scientific questions. Upon crystallisation many of these glasses transform to bulk nanocrystals and nanoquasicrystals. A detailed study of the structure and the crystallisation behaviour of glasses has enabled the elucidation of the possible atomic configuration in liquid alloys. Their crystallisation behaviour can be exploited to synthesise novel nanocomposite microstructures and their mechanical properties can be enhanced. A broad overview of the present status of the science and technology of bulk metallic glasses and their potential technological uses is presented.     

A new class of very efficient algorithms for local dimming

One of the main aspects of today’s computing, especially on mobile devices, is power consumption. It affects the lifetime of batteries and has ecological aspects. In the near future, a significant proportion of the energy of mobile devices will be spent on displays. Thus, dimming, especially local dimming of displays, increases the comfort of these mobile devices. A convenient side-effect of local dimming is contrast enhancement and a better black level. Local dimming has three main aspects: the image processing aspect, the optimization aspect of the core algorithm and real-time requirements. We deal with the optimizer part, also focusing on real-time aspects. In this article, a new class of generalized dimming algorithms GDA(n) is developed. This class depends on a single parameter, allowing us to steer between power efficiency and smoothness of the solution. The smoothness properties of the proposed algorithms allow them to be treated as regularizations of the sorted sector covering (SSC) algorithm. The SSC algorithm forms a foundation for our algorithms, and it will be described later in this article. The implementation of the proposed algorithms is quite simple, e.g. on the basis of an existing implementation of the SSC, and they are highly effective. Most important, their smoothness is an inherent part of the algorithm, thus reducing flickering effects before they are created. Numerical examples comparing GDA(n) to established algorithms are given, substantiating the efficiency and quality of the new method. By steering the parameter n, we can switch from a smooth distribution of the LED values (n small) to a volatile distribution of the LED values (n large), while preserving the required brightness of the backlight of the display. In the first case, we suppress LED flashlighting and, especially for videos, flickering. In the latter case we adapt the LED backlight better to the image brightness, obtaining dark LED values in dark areas of the image and bright LED values in bright areas of the image.