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geometric optics for One-Dimensional Schrodinger-Poisson System

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Chinese Annals of Mathematics,Series B 2006年第3期27卷 353-362页

作者： Zhifei ZHANG Qionglei CHEN School of Mathematical Sciences Peking University Beijing 100871 China. Institute of Applied Physics and Computational Mathematics Beijing 100088 China.

This paper considers a family of Schroedinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of th... 详细信息

关键词： Schrodinger-Poisson geometric optics Lagrangian integral

INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF geometric optics

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Acta Mathematica Scientia 2011年第6期31卷 2141-2158页

作者： Guy Mtivier Jeffrey Rauch Institut de Mathmatiques de Bordeaux Universit de Bordeaux Department of Mathematics University of Michigan

The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.

关键词： geometric optics profile equation localisation vector bundles propagation cones

Oscillation Modes of Weld Pool in Stationary GTA Welding Using Structure Laser Method

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Chinese Journal of Mechanical Engineering 2021年第5期34卷 243-258页

作者： Xingpei Wu Jiankang Huang Jing He Shien Liu Guangyin Liu Ding Fan School of Materials Science and Engineering Lanzhou University of TechnologyLanzhou 730050China Department of Mechanical Energy Engineering Southern University of Science and TechnologyShenzhen 518055China State Key Laboratory of Advanced Processing and Recycling of Non-Ferrous Metals Lanzhou University of TechnologyLanzhou 730050China

Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision ***,the deficiency of simulation software will result in significant capital *** simulations and experiments are performed in this study,and the Bessel equation is used to analyze the oscillation mode of a weld *** laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement *** oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser *** show that the simulated laser dot matrix images are consistent with the experiment *** oscillation mode of the weld pool can be recognized based on the laser dot matrix *** study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.

关键词： Weld pool surface GTA welding Bessel function Oscillation mode geometric optics

Energy flow in negative index materials

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Chinese optics Letters 2004年第7期2卷 428-430页

作者： Lorenzo Bolla Michele Midrio Carlo G.Someda The Istituto Nazionale per la Fisica della Materia (I. N. F. M.) Dipartimento di Ingegneria Elettrica Gestionale e Meccanica Universita degli Studi di Udine viale delle Scienze 208 33100 Udine Italy I. N. F. M. Dipartimento di Ingegneria dell'Informazione via G. Gradenigo 6/B 35131 Padova Italy

Prom Maxwell's equations, we compute the speed and the direction of propagation of active power refracted from air into a negative index material. We prove, both analytically and numerically that the power may refract positively even if phase fronts refract negatively. Considerations on the usage of ray optics in problems involving negative index materials are drawn.

关键词： geometric optics Negative index materials

Computation of High Frequency Wave Diffraction by a Half Plane via the Liouville Equation and geometric Theory of Diffraction

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Communications in Computational Physics 2008年第10期4卷 1106-1128页

作者： Shi Jin Dongsheng Yin Department of Mathematics University of WisconsinMadisonWI 53706USA Department ofMathematical Sciences TsinghuaUniversityBeijing 100084China

We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half *** first introduce a condition,based on the GTD theory,at the vertex of the half plane to account for the diffractions,and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville *** experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.

关键词： High frequency waves Liouville equation geometric theory of diffraction geometric optics

Ray transfer matrix perturbation for an optical component with aberration

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Chinese optics Letters 2012年第8期10卷 11-13页

作者： Jerry T.Barretto Clark Kendrick C.Go Stein Alec C.Baluyot Department of Physics School of Science and EngineeringAteneo de Manila University Department of Mathematics School of Science and EngineeringAteneo de Manila University

The perturbation theory of matrices is applied to ray transfer matrices （RTMs） to describe an optical component with aberration. A quantitative description of the perturbation extent corresponding to aberration strength is provided using condition numbers and absolute errors for the perturbed RTM. An application to a single small aberration is presented, and the results are compared with those of the diffraction theory of aberrations.

关键词： 080.0080 geometric optics 080.2720 Mathematical methods (general) 080.2730 Matrix methods in paraxial optics

Calculation of infrared properties of low emissivity coatings containing metallic flake pigments

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Chinese optics Letters 2013年第13期11卷 12-15页

作者：袁乐翁小龙邓龙江 State Key Laboratory of Electronic Thin Films and Integrated Devices University of Electronic Science and Technology of China Chengdu 610054 China

The infrared emissivity of low emissivity coating can be significantly reduced by adding high content concentrations of parallel distributed metallic flake pigment. However, the infrared emissivity is very difficult to calculate by the existing theory models, such as the light scattering theory and traditional Kubelka-Munk radiative transfer model, because of shape and distribution anisotropy of flake pigments. Thus, the low emissivity coating is assumed to be the superposition structure of homogeneous layers and metallic flakes are approximately uniform and parallel arrangement in each layer. Based on geometric optics theory and Kubelka＇s layer model, considering multiple reflection, transmission and absorption of infrared radiation among different layers, the theoretical model is established to calculate the coating emissivity. The facts of binder, pigment concentration and thickness are also systematic discussed. The result shows that the law of influence on infrared emissivity can be correctly simulated by this theoretical model. Transparent binder, high volume concentration of thin flake pigment can facilitate to reduce infrared emissivity. Moreover, this model offers the possibility of predicting the infrared optical properties of coatings by their optical constants.

关键词： 200.0200 optics in computing 350.0350 Other areas of optics 080.0080 geometric optics

Research of Millimeter-wave Shaped Offset Feed Dual-reflector Antenna

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Research of Millimeter-wave Shaped Offset Feed Dual-reflecto...