Geometrical optics model of Mie resonances
Roll; Schweiger
2000-07-01
The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.
Geometrical optics modeling of the grating-slit test.
Liang, Chao-Wen; Sasian, Jose
2007-02-19
A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.
Strahler, Alan H.; Jupp, David L. B.
1990-01-01
Geometric-optical discrete-element mathematical models for forest canopies have been developed using the Boolean logic and models of Serra. The geometric-optical approach is considered to be particularly well suited to describing the bidirectional reflectance of forest woodland canopies, where the concentration of leaf material within crowns and the resulting between-tree gaps make plane-parallel, radiative-transfer models inappropriate. The approach leads to invertible formulations, in which the spatial and directional variance provides the means for remote estimation of tree crown size, shape, and total cover from remotedly sensed imagery.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Bakker schut, T.C.; Bakker Schut, Tom C.; Hesselink, Gerlo; Hesselink, Gerlo; de Grooth, B.G.; Greve, Jan
1991-01-01
We have developed a computer program based on the geometrical optics approach proposed by Roosen to calculate the forces on dielectric spheres in focused laser beams. We have explicitly taken into account the polarization of the laser light and thd divergence of the laser beam. The model can be used
International Nuclear Information System (INIS)
Liang, Hongbo; You, Shijun; Zhang, Huan
2016-01-01
A PTC (parabolic trough solar collector) focuses direct solar radiation reflected by the reflector onto a receiver located on its focal line. The solar flux distribution on the absorber is non-uniform generally, thus it needs to carry out optical simulation to analyze the concentrated flux density and optical performance. In this paper, three different optical models based on ray tracing for a PTC were proposed and compared in detail. They were proved to be feasible and reliable in comparison with other literature. Model 1 was based on MCM (Monte Carlo Method). Model 2 initialized photon distribution with FVM (Finite Volume Method), and calculated reflection, transmission, and absorption by means of MCM. Model 3 utilized FVM to determine ray positions initially, while it changed the photon energy by multiplying reflectivity, transmissivity and absorptivity. The runtime and computation effort of Model 3 were approximately 40% and 60% of that of Model 1 in the present work. Moreover, the simulation result of Model 3 was not affected by the algorithm for generating random numbers, however, it needed to take account of suitable grid configurations for different sections of the system. Additionally, effects of varying the geometric parameters for a PTC on optical efficiency were estimated. Effect of offsetting the absorber in width direction of aperture was greater than that in its normal direction at the same offset distance, which was more obvious with offset distance increasing. Furthermore, absorber offset at the opposite direction of tracking error was beneficial for improving optical performance. The larger rim angle (≤90°) was, the less sensitive optical efficiency was to tracking error for the same aperture width of a PTC. In contrast, a larger aperture width was more sensitive to tracking error for a certain rim angle. - Highlights: • Three different optical models for parabolic trough solar collectors were derived. • Their running time, computation
Optical traps with geometric aberrations
International Nuclear Information System (INIS)
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.
2006-01-01
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems
Expression of the degree of polarization based on the geometrical optics pBRDF model.
Wang, Kai; Zhu, Jingping; Liu, Hong; Du, Bingzheng
2017-02-01
An expression of the degree of polarization (DOP) based on the geometrical optics polarimetric bidirectional reflectance distribution function model is presented. In this expression, the DOP is related to the surface roughness and decreases at different reflection angles because diffuse reflection is taken into consideration. A shadowing/masking function introduced into the specular reflection expression makes the DOP values decrease as the angle of incidence or observation approaches grazing. Different kinds of materials were measured to validate the accuracy of this DOP expression. The measured results suggest that the errors of the DOP are reduced significantly, and the polarized reflection characteristics can be described more reasonably and accurately.
Strahler, Alan H.; Li, Xiao-Wen; Jupp, David L. B.
1991-01-01
The bidirectional radiance or reflectance of a forest or woodland can be modeled using principles of geometric optics and Boolean models for random sets in a three dimensional space. This model may be defined at two levels, the scene includes four components; sunlight and shadowed canopy, and sunlit and shadowed background. The reflectance of the scene is modeled as the sum of the reflectances of the individual components as weighted by their areal proportions in the field of view. At the leaf level, the canopy envelope is an assemblage of leaves, and thus the reflectance is a function of the areal proportions of sunlit and shadowed leaf, and sunlit and shadowed background. Because the proportions of scene components are dependent upon the directions of irradiance and exitance, the model accounts for the hotspot that is well known in leaf and tree canopies.
Directory of Open Access Journals (Sweden)
Congrong Li
2015-08-01
Full Text Available Forest canopy leaf area index (LAI inversion based on remote sensing data is an important method to obtain LAI. Currently, the most widely-used model to achieve forest canopy structure parameters is the Li-Strahler geometric-optical bidirectional reflectance model, by considering the effect of crown shape and mutual shadowing, which is referred to as the GOMS model. However, it is difficult to retrieve LAI through the GOMS model directly because LAI is not a fundamental parameter of the model. In this study, a gap probability model was used to obtain the relationship between the canopy structure parameter nR2 and LAI. Thus, LAI was introduced into the GOMS model as an independent variable by replacing nR2 The modified GOMS (MGOMS model was validated by application to Dayekou in the Heihe River Basin of China. The LAI retrieved using the MGOMS model with optical multi-angle remote sensing data, high spatial resolution images and field-measured data was in good agreement with the field-measured LAI, with an R-square (R2 of 0.64, and an RMSE of 0.67. The results demonstrate that the MGOMS model obtained by replacing the canopy structure parameter nR2 of the GOMS model with LAI can be used to invert LAI directly and precisely.
Geometrical optics in general relativity
Loinger, A.
2006-01-01
General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
Munro, Peter R T; Ignatyev, Konstantin; Speller, Robert D; Olivo, Alessandro
2010-03-01
X-ray phase contrast imaging is a very promising technique which may lead to significant advancements in medical imaging. One of the impediments to the clinical implementation of the technique is the general requirement to have an x-ray source of high coherence. The radiation physics group at UCL is currently developing an x-ray phase contrast imaging technique which works with laboratory x-ray sources. Validation of the system requires extensive modelling of relatively large samples of tissue. To aid this, we have undertaken a study of when geometrical optics may be employed to model the system in order to avoid the need to perform a computationally expensive wave optics calculation. In this paper, we derive the relationship between the geometrical and wave optics model for our system imaging an infinite cylinder. From this model we are able to draw conclusions regarding the general applicability of the geometrical optics approximation.
Effects of source shape on the numerical aperture factor with a geometrical-optics model.
Wan, Der-Shen; Schmit, Joanna; Novak, Erik
2004-04-01
We study the effects of an extended light source on the calibration of an interference microscope, also referred to as an optical profiler. Theoretical and experimental numerical aperture (NA) factors for circular and linear light sources along with collimated laser illumination demonstrate that the shape of the light source or effective aperture cone is critical for a correct NA factor calculation. In practice, more-accurate results for the NA factor are obtained when a linear approximation to the filament light source shape is used in a geometric model. We show that previously measured and derived NA factors show some discrepancies because a circular rather than linear approximation to the filament source was used in the modeling.
Problems in Geometrical Optics
Joyce, L. S.
1973-01-01
Ten laboratory exercises on optics are described to clarify concepts involving point objects and converging lenses producing real images. Mathematical treatment is kept to a minimum to stress concepts involved. (PS)
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Vergence, Vision, and Geometric Optics
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Geometrical optics and optimal transport.
Rubinstein, Jacob; Wolansky, Gershon
2017-10-01
The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Coated sphere scattering by geometric optics approximation.
Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang
2014-10-01
A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.
International Nuclear Information System (INIS)
Luo, Yongqiang; Zhang, Ling; Wu, Jing; Wang, Xiliang; Liu, Zhongbing; Wu, Zhenghong
2017-01-01
A system model that can accurately simulate the instantaneous solar transmittance through multilayer glazing façade (MGF) and shading device can provide a solid foundation for the thermal and daylighting performance calculation of MGF as well as indoor visual comfort evaluation. Traditional optical models for venetian blind and glazing façade meet with their limitations to analyze new prototype of shading blind like photovoltaic (PV) blind which has quite different surface optical properties compared with conventional venetian blind. The present study proposed a new system model for MGF using shading blind with arbitrary geometrical and optical features which is suitable for a wide range of applications. Three major calculation types for modeling of shading blinds cover all the possible situations in application. Guess Integer-Valued Function is adopted for delivering a general description on direct radiation transport. The direct-direct, direct-diffuse and diffuse-diffuse radiation transports are separately considered. A series of experiments were carried out to validate the model under various parameter settings and different weather conditions. Parametric study revealed some new findings in the evaluations of influence of ambient radiation situations, geometrical and optical features of blind space on both solar transmittance and solar absorption by blind layer. - Highlights: • Solar transport through glazing façades with PV blind with arbitrary geometry is simulated. • Ray-tracing and radiosity method are coupled in calculation. • Guess Integer-Valued Function is used in calculation of direct radiation transport. • Experiment and simulated data are compared for model validation. • Parametric study is conducted for evaluating the impact of different factors on the system.
Geometrical optics and the diffraction phenomenon
International Nuclear Information System (INIS)
Timofeev, Aleksandr V
2005-01-01
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
MODELING AND SIMULATION OF HIGH RESOLUTION OPTICAL REMOTE SENSING SATELLITE GEOMETRIC CHAIN
Directory of Open Access Journals (Sweden)
Z. Xia
2018-04-01
Full Text Available The high resolution satellite with the longer focal length and the larger aperture has been widely used in georeferencing of the observed scene in recent years. The consistent end to end model of high resolution remote sensing satellite geometric chain is presented, which consists of the scene, the three line array camera, the platform including attitude and position information, the time system and the processing algorithm. The integrated design of the camera and the star tracker is considered and the simulation method of the geolocation accuracy is put forward by introduce the new index of the angle between the camera and the star tracker. The model is validated by the geolocation accuracy simulation according to the test method of the ZY-3 satellite imagery rigorously. The simulation results show that the geolocation accuracy is within 25m, which is highly consistent with the test results. The geolocation accuracy can be improved about 7 m by the integrated design. The model combined with the simulation method is applicable to the geolocation accuracy estimate before the satellite launching.
Advances on geometric flux optical design method
García-Botella, Ángel; Fernández-Balbuena, Antonio Álvarez; Vázquez, Daniel
2017-09-01
Nonimaging optics is focused on the study of methods to design concentrators or illuminators systems. It can be included in the area of photometry and radiometry and it is governed by the laws of geometrical optics. The field vector method, which starts with the definition of the irradiance vector E, is one of the techniques used in nonimaging optics. Called "Geometrical flux vector" it has provide ideal designs. The main property of this model is, its ability to estimate how radiant energy is transferred by the optical system, from the concepts of field line, flux tube and pseudopotential surface, overcoming traditional raytrace methods. Nevertheless this model has been developed only at an academic level, where characteristic optical parameters are ideal not real and the studied geometries are simple. The main objective of the present paper is the application of the vector field method to the analysis and design of real concentration and illumination systems. We propose the development of a calculation tool for optical simulations by vector field, using algorithms based on Fermat`s principle, as an alternative to traditional tools for optical simulations by raytrace, based on reflection and refraction law. This new tool provides, first, traditional simulations results: efficiency, illuminance/irradiance calculations, angular distribution of light- with lower computation time, photometrical information needs about a few tens of field lines, in comparison with million rays needed nowadays. On the other hand the tool will provides new information as vector field maps produced by the system, composed by field lines and quasipotential surfaces. We show our first results with the vector field simulation tool.
Thomas Young's contributions to geometrical optics.
Atchison, David A; Charman, W Neil
2011-07-01
In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young's construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics. © 2011 The Authors. Clinical and Experimental Optometry © 2011 Optometrists Association Australia.
A Practical Guide to Experimental Geometrical Optics
Garbovskiy, Yuriy A.; Glushchenko, Anatoliy V.
2017-12-01
Preface; 1. Markets of optical materials, components, accessories, light sources and detectors; 2. Introduction to optical experiments: light producing, light managing, light detection and measuring; 3. Light detectors based on semiconductors: photoresistors, photodiodes in a photo-galvanic regime. Principles of operation and measurements; 4. Linear light detectors based on photodiodes; 5. Basic laws of geometrical optics: experimental verification; 6. Converging and diverging thin lenses; 7. Thick lenses; 8. Lens systems; 9. Simple optical instruments I: the eye and the magnifier, eyepieces and telescopes; 10. Simple optical instruments II: light illuminators and microscope; 11. Spherical mirrors; 12. Introduction to optical aberrations; 13. Elements of optical radiometry; 14. Cylindrical lenses and vials; 15. Methods of geometrical optics to measure refractive index; 16. Dispersion of light and prism spectroscope; 17. Elements of computer aided optical design; Index.
Geometrical model of multiple production
International Nuclear Information System (INIS)
Chikovani, Z.E.; Jenkovszky, L.L.; Kvaratshelia, T.M.; Struminskij, B.V.
1988-01-01
The relation between geometrical and KNO-scaling and their violation is studied in a geometrical model of multiple production of hadrons. Predictions concerning the behaviour of correlation coefficients at future accelerators are given
Zeng, Y.; Schaepman, M.E.; Wu, B.; Clevers, J.G.P.W.; Bregt, A.K.
2008-01-01
We use the Li-Strahler geometric-optical model combined with a scaling-based approach to detect forest structural changes in the Three Gorges region of China. The physical-based Li-Strahler model can be inverted to retrieve forest structural properties. One of the main input variables for the
A practical guide to experimental geometrical optics
Garbovskiy, Yuriy A
2017-01-01
A concise, yet deep introduction to experimental, geometrical optics, this book begins with fundamental concepts and then develops the practical skills and research techniques routinely used in modern laboratories. Suitable for students, researchers and optical engineers, this accessible text teaches readers how to build their own optical laboratory and to design and perform optical experiments. It uses a hands-on approach which fills a gap between theory-based textbooks and laboratory manuals, allowing the reader to develop their practical skills in this interdisciplinary field, and also explores the ways in which this knowledge can be applied to the design and production of commercial optical devices. Including supplementary online resources to help readers track and evaluate their experimental results, this text is the ideal companion for anyone with a practical interest in experimental geometrical optics.
Accurate geometrical optics model for single-lens stereovision system using a prism.
Cui, Xiaoyu; Lim, Kah Bin; Guo, Qiyong; Wang, DaoLei
2012-09-01
In this paper, we proposed a new method for analyzing the image formation of a prism. The prism was considered as a single optical system composed of some planes. By analyzing each plane individually and then combining them together, we derived a transformation matrix which can express the relationship between an object point and its image by the refraction of a prism. We also explained how to use this matrix for epipolar geometry and three-dimensional point reconstruction. Our method is based on optical geometry and could be used in a multiocular prism. Experimentation results are presented to prove the accuracy of our method is better than former researchers' and is comparable with that of the multicamera stereovision system.
Analysis of NN amplitudes up to 2.5 GeV: an optical model and geometric interpretation
International Nuclear Information System (INIS)
Geramb, H.V. von; Universitaet Hamburg, Hamburg,; Amos, K.A.; Labes, H.; Sander, M.
1998-01-01
We analyse the SM97 partial wave amplitudes for nucleon-nucleon (NN) scattering to 2.5 GeV, in which resonance and meson production effects are evident for energies above pion production threshold. Our analyses are based upon boson exchange or quantum inversion potentials with which the sub-threshold data are fit perfectly. Above 300 MeV they are extrapolations, to which complex short ranged Gaussian potentials are added in the spirit of the optical models of nuclear physics and of diffraction models of high energy physics. The data to 2.5 GeV are all well fit. The energy dependences of these Gaussians are very smooth save for precise effects caused by the known Δ and N* resonances. With this approach, we confirm that the geometrical implications of the profile function found from diffraction scattering are pertinent in the regime 300 MeV to 2.5 GeV and that the overwhelming part of meson production comes from the QCD sector of the nucleons when they have a separation of their centres of 1 to 1.2 fm. This analysis shows that the elastic NN scattering data above 300 MeV can be understood with a local potential operator as well as has the data below 300 MeV
Kotsari, Constantina; Smyrnaiou, Zacharoula
2017-01-01
The central roles that modelling plays in the processes of scientific enquiry and that models play as the outcomes of that enquiry are well established (Gilbert & Boulter, 1998). Besides, there are considerable similarities between the processes and outcomes of science and technology (Cinar, 2016). In this study, we discuss how the use of…
Geometrical optics in correlated imaging systems
International Nuclear Information System (INIS)
Cao Dezhong; Xiong Jun; Wang Kaige
2005-01-01
We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging
Plasma geometric optics analysis and computation
International Nuclear Information System (INIS)
Smith, T.M.
1983-01-01
Important practical applications in the generation, manipulation, and diagnosis of laboratory thermonuclear plasmas have created a need for elaborate computational capabilities in the study of high frequency wave propagation in plasmas. A reduced description of such waves suitable for digital computation is provided by the theory of plasma geometric optics. The existing theory is beset by a variety of special cases in which the straightforward analytical approach fails, and has been formulated with little attention to problems of numerical implementation of that analysis. The standard field equations are derived for the first time from kinetic theory. A discussion of certain terms previously, and erroneously, omitted from the expansion of the plasma constitutive relation is given. A powerful but little known computational prescription for determining the geometric optics field in the neighborhood of caustic singularities is rigorously developed, and a boundary layer analysis for the asymptotic matching of the plasma geometric optics field across caustic singularities is performed for the first time with considerable generality. A proper treatment of birefringence is detailed, wherein a breakdown of the fundamental perturbation theory is identified and circumvented. A general ray tracing computer code suitable for applications to radiation heating and diagnostic problems is presented and described
Digital polarization holography advancing geometrical phase optics.
De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R
2016-08-08
Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed.
Light scattering in porous materials: Geometrical optics and stereological approach
International Nuclear Information System (INIS)
Malinka, Aleksey V.
2014-01-01
Porous material has been considered from the point of view of stereology (geometrical statistics), as a two-phase random mixture of solid material and air. Considered are the materials having the refractive index with the real part that differs notably from unit and the imaginary part much less than unit. Light scattering in such materials has been described using geometrical optics. These two – the geometrical optics laws and the stereological approach – allow one to obtain the inherent optical properties of such a porous material, which are basic in the radiative transfer theory: the photon survival probability, the scattering phase function, and the polarization properties (Mueller matrix). In this work these characteristics are expressed through the refractive index of the material and the random chord length distribution. The obtained results are compared with the traditional approach, modeling the porous material as a pack of particles of different shapes. - Highlights: • Porous material has been considered from the point of view of stereology. • Properties of a two-phase random mixture of solid material and air are considered. • Light scattering in such materials has been described using geometrical optics. • The inherent optical properties of such a porous material have been obtained
Geometric-optical illusions at isoluminance.
Hamburger, Kai; Hansen, Thorsten; Gegenfurtner, Karl R
2007-12-01
The idea of a largely segregated processing of color and form was initially supported by observations that geometric-optical illusions vanish under isoluminance. However, this finding is inconsistent with some psychophysical studies and also with physiological evidence showing that color and luminance are processed together by largely overlapping sets of neurons in the LGN, in V1, and in extrastriate areas. Here we examined the strength of nine geometric-optical illusions under isoluminance (Delboeuf, Ebbinghaus, Hering, Judd, Müller-Lyer, Poggendorff, Ponzo, Vertical, Zöllner). Subjects interactively manipulated computer-generated line drawings to counteract the illusory effect. In all cases, illusions presented under isoluminance (both for colors drawn from the cardinal L-M or S-(L+M) directions of DKL color space) were as effective as the luminance versions (both for high and low contrast). The magnitudes of the illusion effects were highly correlated across subjects for the different conditions. In two additional experiments we determined that the strong illusions observed under isoluminance were not due to individual deviations from the photometric point of isoluminance or due to chromatic aberrations. Our findings show that our conscious percept is affected similarly for both isoluminance and luminance conditions, suggesting that the joint processing for chromatic and luminance defined contours may extend well beyond early visual areas.
Two solvable problems of planar geometrical optics.
Borghero, Francesco; Bozis, George
2006-12-01
In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.
Rayleigh's hypothesis and the geometrical optics limit.
Elfouhaily, Tanos; Hahn, Thomas
2006-09-22
The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.
Geometrical charged-particle optics. 2. ed.
International Nuclear Information System (INIS)
Rose, Harald
2013-01-01
Provides a unique theoretical treatment of charged-particle optics. Displays novel unpublished results on several topics. Provides insight into the properties of charged-particle devices. Treats wave optical properties of the electron. Presents the resolution limit of electron microscopes and novel theoretical treatment of the Stern-Gerlach effect. This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern
Wang, Cong; Du, Hua-qiang; Zhou, Guo-mo; Xu, Xiao-jun; Sun, Shao-bo; Gao, Guo-long
2015-05-01
This research focused on the application of remotely sensed imagery from unmanned aerial vehicle (UAV) with high spatial resolution for the estimation of crown closure of moso bamboo forest based on the geometric-optical model, and analyzed the influence of unconstrained and fully constrained linear spectral mixture analysis (SMA) on the accuracy of the estimated results. The results demonstrated that the combination of UAV remotely sensed imagery and geometric-optical model could, to some degrees, achieve the estimation of crown closure. However, the different SMA methods led to significant differentiation in the estimation accuracy. Compared with unconstrained SMA, the fully constrained linear SMA method resulted in higher accuracy of the estimated values, with the coefficient of determination (R2) of 0.63 at 0.01 level, against the measured values acquired during the field survey. Root mean square error (RMSE) of approximate 0.04 was low, indicating that the usage of fully constrained linear SMA could bring about better results in crown closure estimation, which was closer to the actual condition in moso bamboo forest.
A fast method for linear waves based on geometrical optics
Stolk, C.C.
2009-01-01
We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the
Active Learning Environment with Lenses in Geometric Optics
Tural, Güner
2015-01-01
Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…
One step geometrical calibration method for optical coherence tomography
International Nuclear Information System (INIS)
Díaz, Jesús Díaz; Ortmaier, Tobias; Stritzel, Jenny; Rahlves, Maik; Reithmeier, Eduard; Roth, Bernhard; Majdani, Omid
2016-01-01
We present a novel one-step calibration methodology for geometrical distortion correction for optical coherence tomography (OCT). A calibration standard especially designed for OCT is introduced, which consists of an array of inverse pyramidal structures. The use of multiple landmarks situated on four different height levels on the pyramids allow performing a 3D geometrical calibration. The calibration procedure itself is based on a parametric model of the OCT beam propagation. It is validated by experimental results and enables the reduction of systematic errors by more than one order of magnitude. In future, our results can improve OCT image reconstruction and interpretation for medical applications such as real time monitoring of surgery. (paper)
Life Science-Related Physics Laboratory on Geometrical Optics
Edwards, T. H.; And Others
1975-01-01
Describes a laboratory experiment on geometrical optics designed for life science majors in a noncalculus introductory physics course. The thin lens equation is used by the students to calculate the focal length of the lens necessary to correct a myopic condition in an optical bench simulation of a human eye. (Author/MLH)
Salah, Wa'el; Sanchez del Rio, Manuel
2011-05-01
The layout and the optical performance of the SGM branch of the D09 bending-magnet beamline, under construction at SESAME, are presented. The beamline is based on the Dragon-type design and delivers photons over the spectral range 15-250 eV. One fixed entrance slit and a movable exit slit are used. The performance of the beamline has been characterized by calculating the mirror reflectivities and the grating efficiencies. The flux and resolution were calculated by ray-tracing using SHADOW. The grating diffraction efficiencies were calculated using the GRADIF code. The results and the overall shapes of the predicted curves are in reasonable agreement with those obtained using an analytical formula.
Resonant inelastic scattering by use of geometrical optics.
Schulte, Jörg; Schweiger, Gustav
2003-02-01
We investigate the inelastic scattering on spherical particles that contain one concentric inclusion in the case of input and output resonances, using a geometrical optics method. The excitation of resonances is included in geometrical optics by use of the concept of tunneled rays. To get a quantitative description of optical tunneling on spherical surfaces, we derive appropriate Fresnel-type reflection and transmission coefficients for the tunneled rays. We calculate the inelastic scattering cross section in the case of input and output resonances and investigate the influence of the distribution of the active material in the particle as well as the influence of the inclusion on inelastic scattering.
Geometrical and wave optics of paraxial beams.
Meron, M; Viccaro, P J; Lin, B
1999-06-01
Most calculational techniques used to evaluate beam propagation are geared towards either fully coherent or fully incoherent beams. The intermediate partial-coherence regime, while in principle known for a long time, has received comparably little attention so far. The resulting shortage of adequate calculational techniques is currently being felt in the realm of x-ray optics where, with the advent of third generation synchrotron light sources, partially coherent beams become increasingly common. The purpose of this paper is to present a calculational approach which, utilizing a "variance matrix" representation of paraxial beams, allows for a straightforward evaluation of wave propagation through an optical system. Being capable of dealing with an arbitrary degree of coherence, this approach covers the whole range from wave to ray optics, in a seamless fashion.
Stress measurement in thin films by geometrical optics
Rossnagel, S. M.; Gilstrap, P.; Rujkorakarn, R.
1982-01-01
A variation of Newton's rings experiment is proposed for measuring film stress. The procedure described, the geometrical optics method, is used to measure radii of curvature for a series of film depositions with Ta, Al, and Mo films. The method has a sensitivity of 1 x 10 to the 9th dyn/sq cm, corresponding to the practical radius limit of about 50 m, and a repeatability usually within five percent. For the purposes of comparison, radii are also measured by Newton's rings method and the Talysurf method; all results are found to be in general agreement. Measurement times are also compared: the geometrical optics method requires only 1/2-1 minute. It is concluded that the geometrical optics method provides an inexpensive, fast, and a reasonably correct technique with which to measure stresses in film.
Maillard, Philippe; Gomes, Marília F.
2016-06-01
This article presents an original algorithm created to detect and count trees in orchards using very high resolution images. The algorithm is based on an adaptation of the "template matching" image processing approach, in which the template is based on a "geometricaloptical" model created from a series of parameters, such as illumination angles, maximum and ambient radiance, and tree size specifications. The algorithm is tested on four images from different regions of the world and different crop types. These images all have the GoogleEarth application. Results show that the algorithm is very efficient at detecting and counting trees as long as their spectral and spatial characteristics are relatively constant. For walnut, mango and orange trees, the overall accuracy was clearly above 90%. However, the overall success rate for apple trees fell under 75%. It appears that the openness of the apple tree crown is most probably responsible for this poorer result. The algorithm is fully explained with a step-by-step description. At this stage, the algorithm still requires quite a bit of user interaction. The automatic determination of most of the required parameters is under development.
Geometrical-optics approximation of forward scattering by coated particles.
Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang
2004-03-20
By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.
Geometrical optics of dense aerosols: forming dense plasma slabs.
Hay, Michael J; Valeo, Ernest J; Fisch, Nathaniel J
2013-11-01
Assembling a freestanding, sharp-edged slab of homogeneous material that is much denser than gas, but much more rarefied than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed field, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the finite particle density reduces the effective Stokes number of the flow, a critical result for controlled focusing.
Comparisons between geometrical optics and Lorenz-Mie theory
Ungut, A.; Grehan, G.; Gouesbet, G.
1981-01-01
Both the Lorenz-Mie and geometrical optics theories are used in calculating the scattered light patterns produced by transparent spherical particles over a wide range of diameters, between 1.0 and 100 microns, and for the range of forward scattering angles from zero to 20 deg. A detailed comparison of the results shows the greater accuracy of the geometrical optics theory in the forward direction. Emphasis is given to the simultaneous sizing and velocimetry of particles by means of pedestal calibration methods.
Renormgroup symmetries in problems of nonlinear geometrical optics
International Nuclear Information System (INIS)
Kovalev, V.F.
1996-01-01
Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)
SOME PROPERTIES OF GEOMETRIC DEA MODELS
Directory of Open Access Journals (Sweden)
Ozren Despić
2013-02-01
Full Text Available Some specific geometric data envelopment analysis (DEA models are well known to the researchers in DEA through so-called multiplicative or log-linear efficiency models. Valuable properties of these models were noted by several authors but the models still remain somewhat obscure and rarely used in practice. The purpose of this paper is to show from a mathematical perspective where the geometric DEA fits in relation to the classical DEA, and to provide a brief overview of some benefits in using geometric DEA in practice of decision making and/or efficiency measurement.
Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.
Liu, Yichao; Sun, Fei; He, Sailing
2018-01-11
In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
Geometrical analysis of the interacting boson model
International Nuclear Information System (INIS)
Dieperink, A.E.L.
1983-01-01
The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)
Geometric optical transfer function and tis computation method
International Nuclear Information System (INIS)
Wang Qi
1992-01-01
Geometric Optical Transfer Function formula is derived after expound some content to be easily ignored, and the computation method is given with Bessel function of order zero and numerical integration and Spline interpolation. The method is of advantage to ensure accuracy and to save calculation
Advanced Geometric Optics on a Programmable Pocket Calculator.
Nussbaum, Allen
1979-01-01
Presents a ray-tracing procedure based on some ideas of Herzberger and the matrix approach to geometrical optics. This method, which can be implemented on a programmable pocket calculator, applies to any conic surface, including paraboloids, spheres, and planes. (Author/GA)
Complementary Huygens principle for geometrical and nongeometrical optics
International Nuclear Information System (INIS)
Luis, Alfredo
2007-01-01
We develop a fundamental principle depicting the generalized ray formulation of optics provided by the Wigner function. This principle is formally identical to the Huygens-Fresnel principle but in terms of opposite concepts, rays instead of waves, and incoherent superpositions instead of coherent ones. This ray picture naturally includes diffraction and interference, and provides a geometrical picture of the degree of coherence
The Zoom Lens: A Case Study in Geometrical Optics.
Cheville, Alan; Scepanovic, Misa
2002-01-01
Introduces a case study on a motion picture company considering the purchase of a newly developed zoom lens in which students act as the engineers designing the zoom lens based on the criteria of company's specifications. Focuses on geometrical optics. Includes teaching notes and classroom management strategies. (YDS)
Geometrical approach to fluid models
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Schep, T.J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics
A geometric morphometric assessment of the optic cup in glaucoma.
Sanfilippo, Paul G; Cardini, Andrea; Sigal, Ian A; Ruddle, Jonathan B; Chua, Brian E; Hewitt, Alex W; Mackey, David A
2010-09-01
The morphologic appearance of the optic disc is of interest in glaucoma. In contrast to descriptive classification systems that are currently used, a quantitative approach to the analysis of optic disc morphology is required. Our goal was to determine the optimal method for quantifying optic cup shape by comparing traditional (ovality, form-factor and neuroretinal rim (NRR) width ratio) and geometric morphometric approaches. Left optic disc stereophotographs of 160 (80 normal and 80 glaucomatous (stratified by severity)) subjects were examined. The optic cup margins were stereoscopically delineated with a custom tracing system and saved as a series of discrete points. The geometric morphometric methods of elliptic Fourier analysis (EFA) and sliding semi-landmark analysis (SSLA) were used to eliminate variation unrelated to shape (e.g. size) and yield a series of shape variables. Differences in optic cup shape between normal and glaucoma groups were investigated. Discriminant functions were computed and the sensitivity and specificity of each technique determined. Receiver operator characteristic (ROC) curves were calculated for all methods and evaluated in their potential to discriminate between normal and glaucomatous eyes based on the shape variables. All geometric morphometric methods revealed differences between normal and glaucomatous eyes in optic cup shape, in addition to the traditional parameters of ovality, form-factor and NRR width ratio (pgeometric morphometric approach for discriminating between normal and glaucomatous eyes in optic cup shape is superior to that provided by traditional single parameter shape measures. Such analytical techniques could be incorporated into future automated optic disc screening modalities. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Geometric phases in astigmatic optical modes of arbitrary order
International Nuclear Information System (INIS)
Habraken, Steven J. M.; Nienhuis, Gerard
2010-01-01
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
A Circumzenithal Arc to Study Optics Concepts with Geometrical Optics
Isik, Hakan
2017-01-01
This paper describes the formation of a circumzenithal arc for the purpose of teaching light and optics. A circumzenithal arc, an optic formation rarely witnessed by people, is formed in this study using a water-filled cylindrical glass illuminated by sunlight. Sunlight refracted at the top and side surfaces of the glass of water is dispersed into…
Geometrical model for the electron
International Nuclear Information System (INIS)
El-Sherbini, T.M.
1985-07-01
A model for an electron of finite dimensions is proposed. This model disregards the concept of electronic charge and leads to Bohr's frequency formula for the hydrogen atom and to Maxwell's equations for electromagnetic fields. The stability of a free electron under the action of centrifugal and transverse forces is discussed. (author)
Geometric characteristics of aberrations of plane-symmetric optical systems
International Nuclear Information System (INIS)
Lu Lijun; Deng Zhiyong
2009-01-01
The geometric characteristics of aberrations of plane-symmetric optical systems are studied in detail with a wave-aberration theory. It is dealt with as an extension of the Seidel aberrations to realize a consistent aberration theory from axially symmetric to plane-symmetric systems. The aberration distribution is analyzed with the spot diagram of a ray and an aberration curve. Moreover, the root-mean-square value and the centroid of aberration distribution are discussed. The numerical results are obtained with the focusing optics of a toroidal mirror at grazing incidence.
Homogenous isotropic invisible cloak based on geometrical optics.
Sun, Jingbo; Zhou, Ji; Kang, Lei
2008-10-27
Invisible cloak derived from the coordinate transformation requires its constitutive material to be anisotropic. In this work, we present a cloak of graded-index isotropic material based on the geometrical optics theory. The cloak is realized by concentric multilayered structure with designed refractive index to achieve the low-scattering and smooth power-flow. Full-wave simulations on such a design of a cylindrical cloak are performed to demonstrate the cloaking ability to incident wave of any polarization. Using normal nature material with isotropy and low absorption, the cloak shows light on a practical path to stealth technology, especially that in the optical range.
Geometrical aspects in optical wave-packet dynamics.
Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
2006-12-01
We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry's phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.
Evaluation of Geometrical Modulation Transfer Function in Optical Lens System
Directory of Open Access Journals (Sweden)
Cheng-Mu Tsai
2015-01-01
Full Text Available This paper presents ray tracing algorithms to evaluate the geometrical modulation transfer function (GMTF of optical lens system. There are two kinds of ray tracings methods that can be applied to help simulate the point spread function (PSF in the image plane, for example, paraxial optics and real ray tracings. The paraxial optics ray tracing is used to calculate the first-order properties such as the effective focal length (EFL and the entrance pupil position through less cost of computation. However, the PSF could have a large tolerance by only using paraxial optics ray tracing for simulation. Some formulas for real ray tracing are applied in the sagittal and tangential line spread function (LSF. The algorithms are developed to demonstrate the simulation of LSF. Finally, the GMTF is evaluated after the fast Fourier transform (FFT of the LSF.
Geometric Models for Collaborative Search and Filtering
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
Geometrical efficiency in computerized tomography: generalized model
International Nuclear Information System (INIS)
Costa, P.R.; Robilotta, C.C.
1992-01-01
A simplified model for producing sensitivity and exposure profiles in computerized tomographic system was recently developed allowing the forecast of profiles behaviour in the rotation center of the system. The generalization of this model for some point of the image plane was described, and the geometrical efficiency could be evaluated. (C.G.C.)
Barrett, Harrison H; Myers, Kyle J; Caucci, Luca
2014-08-17
A fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular and wavelength variables. The mean of this random process is the spectral radiance. The principle of conservation of radiance then allows a full characterization of the noise in the image (conditional on viewing a specified object). To elucidate these connections, we first review the definitions and basic properties of radiance as defined in terms of geometrical optics, radiology, physical optics and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Then we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors. The relation between the radiance and the statistical properties of the detector output is discussed and related to task-based measures of image quality and the information content of a single detected photon.
Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays.
Anttu, Nicklas
2013-03-01
Semiconductor nanowire arrays have shown promise for next-generation photovoltaics and photodetection, but enhanced understanding of the light-nanowire interaction is still needed. Here, we study theoretically the absorption of light in an array of vertical InP nanowires by moving continuously, first from the electrostatic limit to the nanophotonic regime and then to the geometrical optics limit. We show how the absorption per volume of semiconductor material in the array can be varied by a factor of 200, ranging from 10 times weaker to 20 times stronger than in a bulk semiconductor sample.
Refraction at a curved dielectric interface - Geometrical optics solution
Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.
1982-01-01
The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.
Invisibility Cloaking Based on Geometrical Optics for Visible Light
Ichikawa, H.; Oura, M.; Taoda, T.
2013-06-01
Optical cloaking has been one of unattainable dreams and just a subject in fiction until recently. Several different approaches to cloaking have been proposed and demonstrated: stealth technology, active camouflage and transformation optics. The last one would be the most formal approach modifying electromagnetic field around an object to be cloaked with metamaterials. While cloaking based on transformation optics, though valid only at single frequency, is experimentally demonstrated in microwave region, its operation in visible spectrum is still distant from realisation mainly owing to difficulty in fabricating metamaterial structure whose elements are much smaller than wavelength of light. Here we show that achromatic optical cloaking in visible spectrum is possible with the mere principle based on geometrical optics. In combining a pair of polarising beam splitters and right-angled prisms, rays of light to be obstructed by an object can make a detour to an observer, while unobstructed rays go straight through two polarising beam splitters. What is observed eventually through the device is simply background image as if nothing exists in between.
The Young-Laplace equation links capillarity with geometrical optics
International Nuclear Information System (INIS)
Rodriguez-Valverde, M A; Cabrerizo-Vilchez, M A; Hidalgo-Alvarez, R
2003-01-01
Analogies in physics are unusual coincidences that can be very useful to solve problems and to clarify some theoretical concepts. Apart from their own curiosity, analogies are attractive tools because they reduce the abstraction of some complex phenomena in such a way that these can be understood by means of other phenomena closer to daily experience. Usually, two analogous systems share a common aspect, like the movement of particles or transport of matter. On account of this, the analogy presented is exceptional since the involved phenomena are a priori disjoined. The most important equation of capillarity, the Young-Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates the optic power of a thick lens to its geometry and the properties of the media
Analyser-based phase contrast image reconstruction using geometrical optics
International Nuclear Information System (INIS)
Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A
2007-01-01
Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 μm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser
Analyser-based phase contrast image reconstruction using geometrical optics.
Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A
2007-07-21
Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser.
Geometrical scaling vs factorizable eikonal models
Kiang, D
1975-01-01
Among various theoretical explanations or interpretations for the experimental data on the differential cross-sections of elastic proton-proton scattering at CERN ISR, the following two seem to be most remarkable: A) the excellent agreement of the Chou-Yang model prediction of d sigma /dt with data at square root s=53 GeV, B) the general manifestation of geometrical scaling (GS). The paper confronts GS with eikonal models with factorizable opaqueness, with special emphasis on the Chou-Yang model. (12 refs).
Geometric Modelling of Octagonal Lamp Poles
Chan, T. O.; Lichti, D. D.
2014-06-01
Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.
Optical approximation in the theory of geometric impedance
International Nuclear Information System (INIS)
Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.
2007-02-01
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
Maj, Omar
2004-01-01
The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...
Liu, Hong; Zhu, Jingping; Wang, Kai
2015-08-24
The geometrical attenuation model given by Blinn was widely used in the geometrical optics bidirectional reflectance distribution function (BRDF) models. Blinn's geometrical attenuation model based on symmetrical V-groove assumption and ray scalar theory causes obvious inaccuracies in BRDF curves and negatives the effects of polarization. Aiming at these questions, a modified polarized geometrical attenuation model based on random surface microfacet theory is presented by combining of masking and shadowing effects and polarized effect. The p-polarized, s-polarized and unpolarized geometrical attenuation functions are given in their separate expressions and are validated with experimental data of two samples. It shows that the modified polarized geometrical attenuation function reaches better physical rationality, improves the precision of BRDF model, and widens the applications for different polarization.
Hyde, M W; Schmidt, J D; Havrilla, M J
2009-11-23
A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.
Accretion disc boundary layers - geometrically and optically thin case
International Nuclear Information System (INIS)
Regev, Oded; Hougerat, A.A.
1988-01-01
The method of matched asymptotic expansions is applied to an optically and geometrically thin boundary layer between an accretion disc and the accreting star. Analytical solutions are presented for a particular viscosity prescription in the boundary layer. For a typical example we find that the disc closely resembles standard steady-disc theory. It is identical to it everywhere save a narrow boundary layer, where the temperature increases rapidly inward (by an order of magnitude), the angular velocity achieves maximum and decreases to its surface value and other variables also undergo rapid changes. This and previous work can now be used to calculate the emission from accretion discs including the boundary layers for a wide range of parameters. (author)
General analysis of slab lasers using geometrical optics.
Chung, Te-yuan; Bass, Michael
2007-02-01
A thorough and general geometrical optics analysis of a slab-shaped laser gain medium is presented. The length and thickness ratio is critical if one is to achieve the maximum utilization of absorbed pump power by the laser light in such a medium; e.g., the fill factor inside the slab is to be maximized. We point out that the conditions for a fill factor equal to 1, laser light entering and exiting parallel to the length of the slab, and Brewster angle incidence on the entrance and exit faces cannot all be satisfied at the same time. Deformed slabs are also studied. Deformation along the width direction of the largest surfaces is shown to significantly reduce the fill factor that is possible.
Uncertainty in visual processes predicts geometrical optical illusions.
Fermüller, Cornelia; Malm, Henrik
2004-03-01
It is proposed in this paper that many geometrical optical illusions, as well as illusory patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections of lines, or local image movement must be derived. However, there are many sources of noise or uncertainty in the formation and processing of images, and they cause problems in the estimation of these features; in particular, they cause bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. The bias occurs with any visual processing of line features; under average conditions it is not large enough to be noticeable, but illusory patterns are such that the bias is highly pronounced. Thus, the broader message of this paper is that there is a general uncertainty principle which governs the workings of vision systems, and optical illusions are an artifact of this principle.
International Nuclear Information System (INIS)
Franklin, J.; Duncan, J.; Huete, A.R.; Leeuwen, W.J.D. van; Li, X.; Bégué, A.
1994-01-01
To use optical remote sensing to monitor land surface-climate interactions over large areas, algorithms must be developed to relate multispectral measurements to key variables controlling the exchange of matter (water, carbon dioxide) and energy between the land surface and the atmosphere. The proportion of the ground covered by vegetation and the interception of photosynthetically active radiation (PAR) by vegetation are examples of two variables related to evapotranspiration and primary production, respectively. An areal-proportion model of the multispectral reflectance of shrub savanna, composed of scattered shrubs with a grass, forb or soil understory, predicted the reflectance of two 0.5 km 2 sites as the area-weighted average of the shrub and understory or ‘background’ reflectances. Although the shaded crown and shaded background have darker reflectances, ignoring them in the area-weighted model is not serious when shrub cover is low and solar zenith angle is small. A submodel predicted the reflectance of the shrub crown as a function of the foliage reflectance and amount of plant material within the crown, and the background reflectance scattered or transmitted through canopy gaps (referred to as a soil—plant ‘spectral interaction’ term). One may be able to combine these two models to estimate both the fraction of vegetation cover and interception of PAR by green vegetation in a shrub savanna. (author)
Kim, Hwi; Min, Sung-Wook; Lee, Byoungho
2008-12-01
Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.
Geometrical basis for the Standard Model
Potter, Franklin
1994-02-01
The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary plane C 2, the quaternion space Q, and the real space R 4—as well as the real space R 3 uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge group SU(2) L × U(1) Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The ( u, d) and ( c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/ c 2, the b' quark at 80 GeV/ c 2, and the t' quark at 2600 GeV/ c 2.
Geometric Model of a Coronal Cavity
Kucera, Therese A.; Gibson, S. E.; Ratawicki, D.; Dove, J.; deToma, G.; Hao, J.; Hudson, H. S.; Marque, C.; McIntosh, P. S.; Reeves, K. K.;
2010-01-01
We observed a coronal cavity from August 8-18 2007 during a multi-instrument observing campaign organized under the auspices of the International Heliophysical Year (IHY). Here we present initial efforts to model the cavity with a geometrical streamer-cavity model. The model is based the white-light streamer mode] of Gibson et a]. (2003 ), which has been enhanced by the addition of a cavity and the capability to model EUV and X-ray emission. The cavity is modeled with an elliptical cross-section and Gaussian fall-off in length and width inside the streamer. Density and temperature can be varied in the streamer and cavity and constrained via comparison with data. Although this model is purely morphological, it allows for three-dimensional, multi-temperature analysis and characterization of the data, which can then provide constraints for future physical modeling. Initial comparisons to STEREO/EUVI images of the cavity and streamer show that the model can provide a good fit to the data. This work is part of the effort of the International Space Science Institute International Team on Prominence Cavities
A Wave-Optics Approach to Paraxial Geometrical Laws Based on Continuity at Boundaries
Linares, J.; Nistal, M. C.
2011-01-01
We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for…
Geometrical optics in general relativity: A study of the higher order corrections
International Nuclear Information System (INIS)
Anile, A.M.
1976-01-01
The higher order corrections to geometrical optics are studied in general relativity for an electromagnetic test wave. An explicit expression is found for the average energy--momentum tensor which takes into account the first-order corrections. Finally the first-order corrections to the well-known area-intensity law of geometrical optics are derived
Induced subgraph searching for geometric model fitting
Xiao, Fan; Xiao, Guobao; Yan, Yan; Wang, Xing; Wang, Hanzi
2017-11-01
In this paper, we propose a novel model fitting method based on graphs to fit and segment multiple-structure data. In the graph constructed on data, each model instance is represented as an induced subgraph. Following the idea of pursuing the maximum consensus, the multiple geometric model fitting problem is formulated as searching for a set of induced subgraphs including the maximum union set of vertices. After the generation and refinement of the induced subgraphs that represent the model hypotheses, the searching process is conducted on the "qualified" subgraphs. Multiple model instances can be simultaneously estimated by solving a converted problem. Then, we introduce the energy evaluation function to determine the number of model instances in data. The proposed method is able to effectively estimate the number and the parameters of model instances in data severely corrupted by outliers and noises. Experimental results on synthetic data and real images validate the favorable performance of the proposed method compared with several state-of-the-art fitting methods.
Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics.
Cheng, Dewen; Wang, Yongtian; Xu, Chen; Song, Weitao; Jin, Guofan
2014-08-25
Small thickness and light weight are two important requirements for a see-through near-eye display which are achieved in this paper by using two advanced technologies: geometrical waveguide and freeform optics. A major problem associated with the geometrical waveguide is the stray light which can severely degrade the display quality. The causes and solutions to this problem are thoroughly studied. A mathematical model of the waveguide is established and a non-sequential ray tracing algorithm is developed, which enable us to carefully examine the stray light of the planar waveguide and explore a global searching method to find an optimum design with the least amount of stray light. A projection optics using freeform surfaces on a wedge shaped prism is also designed. The near-eye display integrating the projection optics and the waveguide has a field of view of 28°, an exit pupil diameter of 9.6mm and an exit pupil distance of 20mm. In our final design, the proportion of the stray light energy over the image output energy of the waveguide is reduced to 2%, the modulation transfer function values across the entire field of the eyepiece are above 0.5 at 30 line pairs/mm (lps/mm). A proof-of-concept prototype of the proposed geometrical waveguide near-eye display is developed and demonstrated.
Different optical properties in different periodic slot cavity geometrical morphologies
Zhou, Jing; Shen, Meng; Du, Lan; Deng, Caisong; Ni, Haibin; Wang, Ming
2016-09-01
In this paper, optical properties of two-dimensional periodic annular slot cavity arrays in hexagonal close-packing on a silica substrate are theoretically characterized by finite difference time domain (FDTD) simulation method. By simulating reflectance spectra, electric field distribution, and charge distribution, we confirm that multiple cylindrical surface plasmon resonances can be excited in annular inclined slot cavities by linearly polarized light, in which the four reflectance dips are attributed to Fabry-Perot cavity resonances in the coaxial cavity. A coaxial waveguide mode TE11 will exist in these annular cavities, and the wavelengths of these reflectance dips are effectively tailored by changing the geometrical pattern of slot cavity and the dielectric materials filled in the cavities. These resonant wavelengths are localized in annular cavities with large electric field enhancement and dissipate gradually due to metal loss. The formation of an absorption peak can be explained from the aspect of phase matching conditions. We observed that the proposed structure can be tuned over the broad spectral range of 600-4000 nm by changing the outer and inner radii of the annular gaps, gap surface topography. Meanwhile, different lengths of the cavity may cause the shift of resonance dips. Also, we study the field enhancement at different vertical locations of the slit. In addition, dielectric materials filling in the annular gaps will result in a shift of the resonance wavelengths, which make the annular cavities good candidates for refractive index sensors. The refractive index sensitivity of annular cavities can also be tuned by the geometry size and the media around the cavity. Annular cavities with novel applications can be implied as surface enhanced Raman spectra substrates, refractive index sensors, nano-lasers, and optical trappers. Project supported by the National Natural Science Foundation of China (Grant No. 61178044), the Natural Science Foundation
Two-dimensional fast marching for geometrical optics.
Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore
2014-11-03
We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.
Geometrical-optics approximation of forward scattering by gradient-index spheres.
Li, Xiangzhen; Han, Xiang'e; Li, Renxian; Jiang, Huifen
2007-08-01
By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.
Geometrical optics approach in liquid crystal films with three-dimensional director variations.
Panasyuk, G; Kelly, J; Gartland, E C; Allender, D W
2003-04-01
A formal geometrical optics approach (GOA) to the optics of nematic liquid crystals whose optic axis (director) varies in more than one dimension is described. The GOA is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example, the GOA is applied to the calculation of light transmittance for the case of a liquid crystal cell which exhibits the homeotropic to multidomainlike transition (HMD cell). Properties of the GOA solution are explored, and comparison with the Jones calculus solution is also made. For variations on a smaller scale, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating light transmittance. The results of light transmittance calculations for the HMD cell based on the director patterns provided by two methods, direct computer calculation and a previously developed simplified model, are in good agreement.
Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.
Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang
2016-10-31
Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.
Geometric modeling for computer aided design
Schwing, James L.; Olariu, Stephen
1995-01-01
The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes.
Geometrical-optics code for computing the optical properties of large dielectric spheres.
Zhou, Xiaobing; Li, Shusun; Stamnes, Knut
2003-07-20
Absorption of electromagnetic radiation by absorptive dielectric spheres such as snow grains in the near-infrared part of the solar spectrum cannot be neglected when radiative properties of snow are computed. Thus a new, to our knowledge, geometrical-optics code is developed to compute scattering and absorption cross sections of large dielectric particles of arbitrary complex refractive index. The number of internal reflections and transmissions are truncated on the basis of the ratio of the irradiance incident at the nth interface to the irradiance incident at the first interface for a specific optical ray. Thus the truncation number is a function of the angle of incidence. Phase functions for both near- and far-field absorption and scattering of electromagnetic radiation are calculated directly at any desired scattering angle by using a hybrid algorithm based on the bisection and Newton-Raphson methods. With these methods a large sphere's absorption and scattering properties of light can be calculated for any wavelength from the ultraviolet to the microwave regions. Assuming that large snow meltclusters (1-cm order), observed ubiquitously in the snow cover during summer, can be characterized as spheres, one may compute absorption and scattering efficiencies and the scattering phase function on the basis of this geometrical-optics method. A geometrical-optics method for sphere (GOMsphere) code is developed and tested against Wiscombe's Mie scattering code (MIE0) and a Monte Carlo code for a range of size parameters. GOMsphere can be combined with MIE0 to calculate the single-scattering properties of dielectric spheres of any size.
Miyazaki, Hideki T; Miyazaki, Hiroshi; Miyano, Kenjiro
2003-09-01
We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40 degrees to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by
Depth-of-field effects in wiggler radiation sources: Geometrical versus wave optics
Directory of Open Access Journals (Sweden)
Richard P. Walker
2017-02-01
Full Text Available A detailed analysis is carried out of the optical properties of synchrotron radiation emitted by multipole wigglers, concentrating on the effective source size and brightness and the so-called “depth of field” effects, concerning which there has been some controversy in the literature. By comparing calculations made with both geometrical optics and wave optics methods we demonstrate that the two approaches are not at variance, and that the wave optics results tend towards those of geometrical optics under well-defined conditions.
Park, Bum Jun; Furst, Eric M
2014-09-23
We present the optical trapping forces that are generated when a single laser beam strongly focuses on a coated dielectric microsphere. On the basis of geometrical optics approximation (GOA), in which a particle intercepts all of the rays that make up a single laser beam, we calculate the trapping forces with varying coating thickness and refractive index values. To increase the optical trapping efficiency, the refractive index (n(b)) of the coating is selected such that n(a) < n(b) < n(c), where na and nc are the refractive indices of the medium and the core material, respectively. The thickness of the coating also increases trapping efficiency. Importantly, we find that trapping forces for the coated particles are predominantly determined by two rays: the incident ray and the first refracted ray to the medium.
Applicability of geometrical optics to in-plane liquid-crystal configurations
Sluijter, M.; Xu, M.; Urbach, H.P.; De Boer, D.K.G.
2010-01-01
We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices no=1.5 and ne=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations
A New (?) Physiological Effect in a Demonstration Experiment in Geometrical Optics
Ganci, S.
2018-01-01
A surprising phenomenology from a traditional demonstration experiment in Geometrical Optics reveals here an interesting matter of discussion and analysis. Hence, the main focus of this paper is to observe and discuss such an innovative phenomenology.
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Cross-Grade Comparison of Students' Conceptual Understanding with Lenses in Geometric Optics
Tural, G.
2015-01-01
Students commonly find the field of physics difficult. Therefore, they generally have learning problems. One of the subjects with which they have difficulties is optics within a physics discipline. This study aims to determine students' conceptual understanding levels at different education levels relating to lenses in geometric optics. A…
Reiner, Miriam; And Others
1995-01-01
Observations of high school physics students in an instructional experiment with an interactive learning environment in geometrical optics indicated that students in the Optics Dynagrams Project went through major conceptual developments as reflected in the diagrams they constructed. (Author/MKR)
Multipartite geometric entanglement in finite size XY model
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Giampaolo, Salvatore Marco; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
We investigate the behavior of the multipartite entanglement in the finite size XY model by means of the hierarchical geometric measure of entanglement. By selecting specific components of the hierarchy, we study both global entanglement and genuinely multipartite entanglement.
geometric models for lateritic soil stabilized with cement
African Journals Online (AJOL)
user
stabilized lateritic soil and also to develop geometric models. The compaction, California .... on how effective limited field data are put to use in decision-making. ..... silicates was described as the most important phase of cement and the ...
A geometric construction of traveling waves in a bioremediation model
Beck, M.A.; Doelman, A.; Kaper, T.J.
2006-01-01
Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory,
Applicability of geometrical optics to in-plane liquid-crystal configurations.
Sluijter, M; Xu, M; Urbach, H P; de Boer, D K G
2010-02-15
We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices n(o)=1.5 and n(e)=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.
Investigation of the geometrical barrier in Bi-2212 using the magneto-optical technique
International Nuclear Information System (INIS)
Lin, Z.W.
2000-01-01
It has been found that the penetration of vortices into a weak pinning crystal is governed by a geometrical barrier and they form a dome-shaped flux profile across the crystal. Using the powerful magneto-optical technique, we investigated this geometrical barrier in a high-purity Bi 2 Sr 2 CaCu 2 O 8+x single-crystal platelet. Our results show that over the temperature range 20-70 K the dome-shaped profile is observed. Also, the influences of the edge shape and the roughness on the geometrical barrier are discussed. (author)
Flat-field response and geometric distortion measurements of optical streak cameras
International Nuclear Information System (INIS)
Montgomery, D.S.; Drake, R.P.; Jones, B.A.; Wiedwald, J.D.
1987-08-01
To accurately measure pulse amplitude, shape, and relative time histories of optical signals with an optical streak camera, it is necessary to correct each recorded image for spatially-dependent gain nonuniformity and geometric distortion. Gain nonuniformities arise from sensitivity variations in the streak-tube photocathode, phosphor screen, image-intensifier tube, and image recording system. These nonuniformities may be severe, and have been observed to be on the order of 100% for some LLNL optical streak cameras. Geometric distortion due to optical couplings, electron-optics, and sweep nonlinearity not only affects pulse position and timing measurements, but affects pulse amplitude and shape measurements as well. By using a 1.053-μm, long-pulse, high-power laser to generate a spatially and temporally uniform source as input to the streak camera, the combined effects of flat-field response and geometric distortion can be measured under the normal dynamic operation of cameras with S-1 photocathodes. Additionally, by using the same laser system to generate a train of short pulses that can be spatially modulated at the input of the streak camera, we can effectively create a two-dimensional grid of equally-spaced pulses. This allows a dynamic measurement of the geometric distortion of the streak camera. We will discuss the techniques involved in performing these calibrations, will present some of the measured results for LLNL optical streak cameras, and will discuss software methods to correct for these effects. 6 refs., 6 figs
Multiscale geometric modeling of macromolecules II: Lagrangian representation
Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2013-01-01
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599
Geometric and Applied Optics, Science (Experimental): 5318.04.
Sanderson, Robert C.
This unit of instruction presents a laboratory-oriented course which relates the sources and behaviors of light to man's control and uses of light. Successful completion of Algebra I and Plane Geometry is strongly recommended as indicators of success. The course is recommended if the student plans further studies in science, optical technology, or…
Complementary Huygens Principle for Geometrical and Nongeometrical Optics
Luis, Alfredo
2007-01-01
We develop a fundamental principle depicting the generalized ray formulation of optics provided by the Wigner function. This principle is formally identical to the Huygens-Fresnel principle but in terms of opposite concepts, rays instead of waves, and incoherent superpositions instead of coherent ones. This ray picture naturally includes…
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...
Geometrical aspects of solvable two dimensional models
International Nuclear Information System (INIS)
Tanaka, K.
1989-01-01
It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs
Optical rectification using geometrical field enhancement in gold nano-arrays
Piltan, S.; Sievenpiper, D.
2017-11-01
Conversion of photons to electrical energy has a wide variety of applications including imaging, solar energy harvesting, and IR detection. A rectenna device consists of an antenna in addition to a rectifying element to absorb the incident radiation within a certain frequency range. We designed, fabricated, and measured an optical rectifier taking advantage of asymmetrical field enhancement for forward and reverse currents due to geometrical constraints. The gold nano-structures as well as the geometrical parameters offer enhanced light-matter interaction at 382 THz. Using the Taylor expansion of the time-dependent current as a function of the external bias and oscillating optical excitation, we obtained responsivities close to quantum limit of operation. This geometrical approach can offer an efficient, broadband, and scalable solution for energy conversion and detection in the future.
International Nuclear Information System (INIS)
Lopez Moreno, E.; Wolf, K.B.
1989-01-01
Starting from the Snell-Descartes' refraction law, we obtain in a brief and direct way the Hamilton equations of Geometrical Optics. We show the global structure of phase space and compare it with that used in paraxial optics. (Author)
Modeling collective cell migration in geometric confinement
Tarle, Victoria; Gauquelin, Estelle; Vedula, S. R. K.; D'Alessandro, Joseph; Lim, C. T.; Ladoux, Benoit; Gov, Nir S.
2017-06-01
Monolayer expansion has generated great interest as a model system to study collective cell migration. During such an expansion the culture front often develops ‘fingers’, which we have recently modeled using a proposed feedback between the curvature of the monolayer’s leading edge and the outward motility of the edge cells. We show that this model is able to explain the puzzling observed increase of collective cellular migration speed of a monolayer expanding into thin stripes, as well as describe the behavior within different confining geometries that were recently observed in experiments. These comparisons give support to the model and emphasize the role played by the edge cells and the edge shape during collective cell motion.
Boyde, Lars; Ekpenyong, Andrew; Whyte, Graeme; Guck, Jochen
2012-11-20
We present two electromagnetic frameworks to compare the surface stresses on spheroidal particles in the optical stretcher (a dual-beam laser trap that can be used to capture and deform biological cells). The first model is based on geometrical optics (GO) and limited in its applicability to particles that are much greater than the incident wavelength. The second framework is more sophisticated and hinges on the generalized Lorenz-Mie theory (GLMT). Despite the difference in complexity between both theories, the stress profiles computed with GO and GLMT are in good agreement with each other (relative errors are on the order of 1-10%). Both models predict a diminishing of the stresses for larger wavelengths and a strong increase of the stresses for shorter laser-cell distances. Results indicate that surface stresses on a spheroid with an aspect ratio of 1.2 hardly differ from the stresses on a sphere of similar size. Knowledge of the surface stresses and whether or not they redistribute during the stretching process is of crucial importance in real-time applications of the stretcher that aim to discern the viscoelastic properties of cells for purposes of cell characterization, sorting, and medical diagnostics.
A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science
Maurício, Paulo; Valente, Bianor; Chagas, Isabel
2017-01-01
The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the…
Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.
2015-01-01
We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or
Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers
International Nuclear Information System (INIS)
Alagashev, G K; Pryamikov, A D; Kosolapov, A F; Kolyadin, A N; Lukovkin, A Yu; Biriukov, A S
2015-01-01
We analyze the impact of geometrical parameters on such important optical characteristics of negative curvature hollow-core fibers (NCHCFs) as waveguide dispersion, waveguide losses and the structure of transmission bands. We consider both theoretically and experimentally the resonance effects and formation of band edges under bending in NCHCFs. (paper)
Designing and Using an Open Graphic Interface for Instruction in Geometrical Optics.
Ronen, Miky; And Others
1993-01-01
Discusses conceptual difficulties in the field of geometrical optics and describes RAY, a microcomputer-based graphic interface that was designed to serve as a teaching aid and as a learning environment. The ability to combine theory and formal representations with real demonstrations and experiments is discussed. (Contains seven references.) (LRW)
van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.
A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity
Geometric model for softwood transverse thermal conductivity. Part I
Hong-mei Gu; Audrey Zink-Sharp
2005-01-01
Thermal conductivity is a very important parameter in determining heat transfer rate and is required for developing of drying models and in industrial operations such as adhesive cure rate. Geometric models for predicting softwood thermal conductivity in the radial and tangential directions were generated in this study based on obervation and measurements of wood...
Lepton and quark generations in the geometrical Rishon model
International Nuclear Information System (INIS)
Elbaz, E.; Uschersohn, J.; Meyer, J.
1981-12-01
We propose a concrete representation of leptons and quarks in different generations in the geometrical approach to the rishon model where rishons behave as the fundamental representations of the SU(3)sub(C) x SU(3)sub(H) group. The model allows a unified description of both hadronic and leptonic decays of elementary particles
3-D Geometric Modeling for the 21st Century.
Ault, Holly K.
1999-01-01
Describes new geometric computer models used in contemporary computer-aided design (CAD) software including wire frame, surface, solid, and parametric models. Reviews their use in engineering design and discusses the impact of these new technologies on the engineering design graphics curriculum. (Author/CCM)
Geometric Modelling with a-Complexes
Gerritsen, B.H.M.; Werff, K. van der; Veltkamp, R.C.
2001-01-01
The shape of real objects can be so complicated, that only a sampling data point set can accurately represent them. Analytic descriptions are too complicated or impossible. Natural objects, for example, can be vague and rough with many holes. For this kind of modelling, a-complexes offer advantages
Analysis of a Thin Optical Lens Model
Ivchenko, Vladimir V.
2011-01-01
In this article a thin optical lens model is considered. It is shown that the limits of its applicability are determined not only by the ratio between the thickness of the lens and the modules of the radii of curvature, but above all its geometric type. We have derived the analytical criteria for the applicability of the model for different types…
Knowledge-based geometric modeling in construction
DEFF Research Database (Denmark)
Bonev, Martin; Hvam, Lars
2012-01-01
a considerably high amount of their recourses is required for designing and specifying the majority of their product assortment. As design decisions are hereby based on knowledge and experience about behaviour and applicability of construction techniques and materials for a predefined design situation, smart......A wider application of IT-based solutions, such as configuration systems and the implementation of modeling standards, has facilitated the trend to produce mass customized products to support inter alia the specification process of the increasing product variety. However, not all industries have...
A Robust Geometric Model for Argument Classification
Giannone, Cristina; Croce, Danilo; Basili, Roberto; de Cao, Diego
Argument classification is the task of assigning semantic roles to syntactic structures in natural language sentences. Supervised learning techniques for frame semantics have been recently shown to benefit from rich sets of syntactic features. However argument classification is also highly dependent on the semantics of the involved lexicals. Empirical studies have shown that domain dependence of lexical information causes large performance drops in outside domain tests. In this paper a distributional approach is proposed to improve the robustness of the learning model against out-of-domain lexical phenomena.
Transverse correlations in triphoton entanglement: Geometrical and physical optics
International Nuclear Information System (INIS)
Wen Jianming; Rubin, Morton H.; Shih Yanhua; Xu, P.
2007-01-01
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function F of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a
Geometric and potential dynamics interpretation of the optic ring resonator bistability
Chiangga, S.; Chittha, T.; Frank, T. D.
2015-07-01
The optical bistability is a fundamental nonlinear feature of the ring resonator. A geometric and potential dynamics interpretation of the bistability is given. Accordingly, the bistability of the nonlinear system is shown to be a consequence of geometric laws of vector calculus describing the resonator ring. In contrast, the so-called transcendental relations that have been obtained in the literature in order to describe the optical wave are interpreted in terms of potential dynamical systems. The proposed novel interpretation provides new insights into the nature of the ring resonator optical bistability. The fundamental work by Rukhlenko, Premaratne and Agrawal (2010) as well as a more recent study by Chiangga, Pitakwongsaporn, Frank and Yupapin (2013) are considered.
Geometric accuracy of wax bade models manufactured in silicon moulds
Directory of Open Access Journals (Sweden)
G. Budzik
2010-01-01
Full Text Available The article presents the test results of the geometric accuracy of wax blade models manufactured in silicon moulds in the Rapid Tooling process, with the application of the Vacuum Casting technology. In batch production casting waxes are designed for the manufacture of models and components of model sets through injection into a metal die. The objective of the tests was to determine the possibility of using traditional wax for the production of casting models in the rapid prototyping process. Blade models made of five types of casting wax were measured. The definition of the geometric accuracy of wax blade models makes it possible to introduce individual modifications aimed at improving their shape in order to increase the dimensional accuracy of blade models manufactured in the rapid prototyping process.
Recent Advances in Material and Geometrical Modelling in Dental Applications
Directory of Open Access Journals (Sweden)
Waleed M. S. Al Qahtani
2018-06-01
Full Text Available This article touched, in brief, the recent advances in dental materials and geometric modelling in dental applications. Most common categories of dental materials as metallic alloys, composites, ceramics and nanomaterials were briefly demonstrated. Nanotechnology improved the quality of dental biomaterials. This new technology improves many existing materials properties, also, to introduce new materials with superior properties that covered a wide range of applications in dentistry. Geometric modelling was discussed as a concept and examples within this article. The geometric modelling with engineering Computer-Aided-Design (CAD system(s is highly satisfactory for further analysis or Computer-Aided-Manufacturing (CAM processes. The geometric modelling extracted from Computed-Tomography (CT images (or its similar techniques for the sake of CAM also reached a sufficient level of accuracy, while, obtaining efficient solid modelling without huge efforts on body surfaces, faces, and gaps healing is still doubtable. This article is merely a compilation of knowledge learned from lectures, workshops, books, and journal articles, articles from the internet, dental forum, and scientific groups' discussions.
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
Energy Technology Data Exchange (ETDEWEB)
Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)
2014-01-15
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Liu, W.; Wang, H.; Liu, D.; Miu, Y.
2018-05-01
Precise geometric parameters are essential to ensure the positioning accuracy for space optical cameras. However, state-of-the-art onorbit calibration method inevitably suffers from long update cycle and poor timeliness performance. To this end, in this paper we exploit the optical auto-collimation principle and propose a real-time onboard calibration scheme for monitoring key geometric parameters. Specifically, in the proposed scheme, auto-collimation devices are first designed by installing collimated light sources, area-array CCDs, and prisms inside the satellite payload system. Through utilizing those devices, the changes in the geometric parameters are elegantly converted into changes in the spot image positions. The variation of geometric parameters can be derived via extracting and processing the spot images. An experimental platform is then set up to verify the feasibility and analyze the precision index of the proposed scheme. The experiment results demonstrate that it is feasible to apply the optical auto-collimation principle for real-time onboard monitoring.
Mendoza, Carlos I.; Reyes, J. Adrian
2006-08-01
The authors present a geometrical approach to calculate the transmission of light in a hybrid-aligned nematic cell under the influence of an applied electric field. Using the framework of geometrical optics they present results for the ray tracing as well as the transmission of light as a function of the applied low frequency voltage. Dispersion effects are included through a wavelength dependent dielectric function. Their results for the transmittance as a function of the applied voltage show oscillations that are in good qualitative agreement with previously obtained experimental measurements.
Geometric modeling in the problem of ball bearing accuracy
Glukhov, V. I.; Pushkarev, V. V.; Khomchenko, V. G.
2017-06-01
The manufacturing quality of ball bearings is an urgent problem for machine-building industry. The aim of the research is to improve the geometric specifications accuracy of bearings based on evidence-based systematic approach and the method of adequate size, location and form deviations modeling of the rings and assembled ball bearings. The present work addressed the problem of bearing geometric specifications identification and the study of these specifications. The deviation from symmetric planar of rings and bearings assembly and mounting width are among these specifications. A systematic approach to geometric specifications values and ball bearings tolerances normalization in coordinate systems will improve the quality of bearings by optimizing and minimizing the number of specifications. The introduction of systematic approach to the international standards on rolling bearings is a guarantee of a significant increase in accuracy of bearings and the quality of products where they are applied.
Geometric model from microscopic theory for nuclear absorption
International Nuclear Information System (INIS)
John, S.; Townsend, L.W.; Wilson, J.W.; Tripathi, R.K.
1993-07-01
A parameter-free geometric model for nuclear absorption is derived herein from microscopic theory. The expression for the absorption cross section in the eikonal approximation, taken in integral form, is separated into a geometric contribution that is described by an energy-dependent effective radius and two surface terms that cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived from harmonic oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half-density radius for the harmonic oscillator functions. Coulomb corrections are incorporated, and a simplified geometric form of the Bradt-Peters type is obtained. Results spanning the energy range from 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained
Geometric model for nuclear absorption from microscopic theory
International Nuclear Information System (INIS)
John, S.; Townsend, L.W.; Wilson, J.W.; Tripathi, R.K.
1993-01-01
A parameter-free geometric model for nuclear absorption is derived from microscopic theory. The expression for the absorption cross section in the eikonal approximation taken in integral form is separated into a geometric contribution, described by an energy-dependent effective radius, and two surface terms which are shown to cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived using harmonic-oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half density radius for the harmonic-oscillator functions. Coulomb corrections are incorporated and a simplified geometric form of the Bradt-Peters type obtained. Results spanning the energy range of 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained
An extended geometric criterion for chaos in the Dicke model
International Nuclear Information System (INIS)
Li Jiangdan; Zhang Suying
2010-01-01
We extend HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion for chaotic motion to Hamiltonian systems of weak coupling of potential and momenta by defining the 'mean unstable ratio'. We discuss the Dicke model of an unstable Hamiltonian system in detail and show that our results are in good agreement with that of the computation of Lyapunov characteristic exponents.
Geometric Aspects of Force Controllability for a Swimming Model
International Nuclear Information System (INIS)
Khapalov, A. Y.
2008-01-01
We study controllability properties (swimming capabilities) of a mathematical model of an abstract object which 'swims' in the 2-D Stokes fluid. Our goal is to investigate how the geometric shape of this object affects the forces acting upon it. Such problems are of interest in biology and engineering applications dealing with propulsion systems in fluids
Do Lumped-Parameter Models Provide the Correct Geometrical Damping?
DEFF Research Database (Denmark)
Andersen, Lars
response during excitation and the geometrical damping related to free vibrations of a hexagonal footing. The optimal order of a lumped-parameter model is determined for each degree of freedom, i.e. horizontal and vertical translation as well as torsion and rocking. In particular, the necessity of coupling...... between horizontal sliding and rocking is discussed....
Diquark structure in heavy quark baryons in a geometric model
International Nuclear Information System (INIS)
Paria, Lina; Abbas, Afsar
1996-01-01
Using a geometric model to study the structure of hadrons, baryons having one, two and three heavy quarks have been studied here. The study reveals diquark structure in baryons with one and two heavy quarks but not with three heavy identical quarks. (author). 15 refs., 2 figs., 2 tabs
A geometric model for magnetizable bodies with internal variables
Directory of Open Access Journals (Sweden)
Restuccia, L
2005-11-01
Full Text Available In a geometrical framework for thermo-elasticity of continua with internal variables we consider a model of magnetizable media previously discussed and investigated by Maugin. We assume as state variables the magnetization together with its space gradient, subjected to evolution equations depending on both internal and external magnetic fields. We calculate the entropy function and necessary conditions for its existence.
Methods for teaching geometric modelling and computer graphics
Energy Technology Data Exchange (ETDEWEB)
Rotkov, S.I.; Faitel`son, Yu. Ts.
1992-05-01
This paper considers methods for teaching the methods and algorithms of geometric modelling and computer graphics to programmers, designers and users of CAD and computer-aided research systems. There is a bibliography that can be used to prepare lectures and practical classes. 37 refs., 1 tab.
AUTOMATIC MESH GENERATION OF 3—D GEOMETRIC MODELS
Institute of Scientific and Technical Information of China (English)
刘剑飞
2003-01-01
In this paper the presentation of the ball-packing method is reviewed, and a schemeto generate mesh for complex 3-D geometric models is given, which consists of 4 steps: (1) createnodes in 3-D models by ball-packing method, (2) connect nodes to generate mesh by 3-D Delaunaytriangulation, (3) retrieve the boundary of the model after Delaunay triangulation, (4) improve themesh.
AUTOMATIC MESH GENERATION OF 3-D GEOMETRIC MODELS
Institute of Scientific and Technical Information of China (English)
刘剑飞
2003-01-01
In this paper the presentation of the ball-packing method is reviewed,and a scheme to generate mesh for complex 3-D geometric models is given,which consists of 4 steps:(1)create nodes in 3-D models by ball-packing method,(2)connect nodes to generate mesh by 3-D Delaunay triangulation,(3)retrieve the boundary of the model after Delaunay triangulation,(4)improve the mesh.
Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics.
Tanimori, Toru; Mizumura, Yoshitaka; Takada, Atsushi; Miyamoto, Shohei; Takemura, Taito; Kishimoto, Tetsuro; Komura, Shotaro; Kubo, Hidetoshi; Kurosawa, Shunsuke; Matsuoka, Yoshihiro; Miuchi, Kentaro; Mizumoto, Tetsuya; Nakamasu, Yuma; Nakamura, Kiseki; Parker, Joseph D; Sawano, Tatsuya; Sonoda, Shinya; Tomono, Dai; Yoshikawa, Kei
2017-02-03
Since the discovery of nuclear gamma-rays, its imaging has been limited to pseudo imaging, such as Compton Camera (CC) and coded mask. Pseudo imaging does not keep physical information (intensity, or brightness in Optics) along a ray, and thus is capable of no more than qualitative imaging of bright objects. To attain quantitative imaging, cameras that realize geometrical optics is essential, which would be, for nuclear MeV gammas, only possible via complete reconstruction of the Compton process. Recently we have revealed that "Electron Tracking Compton Camera" (ETCC) provides a well-defined Point Spread Function (PSF). The information of an incoming gamma is kept along a ray with the PSF and that is equivalent to geometrical optics. Here we present an imaging-spectroscopic measurement with the ETCC. Our results highlight the intrinsic difficulty with CCs in performing accurate imaging, and show that the ETCC surmounts this problem. The imaging capability also helps the ETCC suppress the noise level dramatically by ~3 orders of magnitude without a shielding structure. Furthermore, full reconstruction of Compton process with the ETCC provides spectra free of Compton edges. These results mark the first proper imaging of nuclear gammas based on the genuine geometrical optics.
International Nuclear Information System (INIS)
Bliokh, K.Yu.; Bliokh, Yu.P.
2004-01-01
We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Applying this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed
Bliokh, K Yu; Bliokh, Yu P
2004-08-01
We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.
Geometric mechanics of ray optics as particle dynamics: refraction index with cylindrical symmetry
Cortés, Emilio; Ruiz, Melina
2017-09-01
Starting from the Fermat principle of geometrical optics, we analyse the ray dynamics in a graded refractive index system device with cylindrical symmetry and a refractive index that decreases parabolically with the radial coordinate. By applying Hamiltonian dynamics to the study of the ray path we obtain the strict equivalence of this optical system with the dynamics of a particle with an equivalent mass moving in a potential function that may exhibit a well, depending on the value of some associated parameters. We analyse the features of this potential function as well as the energy values and the symmetries of the system and see that both the azimuthal and axial components of the optical conjugate momentum are two constants of motion. The phase space relation for the momentum radial component is obtained analytically, and then we can obtain the components of the momentum vector at any point, given the value of the radial coordinate, and from this we have the direction of the ray. We discuss the optical path length as an action functional and we can evaluate this stationary path, with initial and final arbitrary points, as a line integral of the optical momentum, by showing that this momentum is a conservative vector field. We integrate the equations of motion numerically and obtain different ray paths which depend on the initial conditions. We believe that with this work the physics student will appreciate very clearly the close connection between geometrical optics and particle Hamiltonian dynamics.
Parker, Jeffrey B.
2018-05-01
Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.
Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench
Sarkar, Sujit
2013-01-01
The atoms trapped in microcavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We study the dynamics of the geometric phase of this system under the linear quenching process of laser field detuning which shows the XX criticality of the geometric phase in presence of single Rabi frequency oscillation. We also study the quantum criticality for different quenching rate in the presence of single or two Rabi frequencies osci...
Geometrical optics in the near field: local plane-interface approach with evanescent waves.
Bose, Gaurav; Hyvärinen, Heikki J; Tervo, Jani; Turunen, Jari
2015-01-12
We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.
GEOMETRIC MODELLING OF TREE ROOTS WITH DIFFERENT LEVELS OF DETAIL
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J. I. Guerrero Iñiguez
2017-09-01
Full Text Available This paper presents a geometric approach for modelling tree roots with different Levels of Detail, suitable for analysis of the tree anchoring, potentially occupied underground space, interaction with urban elements and damage produced and taken in the built-in environment. Three types of tree roots are considered to cover several species: tap root, heart shaped root and lateral roots. Shrubs and smaller plants are not considered, however, a similar approach can be considered if the information is available for individual species. The geometrical approach considers the difficulties of modelling the actual roots, which are dynamic and almost opaque to direct observation, proposing generalized versions. For each type of root, different geometric models are considered to capture the overall shape of the root, a simplified block model, and a planar or surface projected version. Lower detail versions are considered as compatibility version for 2D systems while higher detail models are suitable for 3D analysis and visualization. The proposed levels of detail are matched with CityGML Levels of Detail, enabling both analysis and aesthetic views for urban modelling.
Geometric Modelling of Tree Roots with Different Levels of Detail
Guerrero Iñiguez, J. I.
2017-09-01
This paper presents a geometric approach for modelling tree roots with different Levels of Detail, suitable for analysis of the tree anchoring, potentially occupied underground space, interaction with urban elements and damage produced and taken in the built-in environment. Three types of tree roots are considered to cover several species: tap root, heart shaped root and lateral roots. Shrubs and smaller plants are not considered, however, a similar approach can be considered if the information is available for individual species. The geometrical approach considers the difficulties of modelling the actual roots, which are dynamic and almost opaque to direct observation, proposing generalized versions. For each type of root, different geometric models are considered to capture the overall shape of the root, a simplified block model, and a planar or surface projected version. Lower detail versions are considered as compatibility version for 2D systems while higher detail models are suitable for 3D analysis and visualization. The proposed levels of detail are matched with CityGML Levels of Detail, enabling both analysis and aesthetic views for urban modelling.
Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere.
Bambino, Túlio M; Breitschaft, Ana Maria S; Barbosa, Valmar C; Guimarães, Luiz G
2003-03-01
This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.
Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface
Energy Technology Data Exchange (ETDEWEB)
Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn; Wang, Mu, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn [National Laboratory of Solid State Microstructures and School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China)
2016-06-27
We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000–1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.
Geometrical-optics solution to light scattering by droxtal ice crystals.
Zhang, Zhibo; Yang, Ping; Kattawar, George W; Tsay, Si-Chee; Baum, Bryan A; Hu, Yongxiang; Heymsfield, Andrew J; Reichardt, Jens
2004-04-20
We investigate the phase matrices of droxtals at wavelengths of 0.66 and 11 microm by using an improved geometrical-optics method. An efficient method is developed to specify the incident rays and the corresponding impinging points on the particle surface necessary to initialize the ray-tracing computations. At the 0.66-microm wavelength, the optical properties of droxtals are different from those of hexagonal ice crystals. At the 11-microm wavelength, the phase functions for droxtals are essentially featureless because of strong absorption within the particles, except for ripple structures that are caused by the phase interference of the diffracted wave.
On geometric optics and surface waves for light scattering by spheres
International Nuclear Information System (INIS)
Liou, K.N.; Takano, Y.; Yang, P.
2010-01-01
A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection-refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz-Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size-wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.
Flat-field response and geometric distortion measurements of optical streak cameras
International Nuclear Information System (INIS)
Montgomery, D.S.; Drake, R.P.; Jones, B.A.; Wiedwald, J.D.
1987-01-01
To accurately measure pulse amplitude, shape, and relative time histories of optical signals with an optical streak camera, it is necessary to correct each recorded image for spatially-dependent gain nonuniformity and geometric distortion. Gain nonuniformities arise from sensitivity variations in the streak-tube photocathode, phosphor screen, image-intensifier tube, and image recording system. By using a 1.053-μm, long-pulse, high-power laser to generate a spatially and temporally uniform source as input to the streak camera, the combined effects of flat-field response and geometric distortion can be measured under the normal dynamic operation of cameras with S-1 photocathodes. Additionally, by using the same laser system to generate a train of short pulses that can be spatially modulated at the input of the streak camera, the authors can create a two-dimensional grid of equally-spaced pulses. This allows a dynamic measurement of the geometric distortion of the streak camera. The author discusses the techniques involved in performing these calibrations, present some of the measured results for LLNL optical streak cameras, and will discuss software methods to correct for these effects
Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation
International Nuclear Information System (INIS)
Hod, Shahar
2009-01-01
It has long been known that null unstable geodesics are related to the characteristic modes of black holes--the so-called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability time scale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null rays is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation waves in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.
Calculation of far-field scattering from nonspherical particles using a geometrical optics approach
Hovenac, Edward A.
1991-01-01
A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.
Geometric Modeling and Reasoning of Human-Centered Freeform Products
Wang, Charlie C L
2013-01-01
The recent trend in user-customized product design requires the shape of products to be automatically adjusted according to the human body’s shape, so that people will feel more comfortable when wearing these products. Geometric approaches can be used to design the freeform shape of products worn by people, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and design of medical devices, etc.). These products are usually composed of very complex geometric shapes (represented by free-form surfaces), and are not driven by a parameter table but a digital human model with free-form shapes or part of human bodies (e.g., wrist, foot, and head models). Geometric Modeling and Reasoning of Human-Centered Freeform Products introduces the algorithms of human body reconstruction, freeform product modeling, constraining and reconstructing freeform products, and shape optimization for improving...
Nemati, Farshad
2009-01-01
Over the past few decades, different theories have been advanced to explain geometric-optical illusions based on various perceptual processes such as assimilation and/or contrast. Consistent with the contradictory effects of assimilation and contrast, Pressey's assimilation theory provided an explanation for the Müller-Lyer illusion, but failed to account for the Titchener (Ebbinghaus) illusion. A model that explains both Müller-Lyer and Titchener illusions according to a common underlying process may outline a unified explanation for a variety of geometric-optical illusions. In order to develop such a model, the concept of empty space is introduced as an area of the illusory figure that is not filled by line drawings. It was predicted that the magnitude of illusion would increase with the area of the empty space around the illusory figures. The effect of empty space on the magnitude of perceptual distortion was measured in Müller-Lyer figures, with outward arrowheads of different length. The results indicated an overestimation of the target stimulus in all of the figures. Nevertheless, consistent with the prediction of the present model, the horizontal line in the Müller-Lyer figure with the longest arrowheads appeared shorter than that with the shortest arrowheads, although the size contrast of these figures was the same. According to the analysis proposed in the present study, the area of empty space not only affects the magnitude of illusion but also serves as a contextual cue for the perceptual system to determine the direction of illusion (orientation). The functional relationships between the size contrast and empty space provide a common explanation for the Müller-Lyer, Titchener, and a variety of other geometric-optical illusions.
Image-Based Geometric Modeling and Mesh Generation
2013-01-01
As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion,...
A Physical – Geometrical Model of an Early Universe
Directory of Open Access Journals (Sweden)
Corneliu BERBENTE
2014-12-01
Full Text Available A physical-geometrical model for a possible early universe is proposed. One considers an initial singularity containing the energy of the whole universe. The singularity expands as a spherical wave at the speed of light generating space and time. The relations of the special theory of relativity, quantum mechanics and gas kinetics are considered applicable. A structuring of the primary wave is adopted on reasons of geometrical simplicity as well as on satisfying the conservation laws. The evolution is able to lead to particles very close to neutrons as mass and radius. The actually admitted values for the radius and mass of the universe as well as the temperature of the ground radiation (3-5 K can be obtained by using the proposed model.
A geometric model for Hochschild homology of Soergel bimodules
DEFF Research Database (Denmark)
Webster, Ben; Williamson, Geordie
2008-01-01
An important step in the calculation of the triply graded link homology of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as B–equivariant intersection cohomology...... on generators whose degree is explicitly determined by the geometry of the orbit closure, and to describe its Hilbert series, proving a conjecture of Jacob Rasmussen....
The geometric Schwinger model on the torus. Pt. 1
International Nuclear Information System (INIS)
Joos, H.
1990-01-01
The author analyzes the Euclidean version of the geometric Schwinger model on the torus. After the calculation of the zero mode wave functions associated with the different topological sectors, which can be expressed by θ functions defined on the two-dimensional torus, he determines the regularized effective action and discusses the propagator related to it. Finally he studies applications to the standard questions like the particle spectrum, the screening of the static potential, and the appearance of the anomaly. (HSI)
Time evolution in a geometric model of a particle
International Nuclear Information System (INIS)
Atiyah, M.F.; Franchetti, G.; Schroers, B.J.
2015-01-01
We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac’s Large Number Hypothesis.
A geometrical model for DNA organization in bacteria.
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Mathias Buenemann
Full Text Available Recent experimental studies have revealed that bacteria, such as C. crescentus, show a remarkable spatial ordering of their chromosome. A strong linear correlation has been found between the position of genes on the chromosomal map and their spatial position in the cellular volume. We show that this correlation can be explained by a purely geometrical model. Namely, self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus together with the action of DNA compaction proteins (that organize the chromosome into topological domains are sufficient to get a linear arrangement of the chromosome along the cell axis. We develop a Monte-Carlo method that allows us to test our model numerically and to analyze the dependence of the spatial ordering on various physiologically relevant parameters. We show that the proposed geometrical ordering mechanism is robust and universal (i.e. does not depend on specific bacterial details. The geometrical mechanism should work in all bacteria that have compacted chromosomes with spatially fixed regions. We use our model to make specific and experimentally testable predictions about the spatial arrangement of the chromosome in mutants of C. crescentus and the growth-stage dependent ordering in E. coli.
Geometric and computer-aided spline hob modeling
Brailov, I. G.; Myasoedova, T. M.; Panchuk, K. L.; Krysova, I. V.; Rogoza, YU A.
2018-03-01
The paper considers acquiring the spline hob geometric model. The objective of the research is the development of a mathematical model of spline hob for spline shaft machining. The structure of the spline hob is described taking into consideration the motion in parameters of the machine tool system of cutting edge positioning and orientation. Computer-aided study is performed with the use of CAD and on the basis of 3D modeling methods. Vector representation of cutting edge geometry is accepted as the principal method of spline hob mathematical model development. The paper defines the correlations described by parametric vector functions representing helical cutting edges designed for spline shaft machining with consideration for helical movement in two dimensions. An application for acquiring the 3D model of spline hob is developed on the basis of AutoLISP for AutoCAD environment. The application presents the opportunity for the use of the acquired model for milling process imitation. An example of evaluation, analytical representation and computer modeling of the proposed geometrical model is reviewed. In the mentioned example, a calculation of key spline hob parameters assuring the capability of hobbing a spline shaft of standard design is performed. The polygonal and solid spline hob 3D models are acquired by the use of imitational computer modeling.
Geometric singularities and spectra of Landau-Ginzburg models
International Nuclear Information System (INIS)
Greene, B.R.; Roan, S.S.; Yau, S.T.
1991-01-01
Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginsburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complementary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance of unorbifolded Landau-Ginzburg theories. (orig.)
The geometric phase and the Schwinger term in some models
International Nuclear Information System (INIS)
Grosse, H.; Langmann, E.
1991-01-01
We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum mechanical system along a closed loop of parameter space may yield a geometric mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization one obtains, in addition, a Schwinger term. Depending on the type of transformation a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space. (authors)
Using geometric algebra to understand pattern rotations in multiple mirror optical systems
International Nuclear Information System (INIS)
Hanlon, J.; Ziock, H.
1997-01-01
Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam
Modeling geophysical complexity: a case for geometric determinism
Directory of Open Access Journals (Sweden)
C. E. Puente
2007-01-01
Full Text Available It has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed.
Wu, Chensheng; Nelson, William; Davis, Christopher C.
2014-10-01
Plenoptic functions are functions that preserve all the necessary light field information of optical events. Theoretical work has demonstrated that geometric based plenoptic functions can serve equally well in the traditional wave propagation equation known as the "scalar stochastic Helmholtz equation". However, in addressing problems of 3D turbulence simulation, the dominant methods using phase screen models have limitations both in explaining the choice of parameters (on the transverse plane) in real-world measurements, and finding proper correlations between neighboring phase screens (the Markov assumption breaks down). Though possible corrections to phase screen models are still promising, the equivalent geometric approach based on plenoptic functions begins to show some advantages. In fact, in these geometric approaches, a continuous wave problem is reduced to discrete trajectories of rays. This allows for convenience in parallel computing and guarantees conservation of energy. Besides the pairwise independence of simulated rays, the assigned refractive index grids can be directly tested by temperature measurements with tiny thermoprobes combined with other parameters such as humidity level and wind speed. Furthermore, without loss of generality one can break the causal chain in phase screen models by defining regional refractive centers to allow rays that are less affected to propagate through directly. As a result, our work shows that the 3D geometric approach serves as an efficient and accurate method in assessing relevant turbulence problems with inputs of several environmental measurements and reasonable guesses (such as Cn 2 levels). This approach will facilitate analysis and possible corrections in lateral wave propagation problems, such as image de-blurring, prediction of laser propagation over long ranges, and improvement of free space optic communication systems. In this paper, the plenoptic function model and relevant parallel algorithm computing
Generating a normalized geometric liver model with warping
International Nuclear Information System (INIS)
Boes, J.L.; Weymouth, T.E.; Meyer, C.R.; Quint, L.E.; Bland, P.H.; Bookstein, F.L.
1990-01-01
This paper reports on the automated determination of the liver surface in abdominal CT scans for radiation treatment, surgery planning, and anatomic visualization. The normalized geometric model of the liver is generated by averaging registered outlines from a set of 15 studies of normal liver. The outlines have been registered with the use of thin-plate spline warping based on a set of five homologous landmarks. Thus, the model consists of an average of the surface and a set of five anatomic landmarks. The accuracy of the model is measured against both the set of studies used in model generation and an alternate set of 15 normal studies with use of, as an error measure, the ratio of nonoverlapping model and study volume to total model volume
Geometric optics theory and design of astronomical optical systems using Mathematica
Romano, Antonio
2016-01-01
This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras. It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae. Each optical combination analyzed is accompanied by a downloadable Mathematica® notebook that automates its third-order design, eliminating the need for lengthy calculations. The essential aspects of an optical system with an axis of rotational symmetry are introduced first, along with a development of Gaussian optics from Fermat’s principal. A simpler approach to third-order monochromatic aberrations based on both Fermat’s principle and stigmatic paths is then described, followed by a new chapter on fifth-order aberrations and their classification. Several specific optical devices are discussed and analyzed, incl...
Simple and practical approach for computing the ray Hessian matrix in geometrical optics.
Lin, Psang Dain
2018-02-01
A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.
Volume-based geometric modeling for radiation transport calculations
International Nuclear Information System (INIS)
Li, Z.; Williamson, J.F.
1992-01-01
Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon's approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed
Tunable orbital angular momentum mode filter based on optical geometric transformation.
Huang, Hao; Ren, Yongxiong; Xie, Guodong; Yan, Yan; Yue, Yang; Ahmed, Nisar; Lavery, Martin P J; Padgett, Miles J; Dolinar, Sam; Tur, Moshe; Willner, Alan E
2014-03-15
We present a tunable mode filter for spatially multiplexed laser beams carrying orbital angular momentum (OAM). The filter comprises an optical geometric transformation-based OAM mode sorter and a spatial light modulator (SLM). The programmable SLM can selectively control the passing/blocking of each input OAM beam. We experimentally demonstrate tunable filtering of one or multiple OAM modes from four multiplexed input OAM modes with vortex charge of ℓ=-9, -4, +4, and +9. The measured output power suppression ratio of the propagated modes to the blocked modes exceeds 14.5 dB.
Directory of Open Access Journals (Sweden)
Kamil Yavuz Kapusuz
2014-06-01
Full Text Available In this study, a method for determining scattering center (or center of scattering points of a multipath is proposed, provided that the direction of arrival of the multipath is known by the receiver. The method is based on classical electromagnetic wave principles in order to determine scattering center over irregular terrain. Geometrical optics (GO along with Fresnel zone concept is employed, as the receiver, the transmitter positions and irregular terrain data are assumed to be provided. The proposed method could be used at UHF bands, especially, operations of radars and electronic warfare applications.
Johann Joseph on Geometrical-Optical Illusions: A Translation and Commentary.
Wade, Nicholas J; Todorović, Dejan; Phillips, David; Lingelbach, Bernd
2017-01-01
The term geometrical-optical illusions was coined by Johann Joseph Oppel (1815-1894) in 1855 in order to distinguish spatial distortions of size and orientation from the broader illusions of the senses. We present a translation of Oppel's article and a commentary on the material described in it. Oppel did much more than give a name to a class of visual spatial distortions. He examined a variety of figures and phenomena that were precursors of later, named illusions, and attempted to quantify and interpret them.
Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations
Watson, Michael D.; Jayroe, Robert, Jr.
1999-01-01
Fresnel lenses have been used for years as solar concentrators in a variety of applications. Several variables effect the final design of these lenses including: lens diameter, image spot distance from the lens, and bandwidth focused in the image spot. Defining the image spot as the geometrical optics circle of least confusion and applying blackbody radiation equations the spot energy distribution can be determined. These equations are used to design a fresnel lens to produce maximum flux for a given spot size, lens diameter, and image distance. This approach results in significant increases in solar efficiency over traditional single wavelength designs.
An integrated introduction to computer graphics and geometric modeling
Goldman, Ronald
2009-01-01
… this book may be the first book on geometric modelling that also covers computer graphics. In addition, it may be the first book on computer graphics that integrates a thorough introduction to 'freedom' curves and surfaces and to the mathematical foundations for computer graphics. … the book is well suited for an undergraduate course. … The entire book is very well presented and obviously written by a distinguished and creative researcher and educator. It certainly is a textbook I would recommend. …-Computer-Aided Design, 42, 2010… Many books concentrate on computer programming and soon beco
Measurement system and model for simultaneously measuring 6DOF geometric errors.
Zhao, Yuqiong; Zhang, Bin; Feng, Qibo
2017-09-04
A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.
Kumarasinghe, Chathurangi S; Premaratne, Malin; Gunapala, Sarath D; Agrawal, Govind P
2016-02-18
We propose a nano-scale current-direction-switching device(CDSD) that operates based on the novel phenomenon of geometrical asymmetry between two hot-electron generating plasmonic nanostructures. The proposed device is easy to fabricate and economical to develop compared to most other existing designs. It also has the ability to function without external wiring in nano or molecular circuitry since it is powered and controlled optically. We consider a such CDSD made of two dissimilar nanorods separated by a thin but finite potential barrier and theoretically derive the frequency-dependent electron/current flow rate. Our analysis takes in to account the quantum dynamics of electrons inside the nanorods under a periodic optical perturbation that are confined by nanorod boundaries, modelled as finite cylindrical potential wells. The influence of design parameters, such as geometric difference between the two nanorods, their volumes and the barrier width on quality parameters such as frequency-sensitivity of the current flow direction, magnitude of the current flow, positive to negative current ratio, and the energy conversion efficiency is discussed by considering a device made of Ag/TiO2/Ag. Theoretical insight and design guidelines presented here are useful for customizing our proposed CDSD for applications such as self-powered logic gates, power supplies, and sensors.
Geometric and Optic Characterization of a Hemispherical Dome Port for Underwater Photogrammetry
Directory of Open Access Journals (Sweden)
Fabio Menna
2016-01-01
Full Text Available The popularity of automatic photogrammetric techniques has promoted many experiments in underwater scenarios leading to quite impressive visual results, even by non-experts. Despite these achievements, a deep understanding of camera and lens behaviors as well as optical phenomena involved in underwater operations is fundamental to better plan field campaigns and anticipate the achievable results. The paper presents a geometric investigation of a consumer grade underwater camera housing, manufactured by NiMAR and equipped with a 7′′ dome port. After a review of flat and dome ports, the work analyzes, using simulations and real experiments, the main optical phenomena involved when operating a camera underwater. Specific aspects which deal with photogrammetric acquisitions are considered with some tests in laboratory and in a swimming pool. Results and considerations are shown and commented.
Geometrical modelling of scanning probe microscopes and characterization of errors
International Nuclear Information System (INIS)
Marinello, F; Savio, E; Bariani, P; Carmignato, S
2009-01-01
Scanning probe microscopes (SPMs) allow quantitative evaluation of surface topography with ultra-high resolution, as a result of accurate actuation combined with the sharpness of tips. SPMs measure sequentially, by scanning surfaces in a raster fashion: topography maps commonly consist of data sets ideally reported in an orthonormal rectilinear Cartesian coordinate system. However, due to scanning errors and measurement distortions, the measurement process is far from the ideal Cartesian condition. The paper addresses geometrical modelling of the scanning system dynamics, presenting a mathematical model which describes the surface metric x-, y- and z- coordinates as a function of the measured x'-, y'- and z'-coordinates respectively. The complete mathematical model provides a relevant contribution to characterization and calibration, and ultimately to traceability, of SPMs, when applied for quantitative characterization
Varney, Michael C. M.; Jenness, Nathan J.; Smalyukh, Ivan I.
2014-02-01
Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.
Geometric model of topological insulators from the Maxwell algebra
Palumbo, Giandomenico
2017-11-01
We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.
Geometric Model of Topological Insulators from the Maxwell Algebra
Palumbo, Giandomenico
I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
Methods for Geometric Data Validation of 3d City Models
Wagner, D.; Alam, N.; Wewetzer, M.; Pries, M.; Coors, V.
2015-12-01
Geometric quality of 3D city models is crucial for data analysis and simulation tasks, which are part of modern applications of the data (e.g. potential heating energy consumption of city quarters, solar potential, etc.). Geometric quality in these contexts is however a different concept as it is for 2D maps. In the latter case, aspects such as positional or temporal accuracy and correctness represent typical quality metrics of the data. They are defined in ISO 19157 and should be mentioned as part of the metadata. 3D data has a far wider range of aspects which influence their quality, plus the idea of quality itself is application dependent. Thus, concepts for definition of quality are needed, including methods to validate these definitions. Quality on this sense means internal validation and detection of inconsistent or wrong geometry according to a predefined set of rules. A useful starting point would be to have correct geometry in accordance with ISO 19107. A valid solid should consist of planar faces which touch their neighbours exclusively in defined corner points and edges. No gaps between them are allowed, and the whole feature must be 2-manifold. In this paper, we present methods to validate common geometric requirements for building geometry. Different checks based on several algorithms have been implemented to validate a set of rules derived from the solid definition mentioned above (e.g. water tightness of the solid or planarity of its polygons), as they were developed for the software tool CityDoctor. The method of each check is specified, with a special focus on the discussion of tolerance values where they are necessary. The checks include polygon level checks to validate the correctness of each polygon, i.e. closeness of the bounding linear ring and planarity. On the solid level, which is only validated if the polygons have passed validation, correct polygon orientation is checked, after self-intersections outside of defined corner points and edges
Geometric Models for Isotropic Random Porous Media: A Review
Directory of Open Access Journals (Sweden)
Helmut Hermann
2014-01-01
Full Text Available Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.
The Effects of Computer-assisted and Distance Learning of Geometric Modeling
Directory of Open Access Journals (Sweden)
Omer Faruk Sozcu
2013-01-01
Full Text Available The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed topics
Geometric and Colour Data Fusion for Outdoor 3D Models
Directory of Open Access Journals (Sweden)
Ricardo Chacón
2012-05-01
Full Text Available This paper deals with the generation of accurate, dense and coloured 3D models of outdoor scenarios from scanners. This is a challenging research field in which several problems still remain unsolved. In particular, the process of 3D model creation in outdoor scenes may be inefficient if the scene is digitalized under unsuitable technical (specific scanner on-board camera and environmental (rain, dampness, changing illumination conditions. We address our research towards the integration of images and range data to produce photorealistic models. Our proposal is based on decoupling the colour integration and geometry reconstruction stages, making them independent and controlled processes. This issue is approached from two different viewpoints. On the one hand, given a complete model (geometry plus texture, we propose a method to modify the original texture provided by the scanner on-board camera with the colour information extracted from external images taken at given moments and under specific environmental conditions. On the other hand, we propose an algorithm to directly assign external images onto the complete geometric model, thus avoiding tedious on-line calibration processes. We present the work conducted on two large Roman archaeological sites dating from the first century A.D., namely, the Theatre of Segobriga and the Fori Porticus of Emerita Augusta, both in Spain. The results obtained demonstrate that our approach could be useful in the digitalization and 3D modelling fields.
Derivative Geometric Modeling of Basic Rotational Solids on CATIA
Institute of Scientific and Technical Information of China (English)
MENG Xiang-bao; PAN Zi-jian; ZHU Yu-xiang; LI Jun
2011-01-01
Hybrid models derived from rotational solids like cylinders, cones and spheres were implemented on CATIA software. Firstly, make the isosceles triangular prism, cuboid, cylinder, cone, sphere, and the prism with tangent conic and curved triangle ends, the cuboid with tangent cylindrical and curved rectangle ends, the cylinder with tangent spherical and curved circular ends as the basic Boolean deference units to the primary cylinders, cones and spheres on symmetrical and some critical geometric conditions, forming a series of variant solid models. Secondly, make the deference units above as the basic union units to the main cylinders, cones, and spheres accordingly, forming another set of solid models. Thirdly, make the tangent ends of union units into oblique conic, cylindrical, or with revolved triangular pyramid, quarterly cylinder and annulus ends on sketch based features to the main cylinders, cones, and spheres repeatedly, thus forming still another set of solid models. It is expected that these derivative models be beneficial both in the structure design, hybrid modeling, and finite element analysis of engineering components and in comprehensive training of spatial configuration of engineering graphics.
International Nuclear Information System (INIS)
Vishnyakova, T.P.; Klychev, Sh.I.
1992-01-01
The use of optical mixers in the optical irradiators of simulators of direct and concentrated solar radiation has been proposed. In this paper, the parameters of an optical mixer are calculated geometrically, and the effect of the parameters of the optical mixer on the unformity of the irradiance distribution η of the radiation flux on the detector is investigated. These investigations show that the light distribution from an optical mixer is close to the characteristics of an ideal uniform emitter within the region from 0 to the limit of α. 5 refs., 4 figs
Soft hadronic production by ECCO in the geometrical branching model
International Nuclear Information System (INIS)
Pan, J.; Hwa, R.C.
1993-01-01
Soft production of hadrons in hadronic collisions is described in the geometrical branching model and implemented by the eikonal cascade code (ECCO). It is shown that the major global features of multiparticle production can be reproduced by one essential characterization of the dynamics of branching, namely, a scaling law for the mass distribution of daughter clusters. Without further adjustment of any parameters, the event generator can produce local features of multiplicity fluctuations in agreement with the NA22 intermittency data. The scaling exponent ν is determined to be 1.522 at √s =22 GeV, independent of the dimensionality of the intermittency analysis. It is shown that ν is approximately independent of the collision energy
Standalone visualization tool for three-dimensional DRAGON geometrical models
International Nuclear Information System (INIS)
Lukomski, A.; McIntee, B.; Moule, D.; Nichita, E.
2008-01-01
DRAGON is a neutron transport and depletion code able to solve one-, two- and three-dimensional problems. To date DRAGON provides two visualization modules, able to represent respectively two- and three-dimensional geometries. The two-dimensional visualization module generates a postscript file, while the three dimensional visualization module generates a MATLAB M-file with instructions for drawing the tracks in the DRAGON TRACKING data structure, which implicitly provide a representation of the geometry. The current work introduces a new, standalone, tool based on the open-source Visualization Toolkit (VTK) software package which allows the visualization of three-dimensional geometrical models by reading the DRAGON GEOMETRY data structure and generating an axonometric image which can be manipulated interactively by the user. (author)
Directory of Open Access Journals (Sweden)
Masuda Kazuhiko
2016-01-01
Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.
Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu
2006-07-10
The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.
International Nuclear Information System (INIS)
Borovikov, V.A.; Kinber, B.E.
1988-01-01
The heuristic criteria (HC) of validity of geometric optics (GO) and of the geometric theory of diffraction (GTD), suggested in [2-7, 13, 14] and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed. Numerous examples of HC invalidity are given, as well as the reasons. In particular, HC provide an incorrect answer for all GO problems with caustics, since in these problems there always exists a ray, whose FV is nonlocal and covers the FV of other rays. The HC are shown to be unsuitable for multiple ray GTD problems, as well as for the simplest problems of diffraction of a cylindrical wave by a half-plane and of a plane wave by a curved half-plane
Constantinides, E. D.; Marhefka, R. J.
1994-01-01
A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly
Rapid world modeling: Fitting range data to geometric primitives
International Nuclear Information System (INIS)
Feddema, J.; Little, C.
1996-01-01
For the past seven years, Sandia National Laboratories has been active in the development of robotic systems to help remediate DOE's waste sites and decommissioned facilities. Some of these facilities have high levels of radioactivity which prevent manual clean-up. Tele-operated and autonomous robotic systems have been envisioned as the only suitable means of removing the radioactive elements. World modeling is defined as the process of creating a numerical geometric model of a real world environment or workspace. This model is often used in robotics to plan robot motions which perform a task while avoiding obstacles. In many applications where the world model does not exist ahead of time, structured lighting, laser range finders, and even acoustical sensors have been used to create three dimensional maps of the environment. These maps consist of thousands of range points which are difficult to handle and interpret. This paper presents a least squares technique for fitting range data to planar and quadric surfaces, including cylinders and ellipsoids. Once fit to these primitive surfaces, the amount of data associated with a surface is greatly reduced up to three orders of magnitude, thus allowing for more rapid handling and analysis of world data
Diffraction, self-focusing, and the geometrical optics limit in laser produced plasmas
International Nuclear Information System (INIS)
Marchand, R.; Rankin, R.; Capjack, C.E.; Birnboim, A.
1987-01-01
The effect of diffraction on the self-modulation of an intense laser beam in an initially uniform hydrogen plasma is investigated. A formalism is used in which the diffraction term in the paraxial wave equation can be arbitrarily reduced by the use of a weight factor iota. In the limit where iota approaches zero, it is shown that the paraxial wave equation correctly reduces to the geometrical optics limit and that the problem then becomes formally equivalent to solving the ray-tracing equations. When iota = 1, the paraxial wave equation takes its usual form and diffraction is fully accounted for. This formalism is applied to the simulation of self-modulation of an intense laser beam in a hydrogen plasma, for which diffraction is shown to be significant
International Nuclear Information System (INIS)
Nohra, R.; Parol, F.; Dubuisson
2015-01-01
The aim of this work is the detection and characterization of cirrus clouds from ground-based lidar measurements acquired at 532 nm wave length. An inversion method has been developed during this work to realize a climatologyof cirrus clouds over Lille, France (50.65°N, 3.08ºE) from 2008 to 2013. The mid-cloud height is generally observed between 7 and 13 km, and a mean thickness is found to be 1.4 ±0.8 km. Visibleclouds, characterized by anoptical thickness between 0.03 and 0.3, present 68 % of the total observed cirrus clouds. The methodology used in this work andthe retrieved geometrical and optical parameters of cirrus clouds are presented in this article. (author)
Generalization of the geometric optical series approach for nonadiabatic scattering problems
International Nuclear Information System (INIS)
Herman, M.F.
1982-01-01
The geometric optical series approach of Bremmer is generalized for multisurface nonadiabatic scattering problems. This method yields the formal solution of the Schroedinger equation as an infinite series of multiple integrals. The zeroth order term corresponds to WKB propagation on a single adiabatic surface, while the general Nth order term involves N reflections and/or transitions between surfaces accompanied by ''free,'' single surface semiclassical propagation between the points of reflection and transition. Each term is integrated over all possible transition and reflection points. The adiabatic and diabatic limits of this expression are discussed. Numerical results, in which all reflections are ignored, are presented for curve crossing and noncrossing problems. These results are compared to exact quantum results and are shown to be highly accurate
Mittra, R.; Rushdi, A.
1979-01-01
An approach for computing the geometrical optic fields reflected from a numerically specified surface is presented. The approach includes the step of deriving a specular point and begins with computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Then, a cluster of three adjacent rays are chosen to define a 'mean ray' and the divergence factor associated with this mean ray. Finally, the ampilitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.
Geometric Aspects and Some Uses of Deformed Models of Thermostatistics
Directory of Open Access Journals (Sweden)
Alexandre Gavrilik
2018-02-01
Full Text Available We consider diverse deformed Bose gas models (DBGMs focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called μ -deformed Bose gas model ( μ -DBGM, main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior—Bose-like condensation; we find the critical temperature T c ( μ depending on μ so that T c ( μ > T c ( Bose for μ > 0 . This fact and other advantages of μ -DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter μ , allow us to consider the condensate in μ -DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter ( μ ˜ , q -deformed BGM for effective description of the peculiar (non-Bose like behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven. Herein, we point out the transparent role of the two deformation parameters μ ˜ and q as being responsible for compositeness and (effective account of interactions of pions, respectively.
Reichardt, J; Hess, M; Macke, A
2000-04-20
Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.
International Nuclear Information System (INIS)
Bi Lei; Yang Ping; Kattawar, George W.; Hu Yongxiang; Baum, Bryan A.
2011-01-01
A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a 'benchmark' within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.
On unified field theories, dynamical torsion and geometrical models: II
International Nuclear Information System (INIS)
Cirilo-Lombardo, D.J.
2011-01-01
We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl, Lett. 2010. V.7, No.5. P.299-307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean RxO 3 ∼ RxSU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: i) the torsion is not identified directly with the Yang-Mills type strength field, ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor a with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and iii) of two possible structures of the torsion the 'tratorial' form (the only one studied here) forbid wormhole configurations, leading only to cosmological instanton space-time in eternal expansion
International Nuclear Information System (INIS)
Karimi, M.J.; Rezaei, G.; Nazari, M.
2014-01-01
Based on the effective mass and parabolic one band approximations, simultaneous effects of the geometrical size, hydrogenic impurity, hydrostatic pressure, and temperature on the intersubband optical absorption coefficients and refractive index changes in multilayered spherical quantum dots are studied. Energy eigenvalues and eigenvectors are calculated using the fourth-order Runge–Kutta method and optical properties are obtained using the compact density matrix approach. The results indicate that the hydrogenic impurity, hydrostatic pressure, temperature and geometrical parameters such as the well and barrier widths have a great influence on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes. -- Highlights: • Hydrogenic impurity effects on the optical properties of a MSQD are investigated. • Hydrostatic pressure and temperature effects are also studied. • Hydrogenic impurity has a great influence on the linear and nonlinear ACs and RICs. • Hydrostatic pressure and temperature change the linear and nonlinear ACs and RICs
Cahuantzi, Roberto; Buckley, Alastair
2017-09-01
Making accurate and reliable measurements of solar irradiance is important for understanding performance in the photovoltaic energy sector. In this paper, we present design details and performance of a number of fibre optic couplers for use in irradiance measurement systems employing remote light sensors applicable for either spectrally resolved or broadband measurement. The angular and spectral characteristics of different coupler designs are characterised and compared with existing state-of-the-art commercial technology. The new coupler designs are fabricated from polytetrafluorethylene (PTFE) rods and operate through forward scattering of incident sunlight on the front surfaces of the structure into an optic fibre located in a cavity to the rear of the structure. The PTFE couplers exhibit up to 4.8% variation in scattered transmission intensity between 425 nm and 700 nm and show minimal specular reflection, making the designs accurate and reliable over the visible region. Through careful geometric optimization near perfect cosine dependence on the angular response of the coupler can be achieved. The PTFE designs represent a significant improvement over the state of the art with less than 0.01% error compared with ideal cosine response for angles of incidence up to 50°.
Cahuantzi, Roberto; Buckley, Alastair
2017-09-01
Making accurate and reliable measurements of solar irradiance is important for understanding performance in the photovoltaic energy sector. In this paper, we present design details and performance of a number of fibre optic couplers for use in irradiance measurement systems employing remote light sensors applicable for either spectrally resolved or broadband measurement. The angular and spectral characteristics of different coupler designs are characterised and compared with existing state-of-the-art commercial technology. The new coupler designs are fabricated from polytetrafluorethylene (PTFE) rods and operate through forward scattering of incident sunlight on the front surfaces of the structure into an optic fibre located in a cavity to the rear of the structure. The PTFE couplers exhibit up to 4.8% variation in scattered transmission intensity between 425 nm and 700 nm and show minimal specular reflection, making the designs accurate and reliable over the visible region. Through careful geometric optimization near perfect cosine dependence on the angular response of the coupler can be achieved. The PTFE designs represent a significant improvement over the state of the art with less than 0.01% error compared with ideal cosine response for angles of incidence up to 50°.
DEFF Research Database (Denmark)
Primdahl, Fritz; Brauer, Peter; Merayo, José M.G.
2002-01-01
optical or geometrical axes in order to be able to determine the precise orientation of the magnetic coordinate axes in an external reference system. Two methods for determining a reference axis in the sensor coordinates are discussed: (1) using a triaxial coil facility to measure the sensor orientation...
Energy Technology Data Exchange (ETDEWEB)
Cao Liji; Breithaupt, Mathies; Peter, Joerg [Division of Medical Physics in Radiology, German Cancer Research Center, Im Neuenheimer Feld 280, 69120 Heidelberg (Germany)], E-mail: l.cao@dkfz.de
2010-03-21
A mathematical approach for geometric co-calibration of a dual-modal small-animal imaging system is presented. The system comprises an optical imaging setup for in vivo bioluminescence and fluorescence detection, as well as an x-ray CT, both mounted on a common rotatable gantry enabling fully simultaneous imaging at axially overlapping fields-of-view. Geometric co-calibration is performed once by imaging a single cylindrical light-emitting source with both modalities over 360 deg. at two axial positions, respectively. Given the three-dimensional coordinates of the source positions in the reconstructed CT volume data along with their two-dimensional locations projected at the optical detector plane, the following intrinsic system parameters are calculated: (i) the intrinsic geometric parameters of the optical detection system-five parameters for each view and (ii) the relative positional relationship between the optical and CT systems-two parameters for each view. After co-calibration is performed, experimental studies using phantoms demonstrate the high degree of intrinsic positional accuracy between the optical and CT measurements. The most important advantage of this approach is that dual-modal data fusion is accomplished without any post-registration strategies.
Muon reconstruction with a geometrical model in JUNO
Genster, C.; Schever, M.; Ludhova, L.; Soiron, M.; Stahl, A.; Wiebusch, C.
2018-03-01
The Jiangmen Neutrino Underground Observatory (JUNO) is a 20 kton liquid scintillator detector currently under construction near Kaiping in China. The physics program focuses on the determination of the neutrino mass hierarchy with reactor anti-neutrinos. For this purpose, JUNO is located 650 m underground with a distance of 53 km to two nuclear power plants. As a result, it is exposed to a muon flux that requires a precise muon reconstruction to make a veto of cosmogenic backgrounds viable. Established muon tracking algorithms use time residuals to a track hypothesis. We developed an alternative muon tracking algorithm that utilizes the geometrical shape of the fastest light. It models the full shape of the first, direct light produced along the muon track. From the intersection with the spherical PMT array, the track parameters are extracted with a likelihood fit. The algorithm finds a selection of PMTs based on their first hit times and charges. Subsequently, it fits on timing information only. On a sample of through-going muons with a full simulation of readout electronics, we report a spatial resolution of 20 cm of distance from the detector's center and an angular resolution of 1.6o over the whole detector. Additionally, a dead time estimation is performed to measure the impact of the muon veto. Including the step of waveform reconstruction on top of the track reconstruction, a loss in exposure of only 4% can be achieved compared to the case of a perfect tracking algorithm. When including only the PMT time resolution, but no further electronics simulation and waveform reconstruction, the exposure loss is only 1%.
Westheimer, Gerald
2008-09-01
Differences between the geometrical properties of simple configurations and their visual percept are called geometrical-optical illusions. They can be differentiated from illusions in the brightness or color domains, from ambiguous figures and impossible objects, from trompe l'oeil and perspective drawing with perfectly valid views, and from illusory contours. They were discovered independently by several scientists in a short time span in the 1850's. The clear distinction between object and visual space that they imply allows the question to be raised whether the transformation between the two spaces can be productively investigated in terms of differential geometry and metrical properties. Perceptual insight and psychophysical research prepares the ground for investigation of the neural representation of space but, because visual attributes are processed separately in parallel, one looks in vain for a neural map that is isomorphic with object space or even with individual forms it contains. Geometrical-optical illusions help reveal parsing rules for sensory signals by showing how conflicts are resolved when there is mismatch in the output of the processing modules for various primitives as a perceptual pattern's unitary structure is assembled. They point to a hierarchical ordering of spatial primitives: cardinal directions and explicit contours predominate over oblique orientation and implicit contours (Poggendorff illusion); rectilinearity yields to continuity (Hering illusion), point position and line length to contour orientation (Ponzo). Hence the geometrical-optical illusions show promise as analytical tools in unraveling neural processing in vision.
Information Geometric Complexity of a Trivariate Gaussian Statistical Model
Directory of Open Access Journals (Sweden)
Domenico Felice
2014-05-01
Full Text Available We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult it is to make macroscopic predictions about systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that, for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.
Inexpensive demonstration set for teaching geometrical optics made by 3D printer
Havlíček, Karel; Ryston, Matěj
2018-03-01
Good sets for teaching geometric optics are relatively expensive to buy and difficult to make on your own, which often forces teachers to use less than ideal instruments and methods. This is a great shame, since this is a visually appealing topic that can motivate students. For this reason, we have designed a set that is relatively cheap, easy to use and can therefore (in some cases) remedy this situation. Our set is manufactured using 3D printing technology, which limits its users to those that have access to it; however, 3D printing technology is becoming more and more accessible every day (even in schools). On the other hand, 3D printing allows us to let the machines do the majority of the manufacturing work, making the process of building the set almost as simple as ‘download and press print’. This article presents this set, what it consists of, how it is done and where can you find all the necessary files and instructions.
Non-geometrical optics investigation of mode conversion in weakly relativistic inhomogeneous plasmas
International Nuclear Information System (INIS)
Imre, K.
1985-06-01
Electron cyclotron resonance heating of plasmas by waves incident to the fundamental and second harmonic layer is investigated. When the wave propagation is nearly perpendicular to the equilibrium field in a weakly inhomogeneous plasma the standard geometrical optics breaks down and the relativistic corrections become significant at the resonance layer. Unlike the previous studies of this problem, the governing equations are derived from the linearized relativistic Vlasov equation coupled with Maxwell's equations, rather than using the uniform field dispersion relation to construct equations by replacing the refractive index by some spatial differential operations. We employ a boundary layer analysis at the resonance region and match the inner and outer solutions in the usual manner. We obtain not only the full wave solution of the problem, but also the set of physical parameters and their ranges in which the analysis is valid. Although we obtain analytic results for the asymptotic solutions, our analysis usually requires a numerical procedure when the relativistic and/or nonzero parallel refractive index are included
Geometric modelling of a make mandible utilising CT imaging
International Nuclear Information System (INIS)
Baker, N.; Basu, A.; McLean, A.G.; Jamieson, D.; Jonkman, M.
1996-01-01
Full text: The mandible is one of the most important and frequently used bones in the human body. It is responsible for basic actions such as mastication, communication and swallowing. It houses and provides protection for the tongue, teeth and salivary glands. The mandible is unique in that it has two anatomically identical articulations, each providing the same function. Both articulations, however, rarely have synchronous force and motion characteristics. The mandible is the only moveable bone in the skull and is capable of the following motions: depression - lowering the mandible, as in yawning, elevation - raising the mandible, protraction - thrusting the jaw forward, retraction - withdrawing the jaw posteriorly, and lateral deviation - sideways displacement in the transverse plane. The mandible is an irregular bone comprising a broad U shaped body with two ascending rami. The rami are quadrilateral plate like structures with lateral sides which are nearly flat. The mandible is subjected to repetitive loading and is susceptible to wear at its articulations, cyclic fatigue and dislocation. Despite the importance of the mandible little is understood about its mechanical properties and loading parameters. The purpose of this study was to create a three dimensional geometric model of a human mandible based on anatomical data. A 21 year old male with no history of mandible fracture or temporomandibular joint dysfunction was selected. The mandible was non-invasively imaged by Computed Tomography (CT). The subject was imaged lying on his back with the head supported and immobilised by a U shaped head rest. Seventeen parallel cross-sectional images oblique to the transverse plane were constructed. Cortical and cancellous bone boundaries were manually digitised for every image using a Science Accessories Corporation GP-9 digitiser linked to an IBM 286 SX personal computer. The data was transferred to a global coordinate system and entered into MSC/PATRAN finite element
Sheil, Conor J; Bahrami, Mehdi; Goncharov, Alexander V
2014-05-01
We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation.
Models of optical quantum computing
Directory of Open Access Journals (Sweden)
Krovi Hari
2017-03-01
Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.
Modeling of semiconductor optical amplifiers
DEFF Research Database (Denmark)
Mørk, Jesper; Bischoff, Svend; Berg, Tommy Winther
We discuss the modelling of semiconductor optical amplifiers with emphasis on their high-speed properties. Applications in linear amplification as well as ultrafast optical signal processing are reviewed. Finally, the possible role of quantum-dot based optical amplifiers is discussed.......We discuss the modelling of semiconductor optical amplifiers with emphasis on their high-speed properties. Applications in linear amplification as well as ultrafast optical signal processing are reviewed. Finally, the possible role of quantum-dot based optical amplifiers is discussed....
A differential-geometric approach to generalized linear models with grouped predictors
Augugliaro, Luigi; Mineo, Angelo M.; Wit, Ernst C.
We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important
Korte, Dorota; Franko, Mladen
2015-01-01
In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO2, N- and C-doped TiO2, or TiO2/SiO2 composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature.
Directory of Open Access Journals (Sweden)
Dai Guangyao
2018-01-01
Full Text Available Cirrus clouds affect the energy budget and hydrological cycle of the earth’s atmosphere. The Tibetan Plateau (TP plays a significant role in the global and regional climate. Optical and geometrical properties of cirrus clouds in the TP were measured in July-August 2014 by lidar and radiosonde. The statistics and temperature dependences of the corresponding properties are analyzed. The cirrus cloud formations are discussed with respect to temperature deviation and dynamic processes.
EVALUATION OF RATIONAL FUNCTION MODEL FOR GEOMETRIC MODELING OF CHANG'E-1 CCD IMAGES
Directory of Open Access Journals (Sweden)
Y. Liu
2012-08-01
Full Text Available Rational Function Model (RFM is a generic geometric model that has been widely used in geometric processing of high-resolution earth-observation satellite images, due to its generality and excellent capability of fitting complex rigorous sensor models. In this paper, the feasibility and precision of RFM for geometric modeling of China's Chang'E-1 (CE-1 lunar orbiter images is presented. The RFM parameters of forward-, nadir- and backward-looking CE-1 images are generated though least squares solution using virtual control points derived from the rigorous sensor model. The precision of the RFM is evaluated by comparing with the rigorous sensor model in both image space and object space. Experimental results using nine images from three orbits show that RFM can precisely fit the rigorous sensor model of CE-1 CCD images with a RMS residual error of 1/100 pixel level in image space and less than 5 meters in object space. This indicates that it is feasible to use RFM to describe the imaging geometry of CE-1 CCD images and spacecraft position and orientation. RFM will enable planetary data centers to have an option to supply RFM parameters of orbital images while keeping the original orbit trajectory data confidential.
Roy, G; Bissonnette, L R
2001-09-20
Backscatter and depolarization lidar measurements from clouds and precipitation are reported as functions of the elevation angle of the pointing lidar direction. We recorded the data by scanning the lidar beam (Nd:YAG) at a constant angular speed of ~3.5 degrees /s while operating at a repetition rate of 10 Hz. We show that in rain there is an evident and at times spectacular dependence on the elevation angle. That dependence appears to be sensitive to raindrop size. We have developed a three-dimensional polarization-dependent ray-tracing algorithm to calculate the backscatter and the depolarization ratio by large nonspherical droplets. We have applied it to raindrop shapes derived from existing static and dynamic (oscillating) models. We show that many of the observed complex backscatter and depolarization features can be interpreted to a good extent by geometrical optics. These results suggest that there is a definite need for more extensive calculations of the scattering phase matrix elements for large deformed raindrops as functions of the direction of illumination. Obvious applications are retrieval of information on the liquid-solid phase of precipitation and on the size and the vibration state of raindrops.
Modeling thermodynamic distance, curvature and fluctuations a geometric approach
Badescu, Viorel
2016-01-01
This textbook aims to briefly outline the main directions in which the geometrization of thermodynamics has been developed in the last decades. The textbook is accessible to people trained in thermal sciences but not necessarily with solid formation in mathematics. For this, in the first chapters a summary of the main mathematical concepts is made. In some sense, this makes the textbook self-consistent. The rest of the textbook consists of a collection of results previously obtained in this young branch of thermodynamics. The manner of presentation used throughout the textbook is adapted for ease of access of readers with education in natural and technical sciences.
Geometrical Optimization Approach to Isomerization: Models and Limitations.
Chang, Bo Y; Shin, Seokmin; Engel, Volker; Sola, Ignacio R
2017-11-02
We study laser-driven isomerization reactions through an excited electronic state using the recently developed Geometrical Optimization procedure. Our goal is to analyze whether an initial wave packet in the ground state, with optimized amplitudes and phases, can be used to enhance the yield of the reaction at faster rates, driven by a single picosecond pulse or a pair of femtosecond pulses resonant with the electronic transition. We show that the symmetry of the system imposes limitations in the optimization procedure, such that the method rediscovers the pump-dump mechanism.
Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review
Directory of Open Access Journals (Sweden)
Gianpaolo Savio
2018-01-01
Full Text Available Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed.
Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review.
Savio, Gianpaolo; Rosso, Stefano; Meneghello, Roberto; Concheri, Gianmaria
2018-01-01
Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed.
Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review
Rosso, Stefano; Meneghello, Roberto; Concheri, Gianmaria
2018-01-01
Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed. PMID:29487626
Singh, A.; Seitz, F.; Schwatke, C.; Güntner, A.
2012-04-01
Satellite altimetry is capable of measuring surface water level changes of large water bodies. This is especially interesting for regions where in-situ gauges are sparse or not available. Temporal variations of coastline and horizontal extent of a water body can be derived from optical remote sensing data. A joint analysis of both data types together with a digital elevation model allows for the estimation of water volume changes. Related variations of water mass map into the observations of the satellite gravity field mission GRACE. In this presentation, we demonstrate the application of heterogeneuous remote sensing methods for studying chages of water volume and mass of the Aral Sea and compare the results with respect to their consistency. Our analysis covers the period 2002-2011. In particular we deal with data from multi-mission radar and laser satellite altimetry that are analyzed in combination with coastlines from Landsat images. The resultant vertical and horizontal variations of the lake surface are geometrically intersected with the bathymetry of the Aral Sea in order to compute volumetric changes. These are transformed into variations of water mass that are subsequently compared with storage changes derived from GRACE satellite gravimetry. Hence we obtain a comprehensive picture of the hydrological changes in the region. Observations from all datasets correspond quite well with each other with respect to their temporal development. However, geometrically determined volume changes and mass changes observed by GRACE agree less well during years of heavy water inflow in to the Aral Sea from its southern tributary 'Amu Darya' since the GRACE signals are contaminated by the large mass of water stored in the river delta and prearalie region On the other hand, GRACE observations of the river basins of Syr Darya and Amu Dayra correspond very well with hydrological models and mass changes computed from the balance of precipitation, evaporation and runoff
Analysis of Geometric Thinking Students’ and Process-Guided Inquiry Learning Model
Hardianti, D.; Priatna, N.; Priatna, B. A.
2017-09-01
This research aims to analysis students’ geometric thinking ability and theoretically examine the process-oriented guided iquiry (POGIL) model. This study uses qualitative approach with descriptive method because this research was done without any treatment on subjects. Data were collected naturally. This study was conducted in one of the State Junior High School in Bandung. The population was second grade students and the sample was 32 students. Data of students’ geometric thinking ability were collected through geometric thinking test. These questions are made based on the characteristics of geometry thinking based on van hiele’s theory. Based on the results of the analysis and discussion, students’ geometric thinking ability is still low so it needs to be improved. Therefore, an effort is needed to overcome the problems related to students’ geometric thinking ability. One of the efforts that can be done by doing the learning that can facilitate the students to construct their own geometry concept, especially quadrilateral’s concepts so that students’ geometric thinking ability can enhance maximally. Based on study of the theory, one of the learning models that can enhance the students’ geometric thinking ability is POGIL model.
The Wigner distribution function and Hamilton's characteristics of a geometric-optical system
Bastiaans, M.J.
1979-01-01
Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner
Kotsifaki, Domna G.; Mackenzie, Mark D.; Polydefki, Georgia; Kar, Ajoy K.; Makropoulou, Mersini; Serafetinides, Alexandros A.
2017-12-01
Microfluidic devices provide a platform with wide ranging applications from environmental monitoring to disease diagnosis. They offer substantive advantages but are often not optimized or designed to be used by nonexpert researchers. Microchannels of a microanalysis platform and their geometrical characterization are of eminent importance when designing such devices. We present a method that is used to optimize each microchannel within a device using high-throughput particle manipulation. For this purpose, glass-based microfluidic devices, with three-dimensional channel networks of several geometrical sizes, were fabricated by employing laser fabrication techniques. The effect of channel geometry was investigated by employing an optical tweezer. The optical trapping force depends on the flow velocity that is associated with the dimensions of the microchannel. We observe a linear dependence of the trapping efficiency and of the fluid flow velocity, with the channel dimensions. We determined that the highest trapping efficiency was achieved for microchannels with aspect ratio equal to one. Numerical simulation validated the impact of the device design dimensions on the trapping efficiency. This investigation indicates that the geometrical characteristics, the flow velocity, and trapping efficiency are crucial and should be considered when fabricating microfluidic devices for cell studies.
Rotenberg, David J.
Artifacts caused by head motion are a substantial source of error in fMRI that limits its use in neuroscience research and clinical settings. Real-time scan-plane correction by optical tracking has been shown to correct slice misalignment and non-linear spin-history artifacts, however residual artifacts due to dynamic magnetic field non-uniformity may remain in the data. A recently developed correction technique, PLACE, can correct for absolute geometric distortion using the complex image data from two EPI images, with slightly shifted k-space trajectories. We present a correction approach that integrates PLACE into a real-time scan-plane update system by optical tracking, applied to a tissue-equivalent phantom undergoing complex motion and an fMRI finger tapping experiment with overt head motion to induce dynamic field non-uniformity. Experiments suggest that including volume by volume geometric distortion correction by PLACE can suppress dynamic geometric distortion artifacts in a phantom and in vivo and provide more robust activation maps.
Svehla, Drazen; Rothacher, Markus; Hugentobler, Urs; Steigenberger, Peter; Ziebart, Marek
2014-05-01
Solar radiation pressure is the main source of errors in the precise orbit determination of GNSS satellites. All deficiencies in the modeling of Solar radiation pressure map into estimated terrestrial reference frame parameters as well as into derived gravity field coefficients and altimetry results when LEO orbits are determined using GPS. Here we introduce a new approach to geometrically map radial orbit perturbations of GNSS satellites using highly-performing clocks on board the first Galileo satellites. Only a linear model (time bias and time drift) needs to be removed from the estimated clock parameters and the remaining clock residuals map all radial orbit perturbations along the orbit. With the independent SLR measurements, we show that a Galileo clock is stable enough to map radial orbit perturbations continuously along the orbit with a negative sign in comparison to SLR residuals. Agreement between the SLR residuals and the clock residuals is at the 1 cm RMS for an orbit arc of 24 h. Looking at the clock parameters determined along one orbit revolution over a period of one year, we show that the so-called SLR bias in Galileo and GPS orbits can be explained by the translation of the determined orbit in the orbital plane towards the Sun. This orbit translation is due to thermal re-radiation and not accounting for the Sun elevation in the parameterization of the estimated Solar radiation pressure parameters. SLR ranging to GNSS satellites takes place typically at night, e.g. between 6 pm and 6 am local time when the Sun is in opposition to the satellite. Therefore, SLR observes only one part of the GNSS orbit with a negative radial orbit error that is mapped as an artificial bias in SLR observables. The Galileo clocks clearly show orbit translation for all Sun elevations: the radial orbit error is positive when the Sun is in conjuction (orbit noon) and negative when the Sun is in opposition (orbit midnight). The magnitude of this artificial negative SLR bias
Galilean generalized Robertson-Walker spacetimes: A new family of Galilean geometrical models
de la Fuente, Daniel; Rubio, Rafael M.
2018-02-01
We introduce a new family of Galilean spacetimes, the Galilean generalized Robertson-Walker spacetimes. This new family is relevant in the context of a generalized Newton-Cartan theory. We study its geometrical structure and analyse the completeness of its inextensible free falling observers. This sort of spacetimes constitutes the local geometric model of a much wider family of spacetimes admitting certain conformal symmetry. Moreover, we find some sufficient geometric conditions which guarantee a global splitting of a Galilean spacetime as a Galilean generalized Robertson-Walker spacetime.
Geometrical Modeling of Woven Fabrics Weavability-Limit New Relationships
Directory of Open Access Journals (Sweden)
Dalal Mohamed
2017-03-01
Full Text Available The weavability limit and tightness for 2D and 3D woven fabrics is an important factor and depends on many geometric parameters. Based on a comprehensive review of the literature on textile fabric construction and property, and related research on fabric geometry, a study of the weavability limit and tightness relationships of 2D and 3D woven fabrics was undertaken. Experiments were conducted on a representative number of polyester and cotton woven fabrics which have been woven in our workshop, using three machines endowed with different insertion systems (rapier, projectiles and air jet. Afterwards, these woven fabrics have been analyzed in the laboratory to determine their physical and mechanical characteristics using air permeability-meter and KES-F KAWABATA Evaluation System for Fabrics. In this study, the current Booten’s weavability limit and tightness relationships based on Ashenhurst’s, Peirce’s, Love’s, Russell’s, Galuszynskl’s theory and maximum-weavability is reviewed and modified as new relationships to expand their use to general cases (2D and 3D woven fabrics, all fiber materiel, all yarns etc…. The theoretical relationships were examined and found to agree with experimental results. It was concluded that the weavability limit and tightness relationships are useful tools for weavers in predicting whether a proposed fabric construction was weavable and also in predicting and explaining their physical and mechanical properties.
Energy Technology Data Exchange (ETDEWEB)
Ebata, T [Tohoku Univ., Sendai (Japan). Coll. of General Education
1976-06-01
The geometrical distribution inferred from the inelastic cross section is assumed to be proportional to the partial waves. The precocious scaling and the Q/sup 2/-dependence of various quantities are treated from the geometrical point of view. It is shown that the approximate conservation of the orbital angular momentum may be a very practical rule to understand the helicity structure of various hadronic and electromagnetic reactions. The rule can be applied to inclusive reactions as well. The model is also applied to large angle processes. Through the discussion, it is suggested that many peculiar properties of the quark-parton can be ascribed to the geometrical effects.
International Nuclear Information System (INIS)
Gorodetski, Y.; Biener, G.; Niv, A.; Kleiner, V.; Hasman, E.
2005-01-01
Full Text:The behavior of geometrical phase elements illuminated with partially polarized monochromatic beams is being theoretically as well as experimentally investigated. The element discussed in this paper is composed of wave plates with retardation and space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders of right and left-handed circularly polarized states with conjugate geometrical phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix comprises a matrix termed as the vectorial interference matrix. This matrix contains the information concerning the correlation between the two orthogonal circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. Furthermore, we found that the equivalent mutual intensity of the emerging beam is being modulated according to the geometrical phase induced by the element. Other interesting phenomena along propagation will be discussed theoretically and experimentally demonstrated. We demonstrate experimentally our analysis by using a spherical geometrical phase element, which is realized by use of space-variant sub wavelength grating and illuminated with a CO 2 laser radiation of 10.6μm wavelength
Srivastava, Vandana; Jarzembski, Maurice A.
1991-01-01
This paper uses Mie theory to treat electromagnetic scattering and to evaluate field enhancement in the forward direction of a small droplet irradiated by a high-energy beam and compares the results of calculations with the field-enhancement evaluation obtained via geometrical optics treatment. Results of this comparison suggest that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support laser-induced Raman scattering. The results are supported by experimental observations of the interaction of a 120-micron-diam water droplet with a high-energy Nd:YAG laser beam.
Modelling and experimental investigation of geometrically graded NiTi shape memory alloys
International Nuclear Information System (INIS)
Shariat, Bashir S; Liu, Yinong; Rio, Gerard
2013-01-01
To improve actuation controllability of a NiTi shape memory alloy component in applications, it is desirable to create a wide stress window for the stress-induced martensitic transformation in the alloy. One approach is to create functionally graded NiTi with a geometric gradient in the actuation direction. This geometric gradient leads to transformation load and displacement gradients in the structure. This paper reports a study of the pseudoelastic behaviour of geometrically graded NiTi by means of mechanical model analysis and experimentation using three types of sample geometry. Closed-form solutions are obtained for nominal stress–strain variation of such components under cyclic tensile loading and the predictions are validated with experimental data. The geometrically graded NiTi samples exhibit a distinctive positive stress gradient for the stress-induced martensitic transformation and the slope of the stress gradient can be adjusted by sample geometry design. (paper)
The effects of geometric uncertainties on computational modelling of knee biomechanics
Meng, Qingen; Fisher, John; Wilcox, Ruth
2017-08-01
The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.
Mathematical modelling of air-flow in geometrically complicated areas
Fuka, Vladimír
2014-01-01
The Charles University Large-eddy Microscale Model (CLMM) and its application are presented. It is a numerical model for simulation of turbulent flow and dispersion in the planetary boundary layer. CLMM solves the incompressible Navier-Stokes equations in the Boussinesq approximation and describes turbulence using the large eddy simulation. Three applications of the model are presented. In the first case, the model is applied to the stable boundary layer over a flat terrain. The second case p...
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and
The mathematics of geometrical and physical optics. The k-funktion and its ramifications
Energy Technology Data Exchange (ETDEWEB)
Stavroudis, O.N. [Centro de Investigaciones en Optica, Leon, Guanajuato (Mexico)
2006-07-01
In this sequel to his book, 'The Optics of Rays, Wavefronts, and Caustics', Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens. From the contents: Part I: Preliminaries - Calculus of variations - Calculus of variations: differential geometry of space curves (helix and ellipse) - Fermat's principle and the ray equation for inhomogeneous isotropic media - Hilbert integral, the derivation of the Hamilton-Jacobi theory, and the eikonal equation - First-order partial differential equations. Part II: The k-Function - Calculation of surface differential geometry parameters - Ray tracing - Refraction of wavefronts at surfaces - Solution of the Maxwell equation in the context of the k-function. Part III: Applications - Pseudo Maxwell equations - Derivation and discussion of the Cartesian oval - The modern Schiefspiegler - Huygen's principle - Maxwell's model of Gauss' perfect lens. (orig.)
Rahmat-Samii, Yahya
1986-01-01
Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics analysis technique is used to investigate the effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and far-field patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as one wavelength, noticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.
Geometric Performance Analysis of Mutual Exclusion: The Model
Abrams, Marc
1990-01-01
This paper is motivated by the need to better understand parallel program run-time behavior. The paper first formally describes a general model of program execution based on Djkstra's progress graphs. The paper then defines a special case of the model representing two cyclic processes sharing mutually exclusive, reusable resources. Processes synchronize through semaphore operations that are not embedded in conditionally executed code segments. Model parameters are the times at which each ...
Asymptotic approach to the pricing of geometric asian options under the CEV model
International Nuclear Information System (INIS)
Lee, Min-Ku
2016-01-01
This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.
Deuteron microscopic optical model potential
International Nuclear Information System (INIS)
Guo Hairui; Han Yinlu; Shen Qingbiao; Xu Yongli
2010-01-01
A deuteron microscopic optical model potential is obtained by the Green function method through nuclear-matter approximation and local-density approximation based on the effective Skyrme interaction. The microscopic optical model potential is used to calculate the deuteron reaction cross sections and the elastic scattering angular distributions for some target nuclei in the mass range 6≤A≤208 with incident deuteron energies up to 200 MeV. The calculated results are compared with the experimental data.
Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies
Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration
Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.
Accuracy of geometrical modelling of heat transfer from tissue to blood vessels
Leeuwen, van G.M.J.; Kotte, A.N.T.J.; Bree, de J.; Koijk, van der J.F.; Crezee, J.; Lagendijk, J.J.W.
1997-01-01
We have developed a thermal model in which blood vessels are described as geometrical objects, 3D curves with associated diameters. Here the behaviour of the model is examined for low resolutions compared with the vessel diameter and for strongly curved vessels. The tests include a single straight
A Spectral Geometrical Model for Compton Scatter Tomography Based on the SSS Approximation
DEFF Research Database (Denmark)
Kazantsev, Ivan G.; Olsen, Ulrik Lund; Poulsen, Henning Friis
2016-01-01
The forward model of single scatter in the Positron Emission Tomography for a detector system possessing an excellent spectral resolution under idealized geometrical assumptions is investigated. This model has the form of integral equations describing a flux of photons emanating from the same ann...
Improving Completeness of Geometric Models from Terrestrial Laser Scanning Data
Directory of Open Access Journals (Sweden)
Clemens Nothegger
2011-12-01
Full Text Available The application of terrestrial laser scanning for the documentation of cultural heritage assets is becoming increasingly common. While the point cloud by itself is sufficient for satisfying many documentation needs, it is often desirable to use this data for applications other than documentation. For these purposes a triangulated model is usually required. The generation of topologically correct triangulated models from terrestrial laser scans, however, still requires much interactive editing. This is especially true when reconstructing models from medium range panoramic scanners and many scan positions. Because of residual errors in the instrument calibration and the limited spatial resolution due to the laser footprint, the point clouds from different scan positions never match perfectly. Under these circumstances many of the software packages commonly used for generating triangulated models produce models which have topological errors such as surface intersecting triangles, holes or triangles which violate the manifold property. We present an algorithm which significantly reduces the number of topological errors in the models from such data. The algorithm is a modification of the Poisson surface reconstruction algorithm. Poisson surfaces are resilient to noise in the data and the algorithm always produces a closed manifold surface. Our modified algorithm partitions the data into tiles and can thus be easily parallelized. Furthermore, it avoids introducing topological errors in occluded areas, albeit at the cost of producing models which are no longer guaranteed to be closed. The algorithm is applied to scan data of sculptures of the UNESCO World Heritage Site Schönbrunn Palace and data of a petrified oyster reef in Stetten, Austria. The results of the method’s application are discussed and compared with those of alternative methods.
Zlatkina, O. Yu
2018-04-01
There is a relationship between the service properties of component parts and their geometry; therefore, to predict and control the operational characteristics of parts and machines, it is necessary to measure their geometrical specifications. In modern production, a coordinate measuring machine is the advanced measuring instrument of the products geometrical specifications. The analysis of publications has shown that during the coordinate measurements the problems of choosing locating chart of parts and coordination have not been sufficiently studied. A special role in the coordination of the part is played by the coordinate axes informational content. Informational content is the sum of the degrees of freedom limited by the elementary item of a part. The coordinate planes of a rectangular coordinate system have different informational content (three, two, and one). The coordinate axes have informational content of four, two and zero. The higher the informational content of the coordinate plane or axis, the higher its priority for reading angular and linear coordinates is. The geometrical model production of the coordinate measurements object taking into account the information content of coordinate planes and coordinate axes allows us to clearly reveal the interrelationship of the coordinates of the deviations in location, sizes and deviations of their surfaces shape. The geometrical model helps to select the optimal locating chart of parts for bringing the machine coordinate system to the part coordinate system. The article presents an algorithm the model production of geometrical specifications using the example of the piston rod of a compressor.
Geometric data transfer between CAD systems: solid models
DEFF Research Database (Denmark)
Kroszynski, Uri; Palstroem, Bjarne; Trostmann, Erik
1989-01-01
The first phase of the ESPRIT project CAD*I resulted in a specification for the exchange of solid models as well as in some pilot implementations of processors based on this specification. The authors summarize the CAD*I approach, addressing the structure of neutral files for solids, entities......, and attributes supporting three kinds of representations: facilities for the transfer of parametric designs; referencing library components; and other general mechanisms. They also describe the current state of the specification and processor implementations and include an example of a CAD*I neutral file....... Results from cycle and intersystem solid model transfer tests are presented, showing the practicality of the CAD*I proposal. B-rep model transfer results are discussed in some detail. The relationship of this work to standardization efforts is outlined...
Geometrical and kinematical characterization of parallax-free world models
International Nuclear Information System (INIS)
Hasse, W.; Perlick, V.
1988-01-01
An arbitrary general relativistic world model, i.e., a pseudo-Riemannian manifold along with a timelike vector field V, is considered. Such a kinematical world model is called ''parallax-free'' iff the angle under which any two observers (i.e., integral curves of V) are seen by any third observer remains constant in the course of time. It is shown that a model is parallax-free iff V is proportional to some conformal Killing field. In this case V, especially, has to be shear-free. Furthermore a relationship between parallaxes and red shift is presented and a reference is made to considerations concerning the visibility of cosmic rotation
Deformations of Geometric Structures in Topological Sigma Models
International Nuclear Information System (INIS)
Bytsenko, A. A.
2010-01-01
We study a Lie algebra of formal vector fields W n with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra A = (A,Q), Q = ∂-bar+∂ deform, which is defined to be the cohomology of (-1) n Q+d Hoch . Here ∂-bar is the initial non-deformed BRST operator while ∂ deform is the deformed part whose algebra is a Lie algebra of linear vector fields gl n .
The geometric content of the interacting boson model for molecular spectra
International Nuclear Information System (INIS)
Levit, S.; Smilansky, U.
1981-12-01
The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic Hamiltonian onto an exactly solvable geometrical Hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operator in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM. (author)
Software module for geometric product modeling and NC tool path generation
International Nuclear Information System (INIS)
Sidorenko, Sofija; Dukovski, Vladimir
2003-01-01
The intelligent CAD/CAM system named VIRTUAL MANUFACTURE is created. It is consisted of four intelligent software modules: the module for virtual NC machine creation, the module for geometric product modeling and automatic NC path generation, the module for virtual NC machining and the module for virtual product evaluation. In this paper the second intelligent software module is presented. This module enables feature-based product modeling carried out via automatic saving of the designed product geometric features as knowledge data. The knowledge data are afterwards applied for automatic NC program generation for the designed product NC machining. (Author)
Geometrically engineering the standard model: Locally unfolding three families out of E8
International Nuclear Information System (INIS)
Bourjaily, Jacob L.
2007-01-01
This paper extends and builds upon the results of [J. L. Bourjaily, arXiv:0704.0444.], in which we described how to use the tools of geometrical engineering to deform geometrically engineered grand unified models into ones with lower symmetry. This top-down unfolding has the advantage that the relative positions of singularities giving rise to the many 'low-energy' matter fields are related by only a few parameters which deform the geometry of the unified model. And because the relative positions of singularities are necessary to compute the superpotential, for example, this is a framework in which the arbitrariness of geometrically engineered models can be greatly reduced. In [J. L. Bourjaily, arXiv:0704.0444.], this picture was made concrete for the case of deforming the representations of an SU 5 model into their standard model content. In this paper we continue that discussion to show how a geometrically engineered 16 of SO 10 can be unfolded into the standard model, and how the three families of the standard model uniquely emerge from the unfolding of a single, isolated E 8 singularity
International Nuclear Information System (INIS)
Sawan, M.; Wilson, P.; El-Guebaly, L.; Henderson, D.; Sviatoslavsky, G.; Bohm, T.; Kiedrowski, B.; Ibrahim, A.; Smith, B.; Slaybaugh, R.; Tautges, T.
2007-01-01
Fusion systems are, in general, geometrically complex requiring detailed three-dimensional (3-D) nuclear analysis. This analysis is required to address tritium self-sufficiency, nuclear heating, radiation damage, shielding, and radiation streaming issues. To facilitate such calculations, we developed an innovative computational tool that is based on the continuous energy Monte Carlo code MCNP and permits the direct use of CAD-based solid models in the ray-tracing. This allows performing the neutronics calculations in a model that preserves the geometrical details without any simplification, eliminates possible human error in modeling the geometry for MCNP, and allows faster design iterations. In addition to improving the work flow for simulating complex 3- D geometries, it allows a richer representation of the geometry compared to the standard 2nd order polynomial representation. This newly developed tool has been successfully tested for a detailed 40 degree sector benchmark of the International Thermonuclear Experimental Reactor (ITER). The calculations included determining the poloidal variation of the neutron wall loading, flux and nuclear heating in the divertor components, nuclear heating in toroidal field coils, and radiation streaming in the mid-plane port. The tool has been applied to perform 3-D nuclear analysis for several fusion designs including the ARIES Compact Stellarator (ARIES-CS), the High Average Power Laser (HAPL) inertial fusion power plant, and ITER first wall/shield (FWS) modules. The ARIES-CS stellarator has a first wall shape and a plasma profile that varies toroidally within each field period compared to the uniform toroidal shape in tokamaks. Such variation cannot be modeled analytically in the standard MCNP code. The impact of the complex helical geometry and the non-uniform blanket and divertor on the overall tritium breeding ratio and total nuclear heating was determined. In addition, we calculated the neutron wall loading variation in
On Geometric Variational Models for Inpainting Surface Holes (PREPRINT)
2006-01-01
email: haro@ima.umn.edu Phone: (612) 626-1501 Fax: (612) 626-7370 Affiliations: 1 Dept. de Tecnologia , University of Pompeu-Fabra, Passeig de...regions where the 3D model is incomplete. The main cause of holes are occlusions, but these can also be due to low reflectance, constraints in the...major areas where range scanners are used. With the increasing popularity of range scanners as 3D shape acquisition devices, with applications in
Modeling the geometric formation and powder deposition mass in laser induction hybrid cladding
International Nuclear Information System (INIS)
Huang, Yong Jun; Yuan, Sheng Fa
2012-01-01
A new laser induction hybrid cladding technique on cylinder work piece is presented. Based on a series of laser induction hybrid experiments by off axial powder feeding, the predicting models of individual clad geometric formation and powder catchment were developed in terms of powder feeding rate, laser special energy and induction energy density using multiple regression analysis. In addition, confirmation tests were performed to make a comparison between the predicting results and measured ones. Via the experiments and analysis, the conclusions can be lead to that the process parameters have crucial influence on the clad geometric formation and powder catchment, and that the predicting model reflects well the relationship between the clad geometric formation and process parameters in laser induction hybrid cladding
Country neighborhood network on territory and its geometrical model
Xuan, Qi; Wu, Tie-Jun
2009-04-01
The country neighborhood network, where nodes represent countries and two nodes are considered linked if the corresponding countries are neighbors on territory, is created and its giant component, the Asia, Europe, and Africa (AEA) cluster, is carefully studied in this paper. It is found that, as common, the degree distribution and the clustering function of the AEA cluster are both compatible with scale-free property, besides, the AEA cluster presents a little disassortativity, and its near power-law country area-degree relationship with the exponent close to 1.7 may imply a fractal dimension close to 1.2 of country borderlines in the AEA continent. It is also revealed that the average difference of population density between two countries obeys an approximately increasing function of the shortest path length between them, which may suggest a gradual consensus of population density in the AEA cluster. A simple unity rule is then adopted to model the AEA cluster and such model explains the AEA cluster very well in most aspects, e.g., power-law domain area distribution and fractal domain borderlines, etc., except that the network derived by the model has stronger disassortativity, which may be explained by the fact that, in the evolution history of countries, unbalanced neighbors are more likely to be united as one than balanced neighbors. Additionally, the network evolving process can be divided into three periods, defined as formation period, growth period, and combination period, and there are indications that the AEA cluster is in its third period.
Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R
2011-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.
Rak, Iu; Bondarenko, V.
2013-01-01
Objective: The objective of the research is to develop a method based on the geometric modelling for the purpose of improving the effectiveness of fire protection project management in industrial production of fire protection technology systems. Methods: The theoretical inheritance mode of effective management in project-organizational structure of fire protection and specialized technical equipment production using geometric modelling. Results: Mathematical and geometric models of project ma...
Gaussian random bridges and a geometric model for information equilibrium
Mengütürk, Levent Ali
2018-03-01
The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.
Directory of Open Access Journals (Sweden)
HE Handong
2017-08-01
Full Text Available Using GIS, data models of geology via geometric descriptions and expressions are being developed. However, the role played by these data models in terms of the description and expression of geological structure phenomenon is limited. To improve the semantic information in geological GIS data models, this study adopts an object-oriented method that describes and expresses the geometric and semantic features of the geological structure phenomenon using geological objects and designs a data model of regional geological structures by integrating geometry and semantics. Moreover, the study designs a semantic "vocabulary-explanation-graph" method for describing the geological phenomenon of structures. Based on the semantic features of regional geological structures and a linear classification method, it divides the regional geological structure phenomenon into 3 divisions, 10 groups, 33 classes and defines the element set and element class. Moreover, it builds the basic geometric network for geological elements based on the geometric and semantic relations among geological objects. Using the ArcGIS Diagrammer Geodatabase, it considers the regional geological structure of the Ning-Zhen Mountains to verify the data model, and the results indicate a high practicability.
Iron-dextran complex: geometrical structure and magneto-optical features.
Graczykowski, Bartłomiej; Dobek, Andrzej
2011-11-15
Molecular mass of the iron-dextran complex (M(w)=1133 kDa), diameter of its particles (∼8.3 nm) and the content of iron ions in the complex core (N(Fe)=6360) were determined by static light scattering, measurements of refractive index increment and the Cotton-Mouton effect in solution. The known number of iron ions permitted the calculation of the permanent magnetic dipole moment value to be μ(Fe)=3.17×10(-18) erg Oe(-1) and the determination of anisotropy of linear magneto-optical polarizabilities components as Δχ=9.2×10(-21) cm(3). Knowing both values and the value of the mean linear optical polarizability α=7.3×10(-20) cm(3), it was possible to show that the total measured CM effect was due to the reorientation of the permanent and the induced magnetic dipole moments of the complex. Analysis of the measured magneto-optical birefringence indicated very small optical anisotropy of linear optical polarizability components, κ(α), which suggested a homogeneous structure of particles of spherical symmetry. Copyright © 2011 Elsevier Inc. All rights reserved.
On bivariate geometric distribution
Directory of Open Access Journals (Sweden)
K. Jayakumar
2013-05-01
Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
Visualizing the Geometric Series.
Bennett, Albert B., Jr.
1989-01-01
Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)
Influence from cavity decay on geometric quantum computation in the large-detuning cavity QED model
International Nuclear Information System (INIS)
Chen Changyong; Zhang Xiaolong; Deng Zhijiao; Gao Kelin; Feng Mang
2006-01-01
We introduce a general displacement operator to investigate the unconventional geometric quantum computation with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms, based on a previous scheme [S.-B. Zheng, Phys. Rev. A 70, 052320 (2004)] for the large-detuning interaction of the atoms with the cavity mode. The analytical results we present will be helpful for experimental realization of geometric quantum computation in real cavities
Optimal control for mathematical models of cancer therapies an application of geometric methods
Schättler, Heinz
2015-01-01
This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.
A population based statistical model for daily geometric variations in the thorax
Szeto, Yenny Z.; Witte, Marnix G.; van Herk, Marcel; Sonke, Jan-Jakob
2017-01-01
To develop a population based statistical model of the systematic interfraction geometric variations between the planning CT and first treatment week of lung cancer patients for inclusion as uncertainty term in future probabilistic planning. Deformable image registrations between the planning CT and
Modeling cotton (Gossypium spp) leaves and canopy using computer aided geometric design (CAGD)
The goal of this research is to develop a geometrically accurate model of cotton crop canopies for exploring changes in canopy microenvironment and physiological function with leaf structure. We develop an accurate representation of the leaves, including changes in three-dimensional folding and orie...
Ishimoto, Yukitaka; Morishita, Yoshihiro
2014-11-01
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.
Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations
Carles, Ré mi; Dumas, Eric; Sparber, Christof
2010-01-01
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.
Borghero, Francesco; Demontis, Francesco
2016-09-01
In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.
Ons, Bart; Verstraelen, Pol
2010-01-01
Plateau’s irradiation phenomenon in particular describes what one sees when observing a brighter object on a darker background and a physically congruent darker object on a brighter background: the brighter object is seen as being larger. This phenomenon occurs in many optical visual illusions and it involves some fundamental aspects of human vision. We present a general geometrical model of human visual sensation and perception, hereby taking into account the law of Fechner in addition to th...
Methods of Stimulating the Students' Creativity in the Study of Geometrical Optics
Florian, Gabriel; Trocaru, Sorin; Florian, Aurelia-Daniela; Bâna, Alexandru-Dumitru
2015-01-01
The aim of the present article is to focus on the operational aspects referring to the actions--strategies and on the defined modalities of establishing educational objectives/competences. In the achievement of our work a special attention has been paid to the operational aspects of the learning process of the optical phenomena. There were carried…
Maurines, Laurence
2010-01-01
This particular study is part of a research programme on the difficulties encountered by students when learning about wave phenomena in a three-dimensional medium in the absence or presence of obstacles. It focuses on how students reason in situations in which wave optics need to be used: diffraction of light by an aperture, imaging in the…
Active Learning of Geometrical Optics in High School: The ALOP Approach
Alborch, Alejandra; Pandiella, Susana; Benegas, Julio
2017-01-01
A group comparison experiment of two high school classes with pre and post instruction testing has been carried out to study the suitability and advantages of using the active learning of optics and photonics (ALOP) curricula in high schools of developing countries. Two parallel, mixed gender, 12th grade classes of a high school run by the local…
Construction of Ray Diagrams in Geometrical Optics: A Media-Focused Approach
Santana, Alejandro; Rodriguez, Yohany; Gomez, Edgar A.
2012-01-01
Ray diagrams offer a powerful framework for understanding and characterizing many properties of optical systems, such as images and magnifications. However, this construction also introduces many conceptual hurdles for students. The idea of representing the propagation of waves by means of a light ray, which is a line or curve perpendicular to the…
Transformation of Didactic Intensions by Teachers: The Case of Geometrical Optics in Grade 8.
Hirn, Colette; Viennot, Laurence
2000-01-01
Investigates the idea that teachers are not passive transmitters, and that some general trends can be found in the way they transform proposed strategies. Presents the case of elementary optics in grade 8 in France in which four sets of data--interviews before teaching, logbooks, assessment tasks, and video-recorded class observations--lead to…
Li, Zhaoyang; Kurita, Takashi; Miyanaga, Noriaki
2017-10-20
Zigzag and non-zigzag beam waist shifts in a multiple-pass zigzag slab amplifier are investigated based on the propagation of a Gaussian beam. Different incident angles in the zigzag and non-zigzag planes would introduce a direction-dependent waist-shift-difference, which distorts the beam quality in both the near- and far-fields. The theoretical model and analytical expressions of this phenomenon are presented, and intensity distributions in the two orthogonal planes are simulated and compared. A geometrical optics compensation method by a beam with 90° rotation is proposed, which not only could correct the direction-dependent waist-shift-difference but also possibly average the traditional thermally induced wavefront-distortion-difference between the horizontal and vertical beam directions.
Bravo-Abad, J; Martín-Moreno, L; García-Vidal, F J
2004-02-01
In this work we explore the transmission properties of a single slit in a metallic screen. We analyze the dependence of these properties on both slit width and angle of incident radiation. We study in detail the crossover between the subwavelength regime and the geometrical-optics limit. In the subwavelength regime, resonant transmission linked to the excitation of waveguide resonances is analyzed. Linewidth of these resonances and their associated electric-field intensities are controlled by just the width of the slit. More complex transmission spectra appear when the wavelength of light is comparable to the slit width. Rapid oscillations associated with the emergence of different propagating modes inside the slit are the main features appearing in this regime.
Automatic low-order aberration correction based on geometrical optics for slab lasers.
Yu, Xin; Dong, Lizhi; Lai, Boheng; Yang, Ping; Liu, Yong; Kong, Qingfeng; Yang, Kangjian; Tang, Guomao; Xu, Bing
2017-02-20
In this paper, we present a method based on geometry optics to simultaneously correct low-order aberrations and reshape the beams of slab lasers. A coaxial optical system with three lenses is adapted. The positions of the three lenses are directly calculated based on the beam parameters detected by wavefront sensors. The initial sizes of the input beams are 1.8 mm×11 mm, and peak-to-valley (PV) values of the wavefront range up to several tens of microns. After automatic correction, the dimensions may reach nearly 22 mm×22 mm as expected, and PV values of the wavefront are less than 2 μm. The effectiveness and precision of this method are verified with experiments.
Lessons from the History of the Concept of the Ray for Teaching Geometrical Optics
Andreou, C.; Raftopoulos, A.
2011-10-01
There are two indisputable findings in science education research. First, students go to school with some intuitive beliefs about the natural world and physical phenomena that pose an obstacle to the learning of formal science. Second, these beliefs result from the confluence of two factors, namely, their everyday experience as they interact with the world around them and a set of operational constraints or principles that channel both perceptually and conceptually the way these experiences are perceived and interpreted. History of science suggests that the theories of early scientists through which they sought to explain physical phenomena relied mostly on ideas that closely fitted their experiences of the relevant phenomena. This characteristic of the early scientific ideas is the root of the epistemological difficulties that early scientists faced in their attempts to explain the phenomena. In this paper, we focus on the early theories in optics (from ancient Greek to the late Islamic scientific traditions) and argue that students face some of the same epistemological problems as early scientists in explaining vision and optical phenomena for the reason that students' intuitive beliefs are also closely tied to particular phenomena and as a result the underlying notions are fragmentary and lack the necessary generality that would allow them to cover many disparate phenomena. Knowledge of these epistemological problems can help the instructor to identify the key elements for a better understanding of the formal theory of optics and, in turn, lead to a more effective instruction.
Analysis of Data from a Series of Events by a Geometric Process Model
Institute of Scientific and Technical Information of China (English)
Yeh Lam; Li-xing Zhu; Jennifer S. K. Chan; Qun Liu
2004-01-01
Geometric process was first introduced by Lam[10,11]. A stochastic process {Xi, i = 1, 2,…} is called a geometric process (GP) if, for some a > 0, {ai-1Xi, i = 1, 2,…} forms a renewal process. In thispaper, the GP is used to analyze the data from a series of events. A nonparametric method is introduced forthe estimation of the three parameters in the GP. The limiting distributions of the three estimators are studied.Through the analysis of some real data sets, the GP model is compared with other three homogeneous andnonhomogeneous Poisson models. It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.
Radmap: ''as-built'' cad models incorporating geometrical, radiological and material information
International Nuclear Information System (INIS)
Piotrowski, L.; Lubawy, J.L.
2001-01-01
EDF intends to achieve successful and cost-effective dismantling of its obsolete nuclear plants. To reach this goal, EDF is currently extending its ''as-built'' 3-D modelling system to also include the location and characteristics of gamma sources in the geometrical models of its nuclear installations. The resulting system (called RADMAP) is a complete CAD chain covering 3-D and gamma data acquisitions, CAD modelling and exploitation of the final model. Its aim is to describe completely the geometrical and radiological state of a particular nuclear environment. This paper presents an overall view of RADMAP. The technical and functional characteristics of each element of the chain are indicated and illustrated using real (EDF) environments/applications. (author)
Paynter, Ian; Genest, Daniel; Peri, Francesco; Schaaf, Crystal
2018-04-06
Volumetric models with known biases are shown to provide bounds for the uncertainty in estimations of volume for ecologically interesting objects, observed with a terrestrial laser scanner (TLS) instrument. Bounding cuboids, three-dimensional convex hull polygons, voxels, the Outer Hull Model and Square Based Columns (SBCs) are considered for their ability to estimate the volume of temperate and tropical trees, as well as geomorphological features such as bluffs and saltmarsh creeks. For temperate trees, supplementary geometric models are evaluated for their ability to bound the uncertainty in cylinder-based reconstructions, finding that coarser volumetric methods do not currently constrain volume meaningfully, but may be helpful with further refinement, or in hybridized models. Three-dimensional convex hull polygons consistently overestimate object volume, and SBCs consistently underestimate volume. Voxel estimations vary in their bias, due to the point density of the TLS data, and occlusion, particularly in trees. The response of the models to parametrization is analysed, observing unexpected trends in the SBC estimates for the drumlin dataset. Establishing that this result is due to the resolution of the TLS observations being insufficient to support the resolution of the geometric model, it is suggested that geometric models with predictable outcomes can also highlight data quality issues when they produce illogical results.
Okada, Kensuke; Vandekerckhove, Joachim; Lee, Michael D
2018-02-01
People often interact with environments that can provide only a finite number of items as resources. Eventually a book contains no more chapters, there are no more albums available from a band, and every Pokémon has been caught. When interacting with these sorts of environments, people either actively choose to quit collecting new items, or they are forced to quit when the items are exhausted. Modeling the distribution of how many items people collect before they quit involves untangling these two possibilities, We propose that censored geometric models are a useful basic technique for modeling the quitting distribution, and, show how, by implementing these models in a hierarchical and latent-mixture framework through Bayesian methods, they can be extended to capture the additional features of specific situations. We demonstrate this approach by developing and testing a series of models in two case studies involving real-world data. One case study deals with people choosing jokes from a recommender system, and the other deals with people completing items in a personality survey.
Tsao, Thomas R.; Tsao, Doris
1997-04-01
In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.
Modeling and analysis of laser active interference optical path
Shan, Cong-miao; Sun, Hua-yan; Zhao, Yan-zhong; Chen, Jian-biao; Ren, Jian-ying
2017-10-01
By using the geometrical optics and physical optics method, the models of wedge plate interference optical path, Michelson interferometer and Mach Zehnder interferometer thus three different active interference pattern are built. The optical path difference (OPD) launched by different interference patterns, fringe spacing and contrast expression have been derived. The results show that far field interference peak intensity of the wedge plate interference is small, so the detection distance is limited, Michelson interferometer with low contrast affects the performance of detection system, Mach Zehnder interferometer has greater advantages in peak intensity, the variable range of interference fringe spacing and contrast ratio. The results of this study are useful for the theoretical research and practical application of laser active interference detection.
Geant4.10 simulation of geometric model for metaphase chromosome
Energy Technology Data Exchange (ETDEWEB)
Rafat-Motavalli, L., E-mail: rafat@um.ac.ir; Miri-Hakimabad, H.; Bakhtiyari, E.
2016-04-01
In this paper, a geometric model of metaphase chromosome is explained. The model is constructed according to the packing ratio and dimension of the structure from nucleosome up to chromosome. A B-DNA base pair is used to construct 200 base pairs of nucleosomes. Each chromatin fiber loop, which is the unit of repeat, has 49,200 bp. This geometry is entered in Geant4.10 Monte Carlo simulation toolkit and can be extended to the whole metaphase chromosomes and any application in which a DNA geometrical model is needed. The chromosome base pairs, chromosome length, and relative length of chromosomes are calculated. The calculated relative length is compared to the relative length of human chromosomes.
Geometrical origin of tricritical points of various U(1) lattice models
International Nuclear Information System (INIS)
Janke, W.; Kleiert, H.
1989-01-01
The authors review the dual relationship between various compact U(1) lattice models and Abelian Higgs models, the latter being the disorder field theories of line-like topological excitations in the system. The authors point out that the predicted first-order transitions in the Abelian Higgs models (Coleman-Weinberg mechanism) are, in three dimensions, in contradiction with direct numerical investigations in the compact U(1) formulation since these yield continuous transitions in the major part of the phase diagram. In four dimensions, there are indications from Monte Carlo data for a similar situation. Concentrating on the strong-coupling expansion in terms of geometrical objects, surfaces or lines, with certain statistical weights, the authors present semi-quantitative arguments explaining the observed cross-over from first-order to continuous transitions by the balance between the lowest two weights (2:1 ratio) of these geometrical objects
Surface-based geometric modelling using teaching trees for advanced robots
International Nuclear Information System (INIS)
Nakamura, Akira; Ogasawara, Tsukasa; Tsukune, Hideo; Oshima, Masaki
2000-01-01
Geometric modelling of the environment is important in robot motion planning. Generally, shapes can be stored in a data base, so the elements that need to be decided are positions and orientations. In this paper, surface-based geometric modelling using a teaching tree is proposed. In this modelling, combinations of surfaces are considered in order to decide positions and orientations of objects. The combinations are represented by a depth-first tree, which makes it easy for the operator to select one combination out of several. This method is effective not only in the case when perfect data can be obtained, but also when conditions for measurement of three-dimensional data are unfavorable, which often occur in the environment of a working robot. (author)
Institute of Scientific and Technical Information of China (English)
Wei LIU; Zhenyuan JIA; Fuji WANG; Yongshun ZHANG; Dongming GUO
2008-01-01
The geometrical nonlinearity of a giant magne-tostrictive thin film (GMF) can be clearly detected under the magnetostriction effect. Thus, using geometrical linear elastic theory to describe the strain, stress, and constitutive relationship of GMF is inaccurate. According to nonlinear elastic theory, a nonlinear deformation model of the bimorph GMF is established based on assumptions that the magnetostriction effect is equivalent to the effect of body force loaded on the GMF. With Taylor series method, the numerical solution is deduced. Experiments on TbDyFe/Polyimide (PI)/SmFe and TbDyFe/Cu/SmFe are then conducted to verify the proposed model, respectively. Results indicate that the nonlinear deflection curve model is in good conformity with the experimental data.
Geant4.10 simulation of geometric model for metaphase chromosome
International Nuclear Information System (INIS)
Rafat-Motavalli, L.; Miri-Hakimabad, H.; Bakhtiyari, E.
2016-01-01
In this paper, a geometric model of metaphase chromosome is explained. The model is constructed according to the packing ratio and dimension of the structure from nucleosome up to chromosome. A B-DNA base pair is used to construct 200 base pairs of nucleosomes. Each chromatin fiber loop, which is the unit of repeat, has 49,200 bp. This geometry is entered in Geant4.10 Monte Carlo simulation toolkit and can be extended to the whole metaphase chromosomes and any application in which a DNA geometrical model is needed. The chromosome base pairs, chromosome length, and relative length of chromosomes are calculated. The calculated relative length is compared to the relative length of human chromosomes.
International Nuclear Information System (INIS)
Skouri, Safa; Ben Salah, Mohieddine; Bouadila, Salwa; Balghouthi, Moncef; Ben Nasrallah, Sassi
2013-01-01
Highlights: • Design and construction of solar parabolic concentrator. • Photogrammetry study of SPC. • Slope error and optical efficiency of SPC. • Reflector materials of SPC. • Programmed tracking solar system. - Abstract: Renewable energy generation is becoming more prevalent today. It is relevant to consider that solar concentration technologies contribute to provide a real alternative to the consumption of fossil fuels. The purpose of this work is the characterization of a solar parabolic solar concentrator (SPC) designed, constructed and tested in the Research and Technologies Centre of Energy in Tunisia (CRTEn) in order to improve the performance of the system. Photogrammetry measurement used to analyze the slope errors and to determine hence determining the geometric deformation of the SPC system, which presents an average slope error around 0.0002 and 0.0073 mrad respectively in the center and in the extremities. An optimization of the most performed reflector material has been done by an experimental study of three types of reflectors. A two axes programmed tracking system realized, used and tested in this study. An experimental study is carried out to evaluate the solar parabolic concentrator thermal efficiency after the mechanical and the optical SPC optimization. The thermal energy efficiency varies from 40% to 77%, the concentrating system reaches an average concentration factor around 178
Model-based recognition of 3-D objects by geometric hashing technique
International Nuclear Information System (INIS)
Severcan, M.; Uzunalioglu, H.
1992-09-01
A model-based object recognition system is developed for recognition of polyhedral objects. The system consists of feature extraction, modelling and matching stages. Linear features are used for object descriptions. Lines are obtained from edges using rotation transform. For modelling and recognition process, geometric hashing method is utilized. Each object is modelled using 2-D views taken from the viewpoints on the viewing sphere. A hidden line elimination algorithm is used to find these views from the wire frame model of the objects. The recognition experiments yielded satisfactory results. (author). 8 refs, 5 figs
Collision models in quantum optics
Ciccarello, Francesco
2017-12-01
Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of noninteracting yet initially correlated ancillas - have a clear physical origin.
Active learning of geometrical optics in high school: the ALOP approach
Alborch, Alejandra; Pandiella, Susana; Benegas, Julio
2017-09-01
A group comparison experiment of two high school classes with pre and post instruction testing has been carried out to study the suitability and advantages of using the active learning of optics and photonics (ALOP) curricula in high schools of developing countries. Two parallel, mixed gender, 12th grade classes of a high school run by the local university were chosen. One course was randomly selected to follow the experimental instruction, based on teacher and student activities contained in the ALOP Manual. The other course followed the traditional, teacher-centered, instruction previously practiced. Conceptual knowledge of the characteristics of image formation by plane mirrors and single convergent and divergent lenses was measured by applying, in both courses, the multiple-choice test, light and optics conceptual evaluation (LOCE). Measurement before instruction showed that initial knowledge was almost null, and therefore equivalent, in both courses. After instruction testing showed that the conceptual knowledge of students following the ALOP curricula more than doubled that achieved by students in the control course, a situation maintained throughout the six conceptual dimensions tested by the 34 questions of the LOCE test used in this experiment. Using a 60% performance level on the LOCE test as the threshold of satisfactory performance, most (about 90%) of the experimental group achieved this level—independent of initial knowledge, while no student following traditional instruction reached this level of understanding. Some considerations and recommendations for prospective users are also included.
On the Geometric Modeling of the Uplink Channel in a Cellular System
Directory of Open Access Journals (Sweden)
K. B. Baltzis
2008-01-01
Full Text Available To meet the challenges of present and future wireless communications realistic propagation models that consider both spatial and temporal channel characteristics are used. However, the complexity of the complete characterization of the wireless medium has pointed out the importance of approximate but simple approaches. The geometrically based methods are typical examples of low–complexity but adequate solutions. Geometric modeling idealizes the aforementioned wireless propagation environment via a geometric abstraction of the spatial relationships among the transmitter, the receiver, and the scatterers. The paper tries to present an efficient way to simulate mobile channels using geometrical–based stochastic scattering models. In parallel with an overview of the most commonly used propagation models, the basic principles of the method as well the main assumptions made are presented. The study is focused on three well–known proposals used for the description of the Angle–of –Arrival and Time–of–Arrival statistics of the incoming multipaths in the uplink of a cellular communication system. In order to demonstrate the characteristics of these models illustrative examples are given. The physical mechanism and motivations behind them are also included providing us with a better understanding of the physical insight of the propagation medium.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
International Nuclear Information System (INIS)
Bliokh, Konstantin Yu.
2006-01-01
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed
Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect.
Bliokh, Konstantin Yu
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
Research on geometrical model and mechanism for metal deformation based on plastic flow
International Nuclear Information System (INIS)
An, H P; Li, X; Rui, Z Y
2015-01-01
Starting with general conditions of metal plastic deformation, it analyses the relation between the percentage spread and geometric parameters of a forming body with typical machining process are studied. A geometrical model of deforming metal is set up according to the characteristic of a flowing metal particle. Starting from experimental results, the effect of technological parameters and friction between workpiece and dies on plastic deformation of a material were studied and a slippage deformation model of mass points within the material was proposed. Finally, the computing methods for strain and deformation energy and temperature rise are derived from homogeneous deformation. The results can be used to select technical parameters and compute physical quantities such as strain, deformation energy, and temperature rise. (paper)
Gouveia, Diego A.; Barja, Boris; Barbosa, Henrique M. J.; Seifert, Patric; Baars, Holger; Pauliquevis, Theotonio; Artaxo, Paulo
2017-03-01
Cirrus clouds cover a large fraction of tropical latitudes and play an important role in Earth's radiation budget. Their optical properties, altitude, vertical and horizontal coverage control their radiative forcing, and hence detailed cirrus measurements at different geographical locations are of utmost importance. Studies reporting cirrus properties over tropical rain forests like the Amazon, however, are scarce. Studies with satellite profilers do not give information on the diurnal cycle, and the satellite imagers do not report on the cloud vertical structure. At the same time, ground-based lidar studies are restricted to a few case studies. In this paper, we derive the first comprehensive statistics of optical and geometrical properties of upper-tropospheric cirrus clouds in Amazonia. We used 1 year (July 2011 to June 2012) of ground-based lidar atmospheric observations north of Manaus, Brazil. This dataset was processed by an automatic cloud detection and optical properties retrieval algorithm. Upper-tropospheric cirrus clouds were observed more frequently than reported previously for tropical regions. The frequency of occurrence was found to be as high as 88 % during the wet season and not lower than 50 % during the dry season. The diurnal cycle shows a minimum around local noon and maximum during late afternoon, associated with the diurnal cycle of precipitation. The mean values of cirrus cloud top and base heights, cloud thickness, and cloud optical depth were 14.3 ± 1.9 (SD) km, 12.9 ± 2.2 km, 1.4 ± 1.1 km, and 0.25 ± 0.46, respectively. Cirrus clouds were found at temperatures down to -90 °C. Frequently cirrus were observed within the tropical tropopause layer (TTL), which are likely associated to slow mesoscale uplifting or to the remnants of overshooting convection. The vertical distribution was not uniform, and thin and subvisible cirrus occurred more frequently closer to the tropopause. The mean lidar ratio was 23.3 ± 8.0 sr. However, for
Studies on a Double Poisson-Geometric Insurance Risk Model with Interference
Directory of Open Access Journals (Sweden)
Yujuan Huang
2013-01-01
Full Text Available This paper mainly studies a generalized double Poisson-Geometric insurance risk model. By martingale and stopping time approach, we obtain adjustment coefficient equation, the Lundberg inequality, and the formula for the ruin probability. Also the Laplace transformation of the time when the surplus reaches a given level for the first time is discussed, and the expectation and its variance are obtained. Finally, we give the numerical examples.
Geometric branching model of high-energy hadron-hadron collisions
International Nuclear Information System (INIS)
Chen, W.
1988-01-01
A phenomenological model is proposed to describe collisions between hadrons at high energies. In the context of the eikonal formalism, the model consists of two components: soft and hard. The former only involves the production of particles with small transverse momenta; the latter is characterized by jet production. Geometrical scaling is taken as an essential input to describe the geometrical properties of hadrons as extended objects on the one hand, and on the other to define the soft component in both regions below and above the jet threshold. A stochastical Furry branching process is adopted as the mechanism of soft particle production, while the jet fragmentation and gluon initial-state bremsstrahlung are for the production of hadrons in hard collisions. Impact parameter and virtuality are smeared to describe the statistical averaging effects of hadron-hadron collisions. Many otherwise separated issues, ranging from elastic scattering to parton decay function, are connected together in the framework of this model. The descriptions of many prominent features of hadronic collisions are in good agreement with the observed experimental data at all available energies. Multiplicity distributions at all energies are discussed as a major issue in this paper. KNO scaling is achieved for energies within ISR range. The emergence of jets is found to be responsible not only for the violation of both geometrical scaling and KNO scaling, but also for the continuous broadening of the multiplicity distribution with ever increasing energy. It is also shown that the geometrical size of a hadron reaches an asymptote in the energy region of CERN-SppS. A Monte Carlo version of the model for soft production is constructed
Inelasticity in hadron-nucleus collisions in the geometrical two-chain model
International Nuclear Information System (INIS)
Wibig, T.; Sobczynska, D.
1995-01-01
Two features of great importance registered in experiments on hadron-nucleus collisions are the decreased inelasticity and multiplicity in intranucleus collisions. In this paper we show that such behaviour is a natural consequence of the geometrical two-chain model of multi-particle production processes: only the forward-going chain can undergo secondary interactions in the nucleus. A quantitative comparison with the data is presented. (author)
On N = 1 gauge models from geometric engineering in M-theory
International Nuclear Information System (INIS)
Belhaj, A; Drissi, L B; Rasmussen, J
2003-01-01
We study geometric engineering of four-dimensional N = 1 gauge models from M-theory on a seven-dimensional manifold with G 2 holonomy. The manifold is constructed as a K3 fibration over a three-dimensional base space with ADE geometry. The resulting gauge theory is discussed in the realm of (p, q) webs. We discuss how the anomaly cancellation condition translates into a condition on the associated affine ADE Lie algebras
Telfer, Scott; Erdemir, Ahmet; Woodburn, James; Cavanagh, Peter R
2016-01-25
Integration of patient-specific biomechanical measurements into the design of therapeutic footwear has been shown to improve clinical outcomes in patients with diabetic foot disease. The addition of numerical simulations intended to optimise intervention design may help to build on these advances, however at present the time and labour required to generate and run personalised models of foot anatomy restrict their routine clinical utility. In this study we developed second-generation personalised simple finite element (FE) models of the forefoot with varying geometric fidelities. Plantar pressure predictions from barefoot, shod, and shod with insole simulations using simplified models were compared to those obtained from CT-based FE models incorporating more detailed representations of bone and tissue geometry. A simplified model including representations of metatarsals based on simple geometric shapes, embedded within a contoured soft tissue block with outer geometry acquired from a 3D surface scan was found to provide pressure predictions closest to the more complex model, with mean differences of 13.3kPa (SD 13.4), 12.52kPa (SD 11.9) and 9.6kPa (SD 9.3) for barefoot, shod, and insole conditions respectively. The simplified model design could be produced in 3h in the case of the more detailed model, and solved on average 24% faster. FE models of the forefoot based on simplified geometric representations of the metatarsal bones and soft tissue surface geometry from 3D surface scans may potentially provide a simulation approach with improved clinical utility, however further validity testing around a range of therapeutic footwear types is required. Copyright © 2015 Elsevier Ltd. All rights reserved.
Fractal and prefractal geometric models have substantial potential of contributing to the analysis of flow and transport in porous media such as soils and reservoir rocks. In this study, geometric and hydrodynamic parameters of saturated 3D mass and pore-solid prefractal porous media were characteri...
Energy Technology Data Exchange (ETDEWEB)
Munier, Raymond [Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden); Hermanson, Jan [Golder Associates (Sweden)
2001-03-01
This report presents a methodology to construct, visualise and present geoscientific descriptive models based on data from the site investigations, which the SKB currently performs, to build an underground nuclear waste disposal facility in Sweden. It is designed for interaction with SICADA (SKB:s site characterisation database) and RVS (SKB:s Rock Visualisation System). However, the concepts of the methodology are general and can be used with other tools capable of handling 3D geometries and parameters. The descriptive model is intended to be an instrument where site investigation data from all disciplines are put together to form a comprehensive visual interpretation of the studied rock mass. The methodology has four main components: 1. Construction of a geometrical model of the interpreted main structures at the site. 2. Description of the geoscientific characteristics of the structures. 3. Description and geometrical implementation of the geometric uncertainties in the interpreted model structures. 4. Quality system for the handling of the geometrical model, its associated database and some aspects of the technical auditing. The geometrical model forms a basis for understanding the main elements and structures of the investigated site. Once the interpreted geometries are in place in the model, the system allows for adding descriptive and quantitative data to each modelled object through a system of intuitive menus. The associated database allows each geometrical object a complete quantitative description of all geoscientific disciplines, variabilities, uncertainties in interpretation and full version history. The complete geometrical model and its associated database of object descriptions are to be recorded in a central quality system. Official, new and old versions of the model are administered centrally in order to have complete quality assurance of each step in the interpretation process. The descriptive model is a cornerstone in the understanding of the
The neutron optical model potential
International Nuclear Information System (INIS)
Hodgson, P.E.
1989-01-01
The present status of optical model calculations of neutron scattering and interactions is reviewed, with special emphasis on more recent developments and the more promising lines of research. The use of dispersion relations to provide an extra constraint on the potential is discussed, together with their application to studies of the Fermi surface anomaly. The application of potential inversion techniques to determine the form of the potential is also considered. (author). 39 refs, figs
CERN. Geneva
2012-01-01
We present our effort for the creation of a new software library of geometrical primitives, which are used for solid modelling in Monte Carlo detector simulations. We plan to replace and unify current geometrical primitive classes in the CERN software projects Geant4 and ROOT with this library. Each solid is represented by a C++ class with methods suited for measuring distances of particles from the surface of a solid and for determination as to whether the particles are located inside, outside or on the surface of the solid. We use numerical tolerance for determining whether the particles are located on the surface. The class methods also contain basic support for visualization. We use dedicated test suites for validation of the shape codes. These include also special performance and numerical value comparison tests for help with analysis of possible candidates of class methods as well as to verify that our new implementation proposals were designed and implemented properly. Currently, bridge classes are u...
Monte Carlo based geometrical model for efficiency calculation of an n-type HPGe detector
Energy Technology Data Exchange (ETDEWEB)
Padilla Cabal, Fatima, E-mail: fpadilla@instec.c [Instituto Superior de Tecnologias y Ciencias Aplicadas, ' Quinta de los Molinos' Ave. Salvador Allende, esq. Luaces, Plaza de la Revolucion, Ciudad de la Habana, CP 10400 (Cuba); Lopez-Pino, Neivy; Luis Bernal-Castillo, Jose; Martinez-Palenzuela, Yisel; Aguilar-Mena, Jimmy; D' Alessandro, Katia; Arbelo, Yuniesky; Corrales, Yasser; Diaz, Oscar [Instituto Superior de Tecnologias y Ciencias Aplicadas, ' Quinta de los Molinos' Ave. Salvador Allende, esq. Luaces, Plaza de la Revolucion, Ciudad de la Habana, CP 10400 (Cuba)
2010-12-15
A procedure to optimize the geometrical model of an n-type detector is described. Sixteen lines from seven point sources ({sup 241}Am, {sup 133}Ba, {sup 22}Na, {sup 60}Co, {sup 57}Co, {sup 137}Cs and {sup 152}Eu) placed at three different source-to-detector distances (10, 20 and 30 cm) were used to calibrate a low-background gamma spectrometer between 26 and 1408 keV. Direct Monte Carlo techniques using the MCNPX 2.6 and GEANT 4 9.2 codes, and a semi-empirical procedure were performed to obtain theoretical efficiency curves. Since discrepancies were found between experimental and calculated data using the manufacturer parameters of the detector, a detail study of the crystal dimensions and the geometrical configuration is carried out. The relative deviation with experimental data decreases from a mean value of 18-4%, after the parameters were optimized.
A discrete element model for the investigation of the geometrically nonlinear behaviour of solids
Ockelmann, Felix; Dinkler, Dieter
2018-07-01
A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.
Sierra-Vázquez, Vicente; Serrano-Pedraza, Ignacio
2010-04-01
The existence of a special second-order mechanism in the human visual system, able to demodulate the envelope of visual stimuli, suggests that spatial information contained in the image envelope may be perceptually relevant. The Riesz transform, a natural isotropic extension of the Hilbert transform to multidimensional signals, was used here to demodulate band-pass filtered images of well-known visual illusions of length, size, direction, and shape. We show that the local amplitude of the monogenic signal or envelope of each illusion image conveys second-order information related to image holistic spatial structure, whereas the local phase component conveys information about the spatial features. Further low-pass filtering of the illusion image envelopes creates physical distortions that correspond to the subjective distortions perceived in the illusory images. Therefore the envelope seems to be the image component that physically carries the spatial information about these illusions. This result contradicts the popular belief that the relevant spatial information to perceive geometrical-optical illusions is conveyed only by the lower spatial frequencies present in their Fourier spectrum.
Effects of neutron streaming and geometric models on molten fuel recriticality accidents
International Nuclear Information System (INIS)
McLaughlin, T.P.
1975-10-01
A postulated fast reactor accident which has been extant for many years is a recriticality following partial or complete core melting. Independently of the cause or probability of such a situation, certain cases can be defined and some facets of the dynamic history of these cases can be described with more than enough accuracy for safety considerations. Calculations were made with the PAD code for systems with 10 vol percent voids and varying reactivity insertion rates. Additionally, two distinct geometric and equation of state models were investigated in conjunction with a model which accounted for possible neutron streaming reactivity effects. Significant results include fission and kinetic energy, temperatures and pressures
The Transmuted Geometric-Weibull distribution: Properties, Characterizations and Regression Models
Directory of Open Access Journals (Sweden)
Zohdy M Nofal
2017-06-01
Full Text Available We propose a new lifetime model called the transmuted geometric-Weibull distribution. Some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is discussed to estimate the model parameters by means of Monte Carlo simulation study. A new location-scale regression model is introduced based on the proposed distribution. The new distribution is applied to two real data sets to illustrate its flexibility. Empirical results indicate that proposed distribution can be alternative model to other lifetime models available in the literature for modeling real data in many areas.
Owji, Erfan; Keshavarz, Alireza; Mokhtari, Hosein
2017-03-01
In this paper, a GaAs / Alx Ga1-x As quantum dot laser with a semi-parabolic spherical well potential is assumed. By using Runge-Kutta method the eigenenergies and the eigenstates of valence and conduct bands are obtained. The effects of geometrical sizes, external electric fields and hydrogen impurity on the different electronic transitions of the optical gain are studied. The results show that the optical gain peak increases and red-shifts, by increasing the width of well or barrier, while more increasing of the width causes blue-shift and decreases it. The hydrogen impurity decreases the optical gain peak and blue-shifts it. Also, the increasing of the external electric fields cause to increase the peak of the optical gain, and (blue) red shift it. Finally, the optical gain for 1s-1s and 2s-1s transitions is prominent, while it is so weak for other transitions.
International Nuclear Information System (INIS)
Saas, L.; Le Tellier, R.; Bajard, S.
2015-01-01
In this document, we present a simplified geometrical model (0D model) for both the in-core corium propagation transient and the characterization of the mode of corium transfer from the core to the vessel. A degraded core with a formed corium pool is used as an initial state. This initial state can be obtained from a simulation computed with an integral code. This model does not use a grid for the core as integral codes do. Geometrical shapes and 0D models are associated with the corium pool and the other components of the degraded core (debris, heavy reflector, core plate...). During the transient, these shapes evolve taking into account the thermal and stratification behavior of the corium pool and the melting of the core surrounding components. Some results corresponding to the corium pool propagation in core transients obtained with this model on a LWR with a heavy reflector are given and compared to grid approach of the integral codes MAAP4
International Nuclear Information System (INIS)
Liu, Chao; Lee Panetta, R.; Yang, Ping
2013-01-01
Effects of surface roughness on the optical scattering properties of ice crystals are investigated using a random wave superposition model of roughness that is a simplification of models used in studies of scattering by surface water waves. Unlike previous work with models of rough surfaces applicable only in limited size ranges, such as surface perturbation methods in the small particle regime or the tilted-facet (TF) method in the large particle regime, ours uses a single roughness model to cover a range in sizes extending from the Rayleigh to the geometric optics regimes. The basic crystal shape we examine is the hexagonal column but our roughening model can be used for a wide variety of particle geometries. To compute scattering properties over the range of sizes we use the pseudo-spectral time domain method (PSTD) for small to moderate sized particles and the improved geometric optics method (IGOM) for large ones. Use of the PSTD with our roughness model is straightforward. By discretizing the roughened surface with triangular sub-elements, we adapt the IGOM to give full consideration of shadow effects, multiple reflections/refractions at the surface, and possible reentrance of the scattered beams. We measure the degree of roughness of a surface by the variance (σ 2 ) of surface slopes occurring on the surfaces. For moderately roughened surfaces (σ 2 ≤0.1) in the large particle regime, the scattering properties given by the TF and IGOM agree well, but differences in results obtained with the two methods become noticeable as the surface becomes increasingly roughened. Having a definite, albeit idealized, roughness model we are able to use the combination of the PSTD and IGOM to examine how a fixed degree of surface roughness affects the scattering properties of a particle as the size parameter of the particle changes. We find that for moderately rough surfaces in our model, as particle size parameter increases beyond about 20 the influence of surface
Chen, Huipeng; Poulard, David; Forman, Jason; Crandall, Jeff; Panzer, Matthew B
2018-07-04
Evaluating the biofidelity of pedestrian finite element models (PFEM) using postmortem human subjects (PMHS) is a challenge because differences in anthropometry between PMHS and PFEM could limit a model's capability to accurately capture cadaveric responses. Geometrical personalization via morphing can modify the PFEM geometry to match the specific PMHS anthropometry, which could alleviate this issue. In this study, the Total Human Model for Safety (THUMS) PFEM (Ver 4.01) was compared to the cadaveric response in vehicle-pedestrian impacts using geometrically personalized models. The AM50 THUMS PFEM was used as the baseline model, and 2 morphed PFEM were created to the anthropometric specifications of 2 obese PMHS used in a previous pedestrian impact study with a mid-size sedan. The same measurements as those obtained during the PMHS tests were calculated from the simulations (kinematics, accelerations, strains), and biofidelity metrics based on signals correlation (correlation and analysis, CORA) were established to compare the response of the models to the experiments. Injury outcomes were predicted deterministically (through strain-based threshold) and probabilistically (with injury risk functions) and compared with the injuries reported in the necropsy. The baseline model could not accurately capture all aspects of the PMHS kinematics, strain, and injury risks, whereas the morphed models reproduced biofidelic response in terms of trajectory (CORA score = 0.927 ± 0.092), velocities (0.975 ± 0.027), accelerations (0.862 ± 0.072), and strains (0.707 ± 0.143). The personalized THUMS models also generally predicted injuries consistent with those identified during posttest autopsy. The study highlights the need to control for pedestrian anthropometry when validating pedestrian human body models against PMHS data. The information provided in the current study could be useful for improving model biofidelity for vehicle-pedestrian impact scenarios.
International Nuclear Information System (INIS)
Liu Guangyu; Nguang, Sing Kiong; Partridge, Ashton
2011-01-01
Highlights: → A novel and general method is proposed for modeling PV arrays or modules. → A robust algorithm is used for the first time to improve the convergence to solution. → Auxiliary functions in other general methods are not compulsory in our method. → It is novel that geometric configuration is also incorporated. → A case study is performed to show the approach's advantages and unique features. - Abstract: A general method for modeling typical photovoltaic (PV) arrays and modules is proposed to find the exact current and voltage relationship of PV arrays or modules of geometrically and electrically different configurations. Nonlinear characteristic equations of electrical devices in solar array or module systems are numerically constructed without adding any virtual electrical components. Then, a robust damped Newton method is used to find exact I-V relationship of these general nonlinear equations, where the convergence is guaranteed. The model can deal with different mismatch effects such as different configurations of bypass diodes, and partial shading. Geometry coordinates of PV components are also considered to facilitate the modeling of the actual physical configuration. Simulation of a PV array with 48 modules, partially shaded by a concrete structure, is performed to verify the effectiveness and advantages of the proposed method.
Geometric model of pseudo-distance measurement in satellite location systems
Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.
2018-04-01
The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.
Khomchenko, V. G.; Varepo, L. G.; Glukhov, V. I.; Krivokhatko, E. A.
2017-06-01
The geometric model for the synthesis of third-class lever mechanisms is proposed, which allows, by changing the length of the auxiliary link and the position of its fixed hinge, to rearrange the movement of the working organ onto the cyclograms with different predetermined dwell times. It is noted that with the help of the proposed model, at the expense of the corresponding geometric constructions, the best uniform Chebyshev approximation can be achieved at the interval of the standstill.
High-energy pp and p-barp scattering and the model of geometric scaling
International Nuclear Information System (INIS)
Fischer, J.; Jakes, P.; Novak, M.
1982-10-01
The model of geometric scaling is used to predict the evolution of the diffractive dip-peak structure of pp and p-barp differential cross-sections with increasing energy. Previous calculation for pp scattering made by Dias de Deus and Kroll is carried out with new data and their predictions confirmed. Recent data on p-barp scattering are used to make an analogous analysis for this process as well. It turns out that the p-barp differential cross-section behaves analogously, the main difference being that, in the p-barp case, the dip-peak structure should not completely disappear with increasing energy. (author)
Model Study of Wave Overtopping of Marine Structure for a Wide Range of Geometric Parameters
DEFF Research Database (Denmark)
Kofoed, Jens Peter
2000-01-01
The objective of the study described in this paper is to enable estimation of wave overtopping rates for slopes/ramps given by a wide range of geometric parameters when subjected to varying wave conditions. To achieve this a great number of model tests are carried out in a wave tank using irregul...... 2-D waves. On the basis of the first part of these tests an exponential overtopping expression for a linear slope, including the effect of limited draught and varying slope angle, is presented. The plans for further tests with other slope geometries are described....
Matching Aerial Images to 3D Building Models Using Context-Based Geometric Hashing
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Jaewook Jung
2016-06-01
Full Text Available A city is a dynamic entity, which environment is continuously changing over time. Accordingly, its virtual city models also need to be regularly updated to support accurate model-based decisions for various applications, including urban planning, emergency response and autonomous navigation. A concept of continuous city modeling is to progressively reconstruct city models by accommodating their changes recognized in spatio-temporal domain, while preserving unchanged structures. A first critical step for continuous city modeling is to coherently register remotely sensed data taken at different epochs with existing building models. This paper presents a new model-to-image registration method using a context-based geometric hashing (CGH method to align a single image with existing 3D building models. This model-to-image registration process consists of three steps: (1 feature extraction; (2 similarity measure; and matching, and (3 estimating exterior orientation parameters (EOPs of a single image. For feature extraction, we propose two types of matching cues: edged corner features representing the saliency of building corner points with associated edges, and contextual relations among the edged corner features within an individual roof. A set of matched corners are found with given proximity measure through geometric hashing, and optimal matches are then finally determined by maximizing the matching cost encoding contextual similarity between matching candidates. Final matched corners are used for adjusting EOPs of the single airborne image by the least square method based on collinearity equations. The result shows that acceptable accuracy of EOPs of a single image can be achievable using the proposed registration approach as an alternative to a labor-intensive manual registration process.
An atomistic geometrical model of the B-DNA configuration for DNA-radiation interaction simulations
Bernal, M. A.; Sikansi, D.; Cavalcante, F.; Incerti, S.; Champion, C.; Ivanchenko, V.; Francis, Z.
2013-12-01
In this paper, an atomistic geometrical model for the B-DNA configuration is explained. This model accounts for five organization levels of the DNA, up to the 30 nm chromatin fiber. However, fragments of this fiber can be used to construct the whole genome. The algorithm developed in this work is capable to determine which is the closest atom with respect to an arbitrary point in space. It can be used in any application in which a DNA geometrical model is needed, for instance, in investigations related to the effects of ionizing radiations on the human genetic material. Successful consistency checks were carried out to test the proposed model. Catalogue identifier: AEPZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1245 No. of bytes in distributed program, including test data, etc.: 6574 Distribution format: tar.gz Programming language: FORTRAN. Computer: Any. Operating system: Multi-platform. RAM: 2 Gb Classification: 3. Nature of problem: The Monte Carlo method is used to simulate the interaction of ionizing radiation with the human genetic material in order to determine DNA damage yields per unit absorbed dose. To accomplish this task, an algorithm to determine if a given energy deposition lies within a given target is needed. This target can be an atom or any other structure of the genetic material. Solution method: This is a stand-alone subroutine describing an atomic-resolution geometrical model of the B-DNA configuration. It is able to determine the closest atom to an arbitrary point in space. This model accounts for five organization levels of the human genetic material, from the nucleotide pair up to the 30 nm chromatin fiber. This subroutine carries out a series of coordinate transformations
Development of Large Concrete Object Geometrical Model Based on Terrestrial Laser Scanning
Directory of Open Access Journals (Sweden)
Zaczek-Peplinska Janina
2015-02-01
Full Text Available The paper presents control periodic measurements of movements and survey of concrete dam on Dunajec River in Rożnów, Poland. Topographical survey was conducted using laser scanning technique. The goal of survey was data collection and creation of a geometrical model. Acquired cross- and horizontal sections were utilised to create a numerical model of object behaviour at various load depending of changing level of water in reservoir. Modelling was accomplished using finite elements technique. During the project an assessment was conducted to terrestrial laser scanning techniques for such type of research of large hydrotechnical objects such as gravitational water dams. Developed model can be used to define deformations and displacement prognosis.
A simple geometrical model describing shapes of soap films suspended on two rings
Herrmann, Felix J.; Kilvington, Charles D.; Wildenberg, Rebekah L.; Camacho, Franco E.; Walecki, Wojciech J.; Walecki, Peter S.; Walecki, Eve S.
2016-09-01
We measured and analysed the stability of two types of soap films suspended on two rings using the simple conical frusta-based model, where we use common definition of conical frustum as a portion of a cone that lies between two parallel planes cutting it. Using frusta-based we reproduced very well-known results for catenoid surfaces with and without a central disk. We present for the first time a simple conical frusta based spreadsheet model of the soap surface. This very simple, elementary, geometrical model produces results surprisingly well matching the experimental data and known exact analytical solutions. The experiment and the spreadsheet model can be used as a powerful teaching tool for pre-calculus and geometry students.
A porous flow model for the geometrical form of volcanoes - Critical comments
Wadge, G.; Francis, P.
1982-01-01
A critical evaluation is presented of the assumptions on which the mathematical model for the geometrical form of a volcano arising from the flow of magma in a porous medium of Lacey et al. (1981) is based. The lack of evidence for an equipotential surface or its equivalent in volcanoes prior to eruption is pointed out, and the preference of volcanic eruptions for low ground is attributed to the local stress field produced by topographic loading rather than a rising magma table. Other difficulties with the model involve the neglect of the surface flow of lava under gravity away from the vent, and the use of the Dupuit approximation for unconfined flow and the assumption of essentially horizontal magma flow. Comparisons of model predictions with the shapes of actual volcanoes reveal the model not to fit lava shield volcanoes, for which the cone represents the solidification of small lava flows, and to provide a poor fit to composite central volcanoes.
Stochastic Geometric Network Models for Groups of Functional and Structural Connectomes
Friedman, Eric J.; Landsberg, Adam S.; Owen, Julia P.; Li, Yi-Ou; Mukherjee, Pratik
2014-01-01
Structural and functional connectomes are emerging as important instruments in the study of normal brain function and in the development of new biomarkers for a variety of brain disorders. In contrast to single-network studies that presently dominate the (non-connectome) network literature, connectome analyses typically examine groups of empirical networks and then compare these against standard (stochastic) network models. Current practice in connectome studies is to employ stochastic network models derived from social science and engineering contexts as the basis for the comparison. However, these are not necessarily best suited for the analysis of connectomes, which often contain groups of very closely related networks, such as occurs with a set of controls or a set of patients with a specific disorder. This paper studies important extensions of standard stochastic models that make them better adapted for analysis of connectomes, and develops new statistical fitting methodologies that account for inter-subject variations. The extensions explicitly incorporate geometric information about a network based on distances and inter/intra hemispherical asymmetries (to supplement ordinary degree-distribution information), and utilize a stochastic choice of networks' density levels (for fixed threshold networks) to better capture the variance in average connectivity among subjects. The new statistical tools introduced here allow one to compare groups of networks by matching both their average characteristics and the variations among them. A notable finding is that connectomes have high “smallworldness” beyond that arising from geometric and degree considerations alone. PMID:25067815
MATCHING AERIAL IMAGES TO 3D BUILDING MODELS BASED ON CONTEXT-BASED GEOMETRIC HASHING
Directory of Open Access Journals (Sweden)
J. Jung
2016-06-01
Full Text Available In this paper, a new model-to-image framework to automatically align a single airborne image with existing 3D building models using geometric hashing is proposed. As a prerequisite process for various applications such as data fusion, object tracking, change detection and texture mapping, the proposed registration method is used for determining accurate exterior orientation parameters (EOPs of a single image. This model-to-image matching process consists of three steps: 1 feature extraction, 2 similarity measure and matching, and 3 adjustment of EOPs of a single image. For feature extraction, we proposed two types of matching cues, edged corner points representing the saliency of building corner points with associated edges and contextual relations among the edged corner points within an individual roof. These matching features are extracted from both 3D building and a single airborne image. A set of matched corners are found with given proximity measure through geometric hashing and optimal matches are then finally determined by maximizing the matching cost encoding contextual similarity between matching candidates. Final matched corners are used for adjusting EOPs of the single airborne image by the least square method based on co-linearity equations. The result shows that acceptable accuracy of single image's EOP can be achievable by the proposed registration approach as an alternative to labour-intensive manual registration process.
Bucksch, Alexander; Atta-Boateng, Acheampong; Azihou, Akomian F.; Battogtokh, Dorjsuren; Baumgartner, Aly; Binder, Brad M.; Braybrook, Siobhan A.; Chang, Cynthia; Coneva, Viktoirya; DeWitt, Thomas J.; Fletcher, Alexander G.; Gehan, Malia A.; Diaz-Martinez, Diego Hernan; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Klein, Laura L.; Leiboff, Samuel; Li, Mao; Lynch, Jonathan P.; Maizel, Alexis; Maloof, Julin N.; Markelz, R. J. Cody; Martinez, Ciera C.; Miller, Laura A.; Mio, Washington; Palubicki, Wojtek; Poorter, Hendrik; Pradal, Christophe; Price, Charles A.; Puttonen, Eetu; Reese, John B.; Rellán-Álvarez, Rubén; Spalding, Edgar P.; Sparks, Erin E.; Topp, Christopher N.; Williams, Joseph H.; Chitwood, Daniel H.
2017-01-01
The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics. PMID:28659934
Directory of Open Access Journals (Sweden)
Pooyan Vahidi Pashsaki
2016-06-01
Full Text Available Accuracy of a five-axis CNC machine tool is affected by a vast number of error sources. This paper investigates volumetric error modeling and its compensation to the basis for creation of new tool path for improvement of work pieces accuracy. The volumetric error model of a five-axis machine tool with the configuration RTTTR (tilting head B-axis and rotary table in work piece side A΄ was set up taking into consideration rigid body kinematics and homogeneous transformation matrix, in which 43 error components are included. Volumetric error comprises 43 error components that can separately reduce geometrical and dimensional accuracy of work pieces. The machining accuracy of work piece is guaranteed due to the position of the cutting tool center point (TCP relative to the work piece. The cutting tool is deviated from its ideal position relative to the work piece and machining error is experienced. For compensation process detection of the present tool path and analysis of the RTTTR five-axis CNC machine tools geometrical error, translating current position of component to compensated positions using the Kinematics error model, converting newly created component to new tool paths using the compensation algorithms and finally editing old G-codes using G-code generator algorithm have been employed.
Directory of Open Access Journals (Sweden)
Alexander Bucksch
2017-06-01
Full Text Available The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.
Clerici, Giancarlo; Burnside, Walter D.
1989-01-01
In recent years, the compact range has become very popular for measuring Radar Cross Section (RCS) and antenna patterns. The compact range, in fact, offers several advantages due to reduced size, a controlled environment, and privacy. On the other hand, it has some problems of its own, which must be solved properly in order to achieve high quality measurement results. For example, diffraction from the edges of the main reflector corrupts the plane wave in the target zone and creates spurious scattering centers in RCS measurements. While diffraction can be minimized by using rolled edges, the field of an offset single reflector compact range is corrupted by three other errors: the taper of the reflected field, the cross polarization introduced by the tilt of the feed and the aperture blockage introduced by the feed itself. These three errors can be eliminated by the use of a subreflector system. A properly designed subreflector system offers very little aperture blockage, no cross-polarization introduced and a minimization of the taper of the reflected field. A Gregorian configuration has been adopted in order to enclose the feed and the ellipsoidal subreflector in a lower chamber, which is isolated by absorbers from the upper chamber, where the main parabolic reflector and the target zone are enclosed. The coupling between the two rooms is performed through a coupling aperture. The first cut design for such a subreflector system is performed through Geometrical Optics ray tracing techniques (GO), and is greatly simplified by the use of the concept of the central ray introduced by Dragone. The purpose of the GO design is to establish the basic dimensions of the main reflector and subreflector, the size of the primary and secondary illuminating surfaces, the tilt angles of the subreflector and feed, and estimate the feed beamwidth. At the same time, the shape of the coupling aperture is initially determined.
Shi, Pei-Jian; Huang, Jian-Guo; Hui, Cang; Grissino-Mayer, Henri D; Tardif, Jacques C; Zhai, Li-Hong; Wang, Fu-Sheng; Li, Bai-Lian
2015-01-01
Tree-rings are often assumed to approximate a circular shape when estimating forest productivity and carbon dynamics. However, tree rings are rarely, if ever, circular, thereby possibly resulting in under- or over-estimation in forest productivity and carbon sequestration. Given the crucial role played by tree ring data in assessing forest productivity and carbon storage within a context of global change, it is particularly important that mathematical models adequately render cross-sectional area increment derived from tree rings. We modeled the geometric shape of tree rings using the superellipse equation and checked its validation based on the theoretical simulation and six actual cross sections collected from three conifers. We found that the superellipse better describes the geometric shape of tree rings than the circle commonly used. We showed that a spiral growth trend exists on the radial section over time, which might be closely related to spiral grain along the longitudinal axis. The superellipse generally had higher accuracy than the circle in predicting the basal area increment, resulting in an improved estimate for the basal area. The superellipse may allow better assessing forest productivity and carbon storage in terrestrial forest ecosystems.
A simplified geometrical model for transient corium propagation in core for LWR with heavy reflector
Directory of Open Access Journals (Sweden)
Saas Laurent
2017-01-01
Full Text Available In the context of the simulation of the Severe Accidents (SA in Light Water Reactors (LWR, we are interested on the in-core corium pool propagation transient in order to evaluate the corium relocation in the vessel lower head. The goal is to characterize the corium and debris flows from the core to accurately evaluate the corium pool propagation transient in the lower head and so the associated risk of vessel failure. In the case of LWR with heavy reflector, to evaluate the corium relocation into the lower head, we have to study the risk associated with focusing effect and the possibility to stabilize laterally the corium in core with a flooded down-comer. It is necessary to characterize the core degradation and the stratification of the corium pool that is formed in core. We assume that the core degradation until the corium pool formation and the corium pool propagation could be modeled separately. In this document, we present a simplified geometrical model (0D model for the in-core corium propagation transient. A degraded core with a formed corium pool is used as an initial state. This state can be obtained from a simulation computed with an integral code. This model does not use a grid for the core as integral codes do. Geometrical shapes and 0D models are associated with the corium pool and the other components of the degraded core (debris, heavy reflector, core plate…. During the transient, these shapes evolve taking into account the thermal and stratification behavior of the corium pool and the melting of the core surrounding components. Some results corresponding to the corium pool propagation in core transients obtained with this model on a LWR with a heavy reflector are given and compared to grid approach of the integral codes MAAP4.
New geometric design consistency model based on operating speed profiles for road safety evaluation.
Camacho-Torregrosa, Francisco J; Pérez-Zuriaga, Ana M; Campoy-Ungría, J Manuel; García-García, Alfredo
2013-12-01
To assist in the on-going effort to reduce road fatalities as much as possible, this paper presents a new methodology to evaluate road safety in both the design and redesign stages of two-lane rural highways. This methodology is based on the analysis of road geometric design consistency, a value which will be a surrogate measure of the safety level of the two-lane rural road segment. The consistency model presented in this paper is based on the consideration of continuous operating speed profiles. The models used for their construction were obtained by using an innovative GPS-data collection method that is based on continuous operating speed profiles recorded from individual drivers. This new methodology allowed the researchers to observe the actual behavior of drivers and to develop more accurate operating speed models than was previously possible with spot-speed data collection, thereby enabling a more accurate approximation to the real phenomenon and thus a better consistency measurement. Operating speed profiles were built for 33 Spanish two-lane rural road segments, and several consistency measurements based on the global and local operating speed were checked. The final consistency model takes into account not only the global dispersion of the operating speed, but also some indexes that consider both local speed decelerations and speeds over posted speeds as well. For the development of the consistency model, the crash frequency for each study site was considered, which allowed estimating the number of crashes on a road segment by means of the calculation of its geometric design consistency. Consequently, the presented consistency evaluation method is a promising innovative tool that can be used as a surrogate measure to estimate the safety of a road segment. Copyright © 2012 Elsevier Ltd. All rights reserved.
Wan, Wai-Yin; Chan, Jennifer S K
2009-08-01
For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).
Integrable models of quantum optics
Directory of Open Access Journals (Sweden)
Yudson Vladimir
2017-01-01
Full Text Available We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.
Design of Wideband MIMO Car-to-Car Channel Models Based on the Geometrical Street Scattering Model
Directory of Open Access Journals (Sweden)
Nurilla Avazov
2012-01-01
Full Text Available We propose a wideband multiple-input multiple-output (MIMO car-to-car (C2C channel model based on the geometrical street scattering model. Starting from the geometrical model, a MIMO reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS and non-LOS (NLOS propagation environments. The proposed channel model assumes an infinite number of scatterers, which are uniformly distributed in two rectangular areas located on both sides of the street. Analytical solutions are presented for the space-time-frequency cross-correlation function (STF-CCF, the two-dimensional (2D space CCF, the time-frequency CCF (TF-CCF, the temporal autocorrelation function (ACF, and the frequency correlation function (FCF. An efficient sum-of-cisoids (SOCs channel simulator is derived from the reference model. It is shown that the temporal ACF and the FCF of the SOC channel simulator fit very well to the corresponding correlation functions of the reference model. To validate the proposed channel model, the mean Doppler shift and the Doppler spread of the reference model have been matched to real-world measurement data. The comparison results demonstrate an excellent agreement between theory and measurements, which confirms the validity of the derived reference model. The proposed geometry-based channel simulator allows us to study the effect of nearby street scatterers on the performance of C2C communication systems.
Directory of Open Access Journals (Sweden)
Gayo Willy
2016-01-01
Full Text Available Philippine Stock Exchange Composite Index (PSEi is the main stock index of the Philippine Stock Exchange (PSE. PSEi is computed using a weighted mean of the top 30 publicly traded companies in the Philippines, called component stocks. It provides a single value by which the performance of the Philippine stock market is measured. Unfortunately, these weights, which may vary for every trading day, are not disclosed by the PSE. In this paper, we propose a model of forecasting the PSEi by estimating the weights based on historical data and forecasting each component stock using Monte Carlo simulation based on a Geometric Brownian Motion (GBM assumption. The model performance is evaluated and its forecast compared is with the results using a direct GBM forecast of PSEi over different forecast periods. Results showed that the forecasts using WGBM will yield smaller error compared to direct GBM forecast of PSEi.
A geometrical model of VY Canis Majoris for SiO maser lines
International Nuclear Information System (INIS)
Zhou Zhen-Pu; Kaifu, N.
1984-01-01
A new geometrical model of VY CMa is proposed to explain the three-peaked spectra of transition upsilon=1,2 J=1-0 of SiO maser emission. In this model the circumstellar envelope of VY CMa is a rotating disk of gas and dust seen nearly edge-on. The disk consists of two regions: a decelerated steady stream near the photosphere of the star and an accelerated one further away. Other geometries are discussed and eliminated. Calculated profiles of SiO maser lines fit well the observations. It is possible to explain the three-peaked profiles of SiO maser lines emitted by NML Cyg, RR Aql, NML Tau, etc. (orig.)
Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes
Institute of Scientific and Technical Information of China (English)
Ghulam MUSTAFA
2017-01-01
The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes (for any integer m,n ≥ 2).The proposed algorithm has been derived from uniform B-spline blending functions.In particular,we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data.Moreover,we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve.Furthermore,visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.
Rapid Simulation of Flat Knitting Loops Based On the Yarn Texture and Loop Geometrical Model
Directory of Open Access Journals (Sweden)
Lu Zhiwen
2017-06-01
Full Text Available In order to create realistic loop primitives suitable for the fast computer-aided design (CAD of the flat knitted fabric, we have a research on the geometric model of the loop as well as the variation of the loop surface. Establish the texture variation model based on the changing process from the normal yarn to loop that provides the realistic texture of the simulative loop. Then optimize the simulative loop based on illumination variation. This paper develops the computer program with the optimization algorithm and achieves the loop simulation of different yarns to verify the feasibility of the proposed algorithm. Our work provides a fast CAD of the flat knitted fabric with loop simulation, and it is not only more realistic but also material adjustable. Meanwhile it also provides theoretical value for the flat knitted fabric computer simulation.
Woods, Christopher; Fernee, Christianne; Browne, Martin; Zakrzewski, Sonia; Dickinson, Alexander
2017-01-01
This paper introduces statistical shape modelling (SSM) for use in osteoarchaeology research. SSM is a full field, multi-material analytical technique, and is presented as a supplementary geometric morphometric (GM) tool. Lower mandibular canines from two archaeological populations and one modern population were sampled, digitised using micro-CT, aligned, registered to a baseline and statistically modelled using principal component analysis (PCA). Sample material properties were incorporated as a binary enamel/dentin parameter. Results were assessed qualitatively and quantitatively using anatomical landmarks. Finally, the technique's application was demonstrated for inter-sample comparison through analysis of the principal component (PC) weights. It was found that SSM could provide high detail qualitative and quantitative insight with respect to archaeological inter- and intra-sample variability. This technique has value for archaeological, biomechanical and forensic applications including identification, finite element analysis (FEA) and reconstruction from partial datasets.
Directory of Open Access Journals (Sweden)
Christopher Woods
Full Text Available This paper introduces statistical shape modelling (SSM for use in osteoarchaeology research. SSM is a full field, multi-material analytical technique, and is presented as a supplementary geometric morphometric (GM tool. Lower mandibular canines from two archaeological populations and one modern population were sampled, digitised using micro-CT, aligned, registered to a baseline and statistically modelled using principal component analysis (PCA. Sample material properties were incorporated as a binary enamel/dentin parameter. Results were assessed qualitatively and quantitatively using anatomical landmarks. Finally, the technique's application was demonstrated for inter-sample comparison through analysis of the principal component (PC weights. It was found that SSM could provide high detail qualitative and quantitative insight with respect to archaeological inter- and intra-sample variability. This technique has value for archaeological, biomechanical and forensic applications including identification, finite element analysis (FEA and reconstruction from partial datasets.
Modeling Geometric-Temporal Context With Directional Pyramid Co-Occurrence for Action Recognition.
Yuan, Chunfeng; Li, Xi; Hu, Weiming; Ling, Haibin; Maybank, Stephen J
2014-02-01
In this paper, we present a new geometric-temporal representation for visual action recognition based on local spatio-temporal features. First, we propose a modified covariance descriptor under the log-Euclidean Riemannian metric to represent the spatio-temporal cuboids detected in the video sequences. Compared with previously proposed covariance descriptors, our descriptor can be measured and clustered in Euclidian space. Second, to capture the geometric-temporal contextual information, we construct a directional pyramid co-occurrence matrix (DPCM) to describe the spatio-temporal distribution of the vector-quantized local feature descriptors extracted from a video. DPCM characterizes the co-occurrence statistics of local features as well as the spatio-temporal positional relationships among the concurrent features. These statistics provide strong descriptive power for action recognition. To use DPCM for action recognition, we propose a directional pyramid co-occurrence matching kernel to measure the similarity of videos. The proposed method achieves the state-of-the-art performance and improves on the recognition performance of the bag-of-visual-words (BOVWs) models by a large margin on six public data sets. For example, on the KTH data set, it achieves 98.78% accuracy while the BOVW approach only achieves 88.06%. On both Weizmann and UCF CIL data sets, the highest possible accuracy of 100% is achieved.
Spectra and neutron dose of an 18 MV Linac using two geometric models of the head
International Nuclear Information System (INIS)
Barrera, M. T.; Pino, F.; Barros, H.; Sajo-Bohus, L.; Davila, J.; Salcedo, E.; Vega C, H. R.; Benites R, J. L.
2015-10-01
Full text: Using the Monte Carlo method, by MCNP5 code, simulations were performed with different source terms and 2 geometric models of the head to obtain spectra in energy, flow and doses of photo-neutrons at different positions on the stretcher and in the radiotherapy room. The simplest model was a spherical shell of tungsten; the second was the complete model of a heterogeneous head of an accelerator Varian ix. In both models Tosi function was used as a source term. In addition, for the second model Sheikh-Bagheri distribution was used for photons and photo-neutrons were generated. Also in both models the radiotherapy room of Gurve group of the Teaching Medical Center La Trinidad was included, which is equipped with an accelerator Varian Clinic 2100. In this Center passive detectors PADC (Cr-39) were irradiated with neutron converters, with 18 MeV photons radiation. The measured neutron flow was compared with that obtained with Monte Carlo calculations. The Monte Carlo flows are similar to those measured at the isocenter. The simplest model underestimates the neutron flow compared with the calculated flows with the heterogeneous model of the head. (Author)
Optical models of the human eye.
Atchison, David A; Thibos, Larry N
2016-03-01
Optical models of the human eye have been used in visual science for purposes such as providing a framework for explaining optical phenomena in vision, for predicting how refraction and aberrations are affected by change in ocular biometry and as computational tools for exploring the limitations imposed on vision by the optical system of the eye. We address the issue of what is understood by optical model eyes, discussing the 'encyclopaedia' and 'toy train' approaches to modelling. An extensive list of purposes of models is provided. We discuss many of the theoretical types of optical models (also schematic eyes) of varying anatomical accuracy, including single, three and four refracting surface variants. We cover the models with lens structure in the form of nested shells and gradient index. Many optical eye models give accurate predictions only for small angles and small fields of view. If aberrations and image quality are important to consider, such 'paraxial' model eyes must be replaced by 'finite model' eyes incorporating features such as aspheric surfaces, tilts and decentrations, wavelength-dependent media and curved retinas. Many optical model eyes are population averages and must become adaptable to account for age, gender, ethnicity, refractive error and accommodation. They can also be customised for the individual when extensive ocular biometry and optical performance data are available. We consider which optical model should be used for a particular purpose, adhering to the principle that the best model is the simplest fit for the task. We provide a glimpse into the future of optical models of the human eye. This review is interwoven with historical developments, highlighting the important people who have contributed so richly to our understanding of visual optics. © 2016 The Authors. Clinical and Experimental Optometry © 2016 Optometry Australia.
GEOMETRIC CONTEXT AND ORIENTATION MAP COMBINATION FOR INDOOR CORRIDOR MODELING USING A SINGLE IMAGE
Directory of Open Access Journals (Sweden)
A. B. Jahromi
2016-06-01
Full Text Available Since people spend most of their time indoors, their indoor activities and related issues in health, security and energy consumption have to be understood. Hence, gathering and representing spatial information of indoor spaces in form of 3D models become very important. Considering the available data gathering techniques with respect to the sensors cost and data processing time, single images proved to be one of the reliable sources. Many of the current single image based indoor space modeling methods are defining the scene as a single box primitive. This domain-specific knowledge is usually not applicable in various cases where multiple corridors are joined at one scene. Here, we addressed this issue by hypothesizing-verifying multiple box primitives which represents the indoor corridor layout. Middle-level perceptual organization is the foundation of the proposed method, which relies on finding corridor layout boundaries using both detected line segments and virtual rays created by orthogonal vanishing points. Due to the presence of objects, shadows and occlusions, a comprehensive interpretation of the edge relations is often concealed. This necessitates the utilization of virtual rays to create a physically valid layout hypothesis. Many of the former methods used Orientation Map or Geometric Context to evaluate their proposed layout hypotheses. Orientation map is a map that reveals the local belief of region orientations computed from line segments, and in a segmented image geometric context uses color, texture, edge, and vanishing point cues to estimate the likelihood of each possible label for all super-pixels. Here, the created layout hypotheses are evaluated by an objective function which considers the fusion of orientation map and geometric context with respect to the horizontal viewing angle at each image pixel. Finally, the best indoor corridor layout hypothesis which gets the highest score from the scoring function will be selected
Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.
2017-12-01
The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.
Geometric analysis of alternative models of faulting at Yucca Mountain, Nevada
International Nuclear Information System (INIS)
Young, S.R.; Stirewalt, G.L.; Morris, A.P.
1993-01-01
Realistic cross section tectonic models must be retrodeformable to geologically reasonable pre-deformation states. Furthermore, it must be shown that geologic structures depicted on cross section tectonic models can have formed by kinematically viable deformation mechanisms. Simple shear (i.e., listric fault models) is consistent with extensional geologic structures and fault patterns described at Yucca Mountain, Nevada. Flexural slip models yield results similar to oblique simple shear mechanisms, although there is no strong geological evidence for flexural slip deformation. Slip-line deformation is shown to generate fault block geometrics that are a close approximation to observed fault block structures. However, slip-line deformation implies a degree of general ductility for which there is no direct geological evidence. Simple and hybrid 'domino' (i.e., planar fault) models do not adequately explain observed variations of fault block dip or the development of 'rollover' folds adjacent to major bounding faults. Overall tectonic extension may be underestimated because of syn-tectonic deposition (growth faulting) of the Tertiary pyroclastic rocks that comprise Yucca Mountain. A strong diagnostic test of the applicability of the domino model may be provided by improved knowledge of Tertiary volcanic stratigraphy
Geometric Model of Induction Heating Process of Iron-Based Sintered Materials
Semagina, Yu V.; Egorova, M. A.
2018-03-01
The article studies the issue of building multivariable dependences based on the experimental data. A constructive method for solving the issue is presented in the form of equations of (n-1) – surface compartments of the extended Euclidean space E+n. The dimension of space is taken to be equal to the sum of the number of parameters and factors of the model of the system being studied. The basis for building multivariable dependencies is the generalized approach to n-space used for the surface compartments of 3D space. The surface is designed on the basis of the kinematic method, moving one geometric object along a certain trajectory. The proposed approach simplifies the process aimed at building the multifactorial empirical dependencies which describe the process being investigated.
Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces
Directory of Open Access Journals (Sweden)
Yong-Hyuk Kim
2014-01-01
Full Text Available Surrogate models (SMs can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.
A geometric model of a V-slit Sun sensor correcting for spacecraft wobble
Mcmartin, W. P.; Gambhir, S. S.
1994-01-01
A V-Slit sun sensor is body-mounted on a spin-stabilized spacecraft. During injection from a parking or transfer orbit to some final orbit, the spacecraft may not be dynamically balanced. This may result in wobble about the spacecraft spin axis as the spin axis may not be aligned with the spacecraft's axis of symmetry. While the widely used models in Spacecraft Attitude Determination and Control, edited by Wertz, correct for separation, elevation, and azimuthal mounting biases, spacecraft wobble is not taken into consideration. A geometric approach is used to develop a method for measurement of the sun angle which corrects for the magnitude and phase of spacecraft wobble. The algorithm was implemented using a set of standard mathematical routines for spherical geometry on a unit sphere.
Energy Technology Data Exchange (ETDEWEB)
Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)
2006-04-01
In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.
Theoretical study on optical model potential
International Nuclear Information System (INIS)
Lim Hung Gi.
1984-08-01
The optical model potential of non-local effect on the rounded edge of the potential is derived. On the basis of this potential the functional form of the optical model potential, the energy dependence and relationship of its parameters, and the dependency of the values of the parameters on energy change are shown in this paper. (author)
Geometric analysis of the solutions of two-phase flows: two-fluid model
International Nuclear Information System (INIS)
Kestin, J.; Zeng, D.L.
1984-01-01
This report contains a lightly edited draft of a study of the two-fluid model in two-phase flow. The motivation for the study stems from the authors' conviction that the construction of a computer code for any model should be preceded by a geometrical analysis of the pattern of trajectories in the phase space appropriate for the model. Such a study greatly facilitates the understanding of the phenomenon of choking and anticipates the computational difficulties which arise from the existence of singularities. The report contains a derivation of the six conservation equations of the model which includes a consideration of the simplifications imposed on a one-dimensional treatment by the presence of boundary layers at the wall and between the phases. The model is restricted to one-dimensional adiabatic flows of a single substance present in two phases, but thermodynamic equilibrium between the phases is not assumed. The role of closure conditions is defined but no specific closure conditions, or explicit equations of state, are introduced
Li, Ye; Röhrl, Stephan M; Bøe, B; Nordsletten, Lars
2014-09-01
Radiostereometric analysis (RSA) is the gold standard of measurement for in vivo 3D implants migration. The aim of this study was to evaluate the in vivo precision of 2 RSA marker-based systems compared with that of marker-free, elementary geometrical shape modeling RSA. Stem migration was measured in 50 patients recruited from an on-going Randomized Controlled Trial. We performed marker-based analysis with the Um RSA and RSAcore systems and compared these results with those of the elementary geometrical shape RSA. The precision for subsidence was 0.118 mm for Um RSA, 0.141 mm for RSAcore, and 0.136 mm for elementary geometrical shape RSA. The precision for retroversion was 1.3° for elementary geometrical shape RSA, approximately 2-fold greater than that for the other methods. The intraclass correlation coefficient between the marker-based systems and elementary geometrical shape RSA was approximately 0.5 for retroversion. All 3 methods yielded ICCs for subsidence and varus-valgus rotation above 0.9. We found an excellent correlation between marker-based RSA and elementary geometrical shape RSA for subsidence and varus-valgus rotation, independent of the system used. The precisions for out-of-plane migration were inferior for elementary geometrical shape RSA. Therefore, as a mechanism of failure, retroversion may be more difficult to detect early. This is to our knowledge the first study to compare different RSA systems with or without markers on the implant. Marker-based RSA has high precision in all planes, independent of the system used. Elementary geometrical shape RSA is inferior in out-of-plane migration. Copyright © 2014 Elsevier Ltd. All rights reserved.
Samadi, Reza
Technical textiles are increasingly being engineered and used in challenging applications, in areas such as safety, biomedical devices, architecture and others, where they must meet stringent demands including excellent and predictable load bearing capabilities. They also form the bases for one of the most widespread group of composite materials, fibre reinforced polymer-matrix composites (PMCs), which comprise materials made of stiff and strong fibres generally available in textile form and selected for their structural potential, combined with a polymer matrix that gives parts their shape. Manufacturing processes for PMCs and technical textiles, as well as parts and advanced textile structures must be engineered, ideally through simulation, and therefore diverse properties of the textiles, textile reinforcements and PMC materials must be available for predictive simulation. Knowing the detailed geometry of technical textiles is essential to predicting accurately the processing and performance properties of textiles and PMC parts. In turn, the geometry taken by a textile or a reinforcement textile is linked in an intricate manner to its constitutive behaviour. This thesis proposes, investigates and validates a general numerical tool for the integrated and comprehensive analysis of textile geometry and constitutive behaviour as required toward engineering applications featuring technical textiles and textile reinforcements. The tool shall be general with regards to the textiles modelled and the loading cases applied. Specifically, the work aims at fulfilling the following objectives: 1) developing and implementing dedicated simulation software for modelling textiles subjected to various load cases; 2) providing, through simulation, geometric descriptions for different textiles subjected to different load cases namely compaction, relaxation and shear; 3) predicting the constitutive behaviour of the textiles undergoing said load cases; 4) identifying parameters
Vishwakarma, Vinod
Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model (ROM) of a bladed rotor. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data of blades' geometries and sector analyses using ANSYS. For the first time ROM of a geometrically mistuned industrial scale rotor (Transonic rotor) with large size of Finite Element (FE) model is generated using MMDA. Two methods for estimating mass and stiffness mistuning matrices are used a) exact computation from sector FE analysis, b) estimates based on POD mistuning parameters. Modal characteristics such as mistuned natural frequencies, mode shapes and forced harmonic response are obtained from ROM for various cases, and results are compared with full rotor ANSYS analysis and other ROM methods such as Subset of Nominal Modes (SNM) and Fundamental Model of Mistuning (FMM). Accuracy of MMDA ROM is demonstrated with variations in number of POD features and geometric mistuning parameters. It is shown for the aforementioned case b) that the high accuracy of ROM studied in previous work with Academic rotor does not directly translate to the Transonic rotor. Reasons for such mismatch in results are investigated and attributed to higher mistuning in Transonic rotor. Alternate solutions such as estimation of sensitivities via least squares, and interpolation of mass and stiffness matrices on manifolds are developed, and their results are discussed. Statistics such as mean and standard deviations of forced harmonic response peak amplitude are obtained from random permutations, and are shown to have similar results as those of Monte Carlo simulations. These statistics are obtained and compared for 3 degree of freedom (DOF) lumped parameter model (LPM) of rotor, Academic rotor and Transonic rotor. A state -- estimator based on MMDA ROM and Kalman filter is also developed for offline or online estimation of harmonic forcing function from
A new geometric-based model to accurately estimate arm and leg inertial estimates.
Wicke, Jason; Dumas, Geneviève A
2014-06-03
Segment estimates of mass, center of mass and moment of inertia are required input parameters to analyze the forces and moments acting across the joints. The objectives of this study were to propose a new geometric model for limb segments, to evaluate it against criterion values obtained from DXA, and to compare its performance to five other popular models. Twenty five female and 24 male college students participated in the study. For the criterion measures, the participants underwent a whole body DXA scan, and estimates for segment mass, center of mass location, and moment of inertia (frontal plane) were directly computed from the DXA mass units. For the new model, the volume was determined from two standing frontal and sagittal photographs. Each segment was modeled as a stack of slices, the sections of which were ellipses if they are not adjoining another segment and sectioned ellipses if they were adjoining another segment (e.g. upper arm and trunk). Length of axes of the ellipses was obtained from the photographs. In addition, a sex-specific, non-uniform density function was developed for each segment. A series of anthropometric measurements were also taken by directly following the definitions provided of the different body segment models tested, and the same parameters determined for each model. Comparison of models showed that estimates from the new model were consistently closer to the DXA criterion than those from the other models, with an error of less than 5% for mass and moment of inertia and less than about 6% for center of mass location. Copyright © 2014. Published by Elsevier Ltd.
Kou, Jisheng
2015-07-16
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
Directory of Open Access Journals (Sweden)
Konstantinos B. Baltzis
2008-10-01
Full Text Available A common assumption in cellular communications is the circular-cell approximation. In this paper, an alternative analysis based on the hexagonal shape of the cells is presented. A geometrical-based stochastic model is proposed to describe the angle of arrival of the interfering signals in the reverse link of a cellular system. Explicit closed form expressions are derived, and simulations performed exhibit the characteristics and validate the accuracy of the proposed model. Applications in the capacity estimation of WCDMA cellular networks are presented. Dependence of system capacity of the sectorization of the cells and the base station antenna radiation pattern is explored. Comparisons with data in literature validate the accuracy of the proposed model. The degree of error of the hexagonal and the circular-cell approaches has been investigated indicating the validity of the proposed model. Results have also shown that, in many cases, the two approaches give similar results when the radius of the circle equals to the hexagon inradius. A brief discussion on how the proposed technique may be applied to broadband access networks is finally made.
Static aeroelastic analysis including geometric nonlinearities based on reduced order model
Directory of Open Access Journals (Sweden)
Changchuan Xie
2017-04-01
Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.
Kou, Jisheng; Sun, Shuyu
2015-01-01
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
A Novel Geometrical Height Gain Model for Line-of-Sight Urban Micro Cells Below 6 GHz
DEFF Research Database (Denmark)
Rodriguez, Ignacio; Nguyen, Huan Cong; Sørensen, Troels Bundgaard
2016-01-01
This paper presents a novel height gain model applicable to line-of-sight urban micro cell scenarios and frequencies below 6 GHz. The model is knife-edge diffraction-based, and it is founded on simple geometrical and physical relationships. Typical system level simulator scenario parameters...
2015-01-07
Scale X-ray CT Images. Zernike phase contrast is a technique useful for nano-scale X-ray imaging of materials with a low absorption coefficient. It... Zernike phase contrast is a useful technique for nanoscale X-ray computed tomography (CT) of materials with a low X-ray absorption coefficient. It...have developed an image restoration method [5] that models the X-ray phase contrast optics, computes a 3D kernel and minimizes an energy function
Energy Technology Data Exchange (ETDEWEB)
Trivelpiece, Cory L., E-mail: cory@psu.ed [Department of Mechanical and Nuclear Engineering, The Pennsylvania, State University, University Park, PA 16802 (United States); Brenizer, J.S. [Department of Mechanical and Nuclear Engineering, The Pennsylvania, State University, University Park, PA 16802 (United States)
2011-01-01
A diameter of uncertainty (D{sub u}) was derived from a geometric uncertainty model describing the error that would be introduced into position-sensitive, coincidence neutron detection measurements by charged-particle transport phenomena and experimental setup. The transport of {alpha} and Li ions, produced by the {sup 10}B(n,{alpha}) {sup 7}Li reaction, through free-standing boro-phosphosilicate glass (BPSG) films was modeled using the Monte Carlo code SRIM, and the results of these simulations were used as input to determine D{sub u} for position-sensitive, coincidence techniques. The results of these calculations showed that D{sub u} is dependent on encoder separation, the angle of charged particle emission, and film thickness. For certain emission scenarios, the magnitude of D{sub u} is larger than the physical size of the neutron converting media that were being modeled. Spheres of uncertainty were developed that describe the difference in flight path times among the bounding-case emission scenarios that were considered in this work. It was shown the overlapping spheres represent emission angles and particle flight path lengths that would be difficult to resolve in terms of particle time-of-flight measurements. However, based on the timing resolution of current nuclear instrumentation, emission events that yield large D{sub u} can be discriminated by logical arguments during spectral deconvolution.
Progressive Conversion from B-rep to BSP for Streaming Geometric Modeling.
Bajaj, Chandrajit; Paoluzzi, Alberto; Scorzelli, Giorgio
2006-01-01
We introduce a novel progressive approach to generate a Binary Space Partition (BSP) tree and a convex cell decomposition for any input triangles boundary representation (B-rep), by utilizing a fast calculation of the surface inertia. We also generate a solid model at progressive levels of detail. This approach relies on a variation of standard BSP tree generation, allowing for labeling cells as in, out and fuzzy, and which permits a comprehensive representation of a solid as the Hasse diagram of a cell complex. Our new algorithm is embedded in a streaming computational framework, using four types of dataflow processes that continuously produce, transform, combine or consume subsets of cells depending on their number or input/output stream. A varied collection of geometric modeling techniques are integrated in this streaming framework, including polygonal, spline, solid and heterogeneous modeling with boundary and decompositive representations, Boolean set operations, Cartesian products and adaptive refinement. The real-time B-rep to BSP streaming results we report in this paper are a large step forward in the ultimate unification of rapid conceptual and detailed shape design methodologies.
Different faces of chaos in FRW models with scalar fields-geometrical point of view
International Nuclear Information System (INIS)
Hrycyna, Orest; Szydlowski, Marek
2006-01-01
FRW cosmologies with conformally coupled scalar fields are investigated in a geometrical way by the means of geodesics of the Jacobi metric. In this model of dynamics, trajectories in the configuration space are represented by geodesics. Because of the singular nature of the Jacobi metric on the boundary set -bar D of the domain of admissible motion, the geodesics change the cone sectors several times (or an infinite number of times) in the neighborhood of the singular set -bar D. We show that this singular set contains interesting information about the dynamical complexity of the model. Firstly, this set can be used as a Poincare surface for construction of Poincare sections, and the trajectories then have the recurrence property. We also investigate the distribution of the intersection points. Secondly, the full classification of periodic orbits in the configuration space is performed and existence of UPO is demonstrated. Our general conclusion is that, although the presented model leads to several complications, like divergence of curvature invariants as a measure of sensitive dependence on initial conditions, some global results can be obtained and some additional physical insight is gained from using the conformal Jacobi metric. We also study the complex behavior of trajectories in terms of symbolic dynamics
Optical model analysis for 30MeV polarized proton elastic scattering
International Nuclear Information System (INIS)
Pham, D.-L.; Swiniarski, R. de.
1977-05-01
The proton elastic scattering cross sections and analyzing powers at 30MeV have been used to derive optical model parameters for ten elements from 10 B to 32 S. A set of average geometrical parameters (rsub(o)=1.10fm, rsub(LS)=1.0fm and asub(I)=0.60fm) is found to give good fits to the entire data, the other geometrical parameters being rsub(I)=(1.35+-0.15)fm, asub(o)=(0.75+-0.10)fm and asub(LS)=(0.35+-0.07)fm. The dynamical parameters with fixed geometry are presented
Universal fit to p-p elastic diffraction scattering from the Lorentz contracted geometrical model
International Nuclear Information System (INIS)
Hansen, P.H.; Krisch, A.D.
1976-01-01
The prediction of the Lorentz contracted geometical model for proton-proton elastic scattering at small angles is examined. The model assumes that when two high energy particles collide, each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz contraction in the incident direction. It is predicted that dsigma/dt should be independent of energy when plotted against the variable β 2 P 2 sub(perpendicular) sigmasub(TOT)(s)/38.3. Thus the energy dependence of the diffraction peak slope (b in an esup(-b mod(t))plot) is given by b(s)=A 2 β 2 sigmasub(TOT)(s)/38.3 where β is the proton's c.m. velocity and A is its radius. Recently measured values of sigmasub(TOT)(s) were used and an excellent fit obtained to the elastic slope in both t regions [-t 2 and 0.1 2 ] at all energies from s=6 to 4000(GeV/c) 2 . (Auth.)
Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej
2006-06-01
We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.
Directory of Open Access Journals (Sweden)
R. Kaden
2012-07-01
Full Text Available Virtual 3D city models are integrated complex compositions of spatial data of different themes, origin, quality, scale, and dimensions. Within this paper, we address the problem of spatial compatibility of geodata aiming to provide support for ad-hoc integration of virtual 3D city models including geodata of different sources and themes like buildings, terrain, and city furniture. In contrast to related work which is dealing with the integration of redundant geodata structured according to different data models and ontologies, we focus on the integration of complex 3D models of the same representation (here: CityGML but regarding to the geometric-topological consistent matching of non-homologous objects, e.g. a building is connected to a road, and their geometric homogenisation. Therefore, we present an approach including a data model for a Geodata Join and the general concept of an integration procedure using the join information. The Geodata Join aims to bridge the lack of information between fragmented geodata by describing the relationship between adjacent objects from different datasets. The join information includes the geometrical representation of those parts of an object, which have a specific/known topological or geometrical relationship to another object. This part is referred to as a Connector and is either described by points, lines, or surfaces of the existing object geometry or by additional join geometry. In addition, the join information includes the specification of the connected object in the other dataset and the description of the topological and geometrical relationship between both objects, which is used to aid the matching process. Furthermore, the Geodata Join contains object-related information like accuracy values and restrictions of movement and deformation which are used to optimize the integration process. Based on these parameters, a functional model including a matching algorithm, transformation methods, and
International Nuclear Information System (INIS)
Chen Changyong; Liu Zongliang; Kang Shuai; Li Shaohua
2010-01-01
We introduce the double-Hamiltonian evolution technique approach to investigate the unconventional geometric quantum logical gate with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms for the large-detuning interaction of the atoms with the cavity mode. The main advantage of our scheme is of eliminating the photon flutuation in the cavity mode during the gating. The corresponding analytical results will be helpful for experimental realization of speed geometric quantum logical gate in real cavities. (general)
International Nuclear Information System (INIS)
Saverin, Joseph; Peukert, Juliane; Marten, David; Pechlivanoglou, George; Paschereit, Christian Oliver; Greenblatt, David
2016-01-01
The current paper investigates the aeroelastic modelling of large, flexible multi- MW wind turbine blades. Most current performance prediction tools make use of the Blade Element Momentum (BEM) model, based upon a number of simplifying assumptions that hold only under steady conditions. This is why a lifting line free vortex wake (LLFVW) algorithm is used here to accurately resolve unsteady wind turbine aerodynamics. A coupling to the structural analysis tool BeamDyn, based on geometrically exact beam theory, allows for time-resolved aeroelastic simulations with highly deflected blades including bend-twist, coupling. Predictions of blade loading and deformation for rigid and flexible blades are analysed with reference to different aerodynamic and structural approaches. The emergency shutdown procedure is chosen as an examplary design load case causing large deflections to place emphasis on the influence of structural coupling and demonstrate the necessity of high fidelity structural models. (paper)
Colman, Kerri L; Dobbe, Johannes G G; Stull, Kyra E; Ruijter, Jan M; Oostra, Roelof-Jan; van Rijn, Rick R; van der Merwe, Alie E; de Boer, Hans H; Streekstra, Geert J
2017-07-01
Almost all European countries lack contemporary skeletal collections for the development and validation of forensic anthropological methods. Furthermore, legal, ethical and practical considerations hinder the development of skeletal collections. A virtual skeletal database derived from clinical computed tomography (CT) scans provides a potential solution. However, clinical CT scans are typically generated with varying settings. This study investigates the effects of image segmentation and varying imaging conditions on the precision of virtual modelled pelves. An adult human cadaver was scanned using varying imaging conditions, such as scanner type and standard patient scanning protocol, slice thickness and exposure level. The pelvis was segmented from the various CT images resulting in virtually modelled pelves. The precision of the virtual modelling was determined per polygon mesh point. The fraction of mesh points resulting in point-to-point distance variations of 2 mm or less (95% confidence interval (CI)) was reported. Colour mapping was used to visualise modelling variability. At almost all (>97%) locations across the pelvis, the point-to-point distance variation is less than 2 mm (CI = 95%). In >91% of the locations, the point-to-point distance variation was less than 1 mm (CI = 95%). This indicates that the geometric variability of the virtual pelvis as a result of segmentation and imaging conditions rarely exceeds the generally accepted linear error of 2 mm. Colour mapping shows that areas with large variability are predominantly joint surfaces. Therefore, results indicate that segmented bone elements from patient-derived CT scans are a sufficiently precise source for creating a virtual skeletal database.
Zhevlakov, A. P.; Zatsepina, M. E.; Kirillovskii, V. K.
2014-06-01
The principles of transformation of a Foucault shadowgram into a quantitative map of wave-front deformation based on creation of a system of isophotes are unveiled. The presented studies and their results prove that there is a high degree of correspondence between a Foucault shadowgram and the geometrical model of a shear interferogram with respect to displaying wave-front deformations.
van Leeuwen, G. M.; Kotte, A. N.; Crezee, J.; Lagendijk, J. J.
1997-01-01
We have developed a thermal model, for use in hyperthermia treatment planning, in which blood vessels are described as geometrical objects; 3D curves with associated diameters. For the calculation of the heat exchange with the tissue an analytic result is used. To arrive at this result some
International Nuclear Information System (INIS)
Cerny, V.
1983-01-01
A model based estimate is presented of the geometrical acceptance of the HYPERON spectrometer for the detection of the e + e - pairs in the proposed lepton experiment. The results of the Monte Carlo calculation show that the expected acceptance is fairly high. (author)
Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi
2006-07-10
On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.
Modeling of Surface Geometric Structure State After Integratedformed Milling and Finish Burnishing
Berczyński, Stefan; Grochała, Daniel; Grządziel, Zenon
2017-06-01
The article deals with computer-based modeling of burnishing a surface previously milled with a spherical cutter. This method of milling leaves traces, mainly asperities caused by the cutting crossfeed and cutter diameter. The burnishing process - surface plastic treatment - is accompanied by phenomena that take place right in the burnishing ball-milled surface contact zone. The authors present the method for preparing a finite element model and the methodology of tests for the assessment of height parameters of a surface geometrical structure (SGS). In the physical model the workpieces had a cuboidal shape and these dimensions: (width × height × length) 2×1×4.5 mm. As in the process of burnishing a cuboidal workpiece is affected by plastic deformations, the nonlinearities of the milled item were taken into account. The physical model of the process assumed that the burnishing ball would be rolled perpendicularly to milling cutter linear traces. The model tests included the application of three different burnishing forces: 250 N, 500 N and 1000 N. The process modeling featured the contact and pressing of a ball into the workpiece surface till the desired force was attained, then the burnishing ball was rolled along the surface section of 2 mm, and the burnishing force was gradually reduced till the ball left the contact zone. While rolling, the burnishing ball turned by a 23° angle. The cumulative diagrams depict plastic deformations of the modeled surfaces after milling and burnishing with defined force values. The roughness of idealized milled surface was calculated for the physical model under consideration, i.e. in an elementary section between profile peaks spaced at intervals of crossfeed passes, where the milling feed fwm = 0.5 mm. Also, asperities after burnishing were calculated for the same section. The differences of the obtained values fall below 20% of mean values recorded during empirical experiments. The adopted simplification in after
Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration
Li, Huan; Song, Hai-Feng; Liu, Yu
2016-11-01
We calculated the phase diagram of the Kondo-Heisenberg model on a two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions in the presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling J k and frustration strength Q. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnetic valence bond solids (VBS). In addition, we found two distinct VBS. As J k is increased, a phase transition from AF to Kondo paramagnetic (KP) phase occurs, without the intermediate phase coexisting AF order with Kondo screening found in square lattice systems. In the KP phase, the enhancement of frustration weakens the Kondo screening effect, resulting in a phase transition from KP to VBS. We also found a process to recover the AF order from VBS by increasing J k in a wide range of frustration strength. Our work may provide predictions for future experimental observation of new processes of quantum phase transitions in frustrated heavy-fermion compounds.
Directory of Open Access Journals (Sweden)
S. Merkt
2012-01-01
Full Text Available
ENGLISH ABSTRACT: Selective laser melting (SLM is becoming an economically viable choice for manufacturing complex serial parts. This paper focuses on a geometric complexity analysis as part of the integrative technology evaluation model (ITEM presented here. In contrast to conventional evaluation methodologies, the ITEM considers interactions between product and process innovations generated by SLM. The evaluation of manufacturing processes that compete with SLM is the main goal of ITEM. The paper includes a complexity analysis of a test part from Festo AG. The paper closes with a discussion of how the expanded design freedom of SLM can be used to improve company operations, and how the complexity analysis presented here can be seen as a starting point for feature-based complexity analysis..
AFRIKAANSE OPSOMMING: Selektiewe lasersmelting word geleidelik ’n gangbare ekonomiese keuse vir die vervaar-diging van opeenvolgende komplekse onderdele. Die navorsing is toegespits op die ontleding van meetkundige kompleksiteit as ’n gedeelte van ’n integrerende tegnologiese evalueringsmodel. Gemeet teen konvensionele evalueringsmodelle behandel die genoemde metode interaksies tussen produkte- en prosesinnovasies wat gegenereer word. Die navorsing behandel ’n kompleksiteitsontleding van ’n toetsonderdeel van die firma FESTO AG. Die resultaat toon hoe kompleksiteits-analise gebruik kan word as die vertrekpunt vir eienskapsgebaseerde analise.
Development of Camera Model and Geometric Calibration/validation of Xsat IRIS Imagery
Kwoh, L. K.; Huang, X.; Tan, W. J.
2012-07-01
XSAT, launched on 20 April 2011, is the first micro-satellite designed and built in Singapore. It orbits the Earth at altitude of 822 km in a sun synchronous orbit. The satellite carries a multispectral camera IRIS with three spectral bands - 0.52~0.60 mm for Green, 0.63~0.69 mm for Red and 0.76~0.89 mm for NIR at 12 m resolution. In the design of IRIS camera, the three bands were acquired by three lines of CCDs (NIR, Red and Green). These CCDs were physically separated in the focal plane and their first pixels not absolutely aligned. The micro-satellite platform was also not stable enough to allow for co-registration of the 3 bands with simple linear transformation. In the camera model developed, this platform stability was compensated with 3rd to 4th order polynomials for the satellite's roll, pitch and yaw attitude angles. With the camera model, the camera parameters such as the band to band separations, the alignment of the CCDs relative to each other, as well as the focal length of the camera can be validated or calibrated. The results of calibration with more than 20 images showed that the band to band along-track separation agreed well with the pre-flight values provided by the vendor (0.093° and 0.046° for the NIR vs red and for green vs red CCDs respectively). The cross-track alignments were 0.05 pixel and 5.9 pixel for the NIR vs red and green vs red CCDs respectively. The focal length was found to be shorter by about 0.8%. This was attributed to the lower operating temperature which XSAT is currently operating. With the calibrated parameters and the camera model, a geometric level 1 multispectral image with RPCs can be generated and if required, orthorectified imagery can also be produced.
Highway extraction from high resolution aerial photography using a geometric active contour model
Niu, Xutong
Highway extraction and vehicle detection are two of the most important steps in traffic-flow analysis from multi-frame aerial photographs. The traditional method of deriving traffic flow trajectories relies on manual vehicle counting from a sequence of aerial photographs, which is tedious and time-consuming. This research presents a new framework for semi-automatic highway extraction. The basis of the new framework is an improved geometric active contour (GAC) model. This novel model seeks to minimize an objective function that transforms a problem of propagation of regular curves into an optimization problem. The implementation of curve propagation is based on level set theory. By using an implicit representation of a two-dimensional curve, a level set approach can be used to deal with topological changes naturally, and the output is unaffected by different initial positions of the curve. However, the original GAC model, on which the new model is based, only incorporates boundary information into the curve propagation process. An error-producing phenomenon called leakage is inevitable wherever there is an uncertain weak edge. In this research, region-based information is added as a constraint into the original GAC model, thereby, giving this proposed method the ability of integrating both boundary and region-based information during the curve propagation. Adding the region-based constraint eliminates the leakage problem. This dissertation applies the proposed augmented GAC model to the problem of highway extraction from high-resolution aerial photography. First, an optimized stopping criterion is designed and used in the implementation of the GAC model. It effectively saves processing time and computations. Second, a seed point propagation framework is designed and implemented. This framework incorporates highway extraction, tracking, and linking into one procedure. A seed point is usually placed at an end node of highway segments close to the boundary of the
Su, Luning; Li, Wei; Wu, Mingxuan; Su, Yun; Guo, Chongling; Ruan, Ningjuan; Yang, Bingxin; Yan, Feng
2017-08-01
Lobster-eye optics is widely applied to space x-ray detection missions and x-ray security checks for its wide field of view and low weight. This paper presents a theoretical model to obtain spatial distribution of focusing efficiency based on lobster-eye optics in a soft x-ray wavelength. The calculations reveal the competition mechanism of contributions to the focusing efficiency between the geometrical parameters of lobster-eye optics and the reflectivity of the iridium film. In addition, the focusing efficiency image depending on x-ray wavelengths further explains the influence of different geometrical parameters of lobster-eye optics and different soft x-ray wavelengths on focusing efficiency. These results could be beneficial to optimize parameters of lobster-eye optics in order to realize maximum focusing efficiency.
A Hybrid 3D Colon Segmentation Method Using Modified Geometric Deformable Models
Directory of Open Access Journals (Sweden)
S. Falahieh Hamidpour
2007-06-01
Full Text Available Introduction: Nowadays virtual colonoscopy has become a reliable and efficient method of detecting primary stages of colon cancer such as polyp detection. One of the most important and crucial stages of virtual colonoscopy is colon segmentation because an incorrect segmentation may lead to a misdiagnosis. Materials and Methods: In this work, a hybrid method based on Geometric Deformable Models (GDM in combination with an advanced region growing and thresholding methods is proposed. GDM are found to be an attractive tool for structural based image segmentation particularly for extracting the objects with complicated topology. There are two main parameters influencing the overall performance of GDM algorithm; the distance between the initial contour and the actual object’s contours and secondly the stopping term which controls the deformation. To overcome these limitations, a two stage hybrid based segmentation method is suggested to extract the rough but precise initial contours at the first stage of the segmentation. The extracted boundaries are smoothed and improved using a modified GDM algorithm by improving the stopping terms of the algorithm based on the gradient value of image voxels. Results: The proposed algorithm was implemented on forty data sets each containing 400-480 slices. The results show an improvement in the accuracy and smoothness of the extracted boundaries. The improvement obtained for the accuracy of segmentation is about 6% in comparison to the one achieved by the methods based on thresholding and region growing only. Discussion and Conclusion: The extracted contours using modified GDM are smoother and finer. The improvement achieved in this work on the performance of stopping function of GDM model together with applying two stage segmentation of boundaries have resulted in a great improvement on the computational efficiency of GDM algorithm while making smoother and finer colon borders.
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Bonduel, M.; Bassier, M.; Vergauwen, M.; Pauwels, P.; Klein, R.
2017-11-01
The use of Building Information Modeling (BIM) for existing buildings based on point clouds is increasing. Standardized geometric quality assessment of the BIMs is needed to make them more reliable and thus reusable for future users. First, available literature on the subject is studied. Next, an initial proposal for a standardized geometric quality assessment is presented. Finally, this method is tested and evaluated with a case study. The number of specifications on BIM relating to existing buildings is limited. The Levels of Accuracy (LOA) specification of the USIBD provides definitions and suggestions regarding geometric model accuracy, but lacks a standardized assessment method. A deviation analysis is found to be dependent on (1) the used mathematical model, (2) the density of the point clouds and (3) the order of comparison. Results of the analysis can be graphical and numerical. An analysis on macro (building) and micro (BIM object) scale is necessary. On macro scale, the complete model is compared to the original point cloud and vice versa to get an overview of the general model quality. The graphical results show occluded zones and non-modeled objects respectively. Colored point clouds are derived from this analysis and integrated in the BIM. On micro scale, the relevant surface parts are extracted per BIM object and compared to the complete point cloud. Occluded zones are extracted based on a maximum deviation. What remains is classified according to the LOA specification. The numerical results are integrated in the BIM with the use of object parameters.
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016...... approaches. (C) 2016 Optical Society of America...
X-cube model on generic lattices: Fracton phases and geometric order
Slagle, Kevin; Kim, Yong Baek
2018-04-01
Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground-state degeneracy (GSD) which can increase exponentially with system size. In this paper, we present a generic lattice construction (in three dimensions) for a generalized X-cube model of fracton order, where the mobility restrictions of the subdimensional particles inherit the geometry of the lattice. This helps explain a previous result that lattice curvature can produce a robust GSD, even on a manifold with trivial topology. We provide explicit examples to show that the (zero-temperature) phase of matter is sensitive to the lattice geometry. In one example, the lattice geometry confines the dimension-1 particles to small loops, which allows the fractons to be fully mobile charges, and the resulting phase is equivalent to (3+1)-dimensional toric code. However, the phase is sensitive to more than just lattice curvature; different lattices without curvature (e.g., cubic or stacked kagome lattices) also result in different phases of matter, which are separated by phase transitions. Unintuitively, however, according to a previous definition of phase [X. Chen et al., Phys. Rev. B 82, 155138 (2010), 10.1103/PhysRevB.82.155138], even just a rotated or rescaled cubic results in different phases of matter, which motivates us to propose a coarser definition of phase for gapped ground states and fracton order. This equivalence relation between ground states is given by the composition of a local unitary transformation and a quasi-isometry (which can rotate and rescale the lattice); equivalently, ground states are in the same phase if they can be adiabatically connected by varying both the Hamiltonian and the positions of the degrees of freedom (via a quasi-isometry). In light of the importance of geometry, we further propose that fracton orders should be regarded as a geometric order.
Verma, Surender; Bhardwaj, Shankita
2018-05-01
We have investigated a possible connection between the Majorana phases and geometric parameters of Majorana unitarity triangle (MT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of C P violation. As an example, we have considered the two-texture zero neutrino mass model to obtain a relation between Majorana phases and MT parameters that may be probed in various lepton number violating processes. In particular, we find that Majorana phases depend on only one of the three interior angles of the MT in each class of two-texture zero neutrino mass matrix. We have also constructed the MT for class A , B , and C neutrino mass matrices. Nonvanishing areas and nontrivial orientations of these Majorana unitarity triangles indicate nonzero C P violation as a generic feature of this class of mass models.
Modeling and optimization of LCD optical performance
Yakovlev, Dmitry A; Kwok, Hoi-Sing
2015-01-01
The aim of this book is to present the theoretical foundations of modeling the optical characteristics of liquid crystal displays, critically reviewing modern modeling methods and examining areas of applicability. The modern matrix formalisms of optics of anisotropic stratified media, most convenient for solving problems of numerical modeling and optimization of LCD, will be considered in detail. The benefits of combined use of the matrix methods will be shown, which generally provides the best compromise between physical adequacy and accuracy with computational efficiency and optimization fac
Optical model analysis of intermediate energy p-4He scattering
International Nuclear Information System (INIS)
Greben, J.M.; Gourishankar, R.
1983-03-01
Recent Wolfenstein R-parameter data are used to explain and resolve previous problems with optical model descriptions of p- 4 He elastic scattering at 500 MeV. An essential component in this optical model analysis is a qualitative interpretation of different features of the elastic data in terms of the Born approximation. First we show that the R-data require the real spin-orbit potential to have certain geometrical properties which were missing in previous analyses. We can then show that the fast fall-off of the cross-section for small angles, together with the rapid increase and subsequent decrease of the polarization, establishes the need for an attractive tail in the real central potentials can also be inferred from this qualitative analysis, in particular a strong reduction of the spin-orbit potential. Our final potential gives a reduction of the X 2 /datapoint by about 20 in comparison to previous potentials, and underlines the usefulness of the qualitative Born analysis
Optical Coherence Tomography: Advanced Modeling
DEFF Research Database (Denmark)
Andersen, Peter E.; Thrane, Lars; Yura, Harold T.
2013-01-01
- and multiple-scattering regimes is derived. An advanced Monte Carlo model for calculating the OCT signal is also derived, and the validity of this model is shown through a mathematical proof based on the extended Huygens-Fresnel principle. From the analytical model, an algorithm for enhancing OCT images...... are discussed. Finally, the Wigner phase-space distribution function is derived in a closed-form solution, which may have applications in OCT....
International Nuclear Information System (INIS)
Bi, Lei; Yang, Ping
2016-01-01
The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles. - Highlights: • Concepts of diffraction, reflection and tunneling are refined. • The diffraction together with reflection is rigorously treated. • An improved invariant imbedding method is employed to compute the Debye
FDTD method and models in optical education
Lin, Xiaogang; Wan, Nan; Weng, Lingdong; Zhu, Hao; Du, Jihe
2017-08-01
In this paper, finite-difference time-domain (FDTD) method has been proposed as a pedagogical way in optical education. Meanwhile, FDTD solutions, a simulation software based on the FDTD algorithm, has been presented as a new tool which helps abecedarians to build optical models and to analyze optical problems. The core of FDTD algorithm is that the time-dependent Maxwell's equations are discretized to the space and time partial derivatives, and then, to simulate the response of the interaction between the electronic pulse and the ideal conductor or semiconductor. Because the solving of electromagnetic field is in time domain, the memory usage is reduced and the simulation consequence on broadband can be obtained easily. Thus, promoting FDTD algorithm in optical education is available and efficient. FDTD enables us to design, analyze and test modern passive and nonlinear photonic components (such as bio-particles, nanoparticle and so on) for wave propagation, scattering, reflection, diffraction, polarization and nonlinear phenomena. The different FDTD models can help teachers and students solve almost all of the optical problems in optical education. Additionally, the GUI of FDTD solutions is so friendly to abecedarians that learners can master it quickly.
Analytical model of the optical vortex microscope.
Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz
2016-04-20
This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.
Directory of Open Access Journals (Sweden)
O. V. Fomin
2013-10-01
Full Text Available Purpose. Presentation of features and example of the use of the offered determination algorithm of optimum geometrical parameters for the components of freight cars on the basis of the generalized mathematical models, which is realized using computer. Methodology. The developed approach to search for optimal geometrical parameters can be described as the determination of optimal decision of the selected set of possible variants. Findings. The presented application example of the offered algorithm proved its operation capacity and efficiency of use. Originality. The determination procedure of optimal geometrical parameters for freight car components on the basis of the generalized mathematical models was formalized in the paper. Practical value. Practical introduction of the research results for universal open cars allows one to reduce container of their design and accordingly to increase the carrying capacity almost by100 kg with the improvement of strength characteristics. Taking into account the mass of their park this will provide a considerable economic effect when producing and operating. The offered approach is oriented to the distribution of the software packages (for example Microsoft Excel, which are used by technical services of the most enterprises, and does not require additional capital investments (acquisitions of the specialized programs and proper technical staff training. This proves the correctness of the research direction. The offered algorithm can be used for the solution of other optimization tasks on the basis of the generalized mathematical models.
The optical model in atomic physics
International Nuclear Information System (INIS)
McCarthy, I.E.
1978-01-01
The optical model for electron scattering on atoms has quite a short history in comparison with nuclear physics. The main reason for this is that there were insufficient data. Angular distribution for elastic and some inelastic scattering have now been measured for the atoms which exist in gaseous form at reasonable temperatures, inert gases, hydrogen, alkalies and mercury being the main ones out in. The author shows that the optical model makes sense in atomic physics by considering its theory and recent history. (orig./AH) [de
Geometric phase modulation for stellar interferometry
International Nuclear Information System (INIS)
Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.
2002-01-01
Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer
Directory of Open Access Journals (Sweden)
José Ignacio Rojas-Sola
2016-12-01
Full Text Available The present study shows the process followed in making the three-dimensional model and geometric documentation of a historical invention of the renowned Spanish engineer Agustin de Betancourt y Molina, which forms part of his rich legacy. Specifically, this was a wind machine for draining marshy ground, designed in 1789. The present research relies on the computer-aided design (CAD techniques using Autodesk Inventor Professional software, based on the scant information provided by the only two drawings of the machine, making it necessary to propose a number of dimensional and geometric hypotheses as well as a series of movement restrictions (degrees of freedom, to arrive at a consistent design. The results offer a functional design for this historic invention.
Farkašovský, Pavol
2018-05-01
The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.
Bridging the Gap between RF and Optical Patch Antenna Analysis via the Cavity Model.
Unal, G S; Aksun, M I
2015-11-02
Although optical antennas with a variety of shapes and for a variety of applications have been proposed and studied, they are still in their infancy compared to their radio frequency (rf) counterparts. Optical antennas have mainly utilized the geometrical attributes of rf antennas rather than the analysis tools that have been the source of intuition for antenna engineers in rf. This study intends to narrow the gap of experience and intuition in the design of optical patch antennas by introducing an easy-to-understand and easy-to-implement analysis tool in rf, namely, the cavity model, into the optical regime. The importance of this approach is not only its simplicity in understanding and implementation but also its applicability to a broad class of patch antennas and, more importantly, its ability to provide the intuition needed to predict the outcome without going through the trial-and-error simulations with no or little intuitive guidance by the user.
Modeling GMPLS and Optical MPLS Networks
DEFF Research Database (Denmark)
Christiansen, Henrik Lehrmann; Wessing, Henrik
2003-01-01
. The MPLS concept is attractive because it can work as a unifying control structure. covering all technologies. This paper describes how a novel scheme for optical MPLS and circuit switched GMPLS based networks can incorporated in such multi-domain, MPLS-based scenarios and how it could be modeled. Network...
Theoretical aspects of the optical model
International Nuclear Information System (INIS)
Mahaux, C.
1980-01-01
We first recall the definition of the optical-model potential for nucleons and the physical interpretation of the main related quantities. We then survey the recent theoretical progress towards a reliable calculation of this potential. The present limitations of the theory and some prospects for future developments are outlined. (author)
Parametric uncertainty in optical image modeling
Potzick, James; Marx, Egon; Davidson, Mark
2006-10-01
Optical photomask feature metrology and wafer exposure process simulation both rely on optical image modeling for accurate results. While it is fair to question the accuracies of the available models, model results also depend on several input parameters describing the object and imaging system. Errors in these parameter values can lead to significant errors in the modeled image. These parameters include wavelength, illumination and objective NA's, magnification, focus, etc. for the optical system, and topography, complex index of refraction n and k, etc. for the object. In this paper each input parameter is varied over a range about its nominal value and the corresponding images simulated. Second order parameter interactions are not explored. Using the scenario of the optical measurement of photomask features, these parametric sensitivities are quantified by calculating the apparent change of the measured linewidth for a small change in the relevant parameter. Then, using reasonable values for the estimated uncertainties of these parameters, the parametric linewidth uncertainties can be calculated and combined to give a lower limit to the linewidth measurement uncertainty for those parameter uncertainties.
International Nuclear Information System (INIS)
Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.
2014-01-01
Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)
Phenomenological optical potentials and optical model computer codes
International Nuclear Information System (INIS)
Prince, A.
1980-01-01
An introduction to the Optical Model is presented. Starting with the purpose and nature of the physical problems to be analyzed, a general formulation and the various phenomenological methods of solution are discussed. This includes the calculation of observables based on assumed potentials such as local and non-local and their forms, e.g. Woods-Saxon, folded model etc. Also discussed are the various calculational methods and model codes employed to describe nuclear reactions in the spherical and deformed regions (e.g. coupled-channel analysis). An examination of the numerical solutions and minimization techniques associated with the various codes, is briefly touched upon. Several computer programs are described for carrying out the calculations. The preparation of input, (formats and options), determination of model parameters and analysis of output are described. The class is given a series of problems to carry out using the available computer. Interpretation and evaluation of the samples includes the effect of varying parameters, and comparison of calculations with the experimental data. Also included is an intercomparison of the results from the various model codes, along with their advantages and limitations. (author)
Bondarenko, V A; Mitrikas, V G
2007-01-01
The model of a geometrical human body phantom developed for calculating the shielding functions of representative points of the body organs and systems is similar to the anthropomorphic phantom. This form of phantom can be integrated with the shielding model of the ISS Russian orbital segment to make analysis of radiation loading of crewmembers in different compartments of the vehicle. Calculation of doses absorbed by the body systems in terms of the representative points makes it clear that doses essentially depend on the phantom spatial orientation (eye direction). It also enables the absorbed dose evaluation from the shielding functions as the mean of the representative points and phantom orientation.
Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna
2018-03-01
The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.
Shao, Chenxi; Liu, Qingqing; Wang, Tingting; Yin, Peifeng; Wang, Binghong
2013-09-01
Time series is widely exploited to study the innate character of the complex chaotic system. Existing chaotic models are weak in modeling accuracy because of adopting either error minimization strategy or an acceptable error to end the modeling process. Instead, interpolation can be very useful for solving differential equations with a small modeling error, but it is also very difficult to deal with arbitrary-dimensional series. In this paper, geometric theory is considered to reduce the modeling error, and a high-precision framework called Series-NonUniform Rational B-Spline (S-NURBS) model is developed to deal with arbitrary-dimensional series. The capability of the interpolation framework is proved in the validation part. Besides, we verify its reliability by interpolating Musa dataset. The main improvement of the proposed framework is that we are able to reduce the interpolation error by properly adjusting weights series step by step if more information is given. Meanwhile, these experiments also demonstrate that studying the physical system from a geometric perspective is feasible.
International Nuclear Information System (INIS)
Sutter, J.P.; Amboage, M.; Hayama, S.; Diaz-Moreno, S.
2010-01-01
The X-ray focusing properties of a bent single crystal diffracting in Bragg geometry are discussed. First, it is assumed that a polychromatic point source is focused to a point image. The elliptical arc that the crystal must trace and the aberrations caused by bending the crystal cylindrically are derived from the ray paths. For a source of finite size, the magnification is found to vary over the crystal's length, so that rays of different wavelength produce images of different size. More realistic treatments of penetration and diffraction are performed with spherical monochromatic incident waves, using Takagi-Taupin calculations to create the diffracted wave and the Fresnel integral to trace the diffracted wave's evolution. Such 'wave-optical' calculations on a symmetric Si (1 1 1) crystal with 7 keV X-rays predict beam sizes different from those found in ray traces. Optimal sample and detector placement therefore requires wave effects to be considered.
Directory of Open Access Journals (Sweden)
P. Ferracin
2000-12-01
Full Text Available Estimates of random field-shape errors induced by cable mispositioning in superconducting magnets are presented and specific applications to the Large Hadron Collider (LHC main dipoles and quadrupoles are extensively discussed. Numerical simulations obtained with Monte Carlo methods are compared to analytic estimates and are used to interpret the experimental data for the LHC dipole and quadrupole prototypes. The proposed approach can predict the effect of magnet tolerances on geometric components of random field-shape errors, and it is a useful tool to monitor the obtained tolerances during magnet production.
Neuro-fuzzy model for estimating race and gender from geometric distances of human face across pose
Nanaa, K.; Rahman, M. N. A.; Rizon, M.; Mohamad, F. S.; Mamat, M.
2018-03-01
Classifying human face based on race and gender is a vital process in face recognition. It contributes to an index database and eases 3D synthesis of the human face. Identifying race and gender based on intrinsic factor is problematic, which is more fitting to utilizing nonlinear model for estimating process. In this paper, we aim to estimate race and gender in varied head pose. For this purpose, we collect dataset from PICS and CAS-PEAL databases, detect the landmarks and rotate them to the frontal pose. After geometric distances are calculated, all of distance values will be normalized. Implementation is carried out by using Neural Network Model and Fuzzy Logic Model. These models are combined by using Adaptive Neuro-Fuzzy Model. The experimental results showed that the optimization of address fuzzy membership. Model gives a better assessment rate and found that estimating race contributing to a more accurate gender assessment.
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
International Nuclear Information System (INIS)
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V.
2010-01-01
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
International Nuclear Information System (INIS)
Song, William; Battista, Jerry; Van Dyk, Jake
2004-01-01
The convolution method can be used to model the effect of random geometric uncertainties into planned dose distributions used in radiation treatment planning. This is effectively done by linearly adding infinitesimally small doses, each with a particular geometric offset, over an assumed infinite number of fractions. However, this process inherently ignores the radiobiological dose-per-fraction effect since only the summed physical dose distribution is generated. The resultant potential error on predicted radiobiological outcome [quantified in this work with tumor control probability (TCP), equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and generalized equivalent uniform dose (gEUD)] has yet to be thoroughly quantified. In this work, the results of a Monte Carlo simulation of geometric displacements are compared to those of the convolution method for random geometric uncertainties of 0, 1, 2, 3, 4, and 5 mm (standard deviation). The α/β CTV ratios of 0.8, 1.5, 3, 5, and 10 Gy are used to represent the range of radiation responses for different tumors, whereas a single α/β OAR ratio of 3 Gy is used to represent all the organs at risk (OAR). The analysis is performed on a four-field prostate treatment plan of 18 MV x rays. The fraction numbers are varied from 1-50, with isoeffective adjustments of the corresponding dose-per-fractions to maintain a constant tumor control, using the linear-quadratic cell survival model. The average differences in TCP and EUD of the target, and in NTCP and gEUD of the OAR calculated from the convolution and Monte Carlo methods reduced asymptotically as the total fraction number increased, with the differences reaching negligible levels beyond the treatment fraction number of ≥20. The convolution method generally overestimates the radiobiological indices, as compared to the Monte Carlo method, for the target volume, and underestimates those for the OAR. These effects are interconnected and attributed
Energy Technology Data Exchange (ETDEWEB)
Wang, J. Y.; Chiang, M. H.; Sheu, R. J.; Liu, Y. W. H. [Inst. of Nuclear Engineering and Science, National Tsing Hua Univ., Hsinchu 30013, Taiwan (China)
2012-07-01
The fuel element of the High Temperature Engineering Test Reactor (HTTR) presents a doubly heterogeneous geometry, where tiny TRISO fuel particles dispersed in a graphite matrix form the fuel region of a cylindrical fuel rod, and a number of fuel rods together with moderator or reflector then constitute the lattice design of the core. In this study, a series of full-core HTTR criticality calculations were performed with the SCALE6 code system using various geometric and unit-cell options in order to systematically investigate their effects on neutronic analysis. Two geometric descriptions (ARRAY or HOLE) in SCALE6 can be used to construct a complicated and repeated model. The result shows that eliminating the use of HOLE in the HTTR geometric model can save the computation time by a factor of 4. Four unit-cell treatments for resonance self-shielding corrections in SCALE6 were tested to create problem-specific multigroup cross sections for the HTTR core model. Based on the same ENDF/B-VII cross-section library, their results were evaluated by comparing with continuous-energy calculations. The comparison indicates that the INFHOMMEDIUM result overestimates the system multiplication factor (k{sub eff}) by 55 mk, whereas the LATTICECELL and MULTIREGION treatments predict the k{sub eff} values with similar biases of approximately 10 mk overestimation. The DOUBLEHET result shows a more satisfactory agreement, about 4.2 mk underestimation in the k{sub eff} value. In addition, using cell-weighted cross sections instead of an explicit modeling of TRISO particles in fuel region can further reduce the computation time by a factor of 5 without sacrificing accuracy. (authors)
International Nuclear Information System (INIS)
Meng, Haining; Liu, Jianjun; Hei, Xinhong
2015-01-01
Software aging is characterized by an increasing failure rate, progressive performance degradation and even a sudden crash in a long-running software system. Software rejuvenation is an effective method to counteract software aging. A periodically inspected rejuvenation policy for software systems is studied. The consecutive inspection intervals are assumed to be a decreasing geometric sequence, and upon the inspection times of software system and its failure features, software rejuvenation or system recovery is performed. The system availability function and cost rate function are obtained, and the optimal inspection time and rejuvenation interval are both derived to maximize system availability and minimize cost rate. Then, boundary conditions of the optimal rejuvenation policy are deduced. Finally, the numeric experiment result shows the effectiveness of the proposed policy. Further compared with the existing software rejuvenation policy, the new policy has higher system availability. - Highlights: • A periodically inspected rejuvenation policy for software systems is studied. • A decreasing geometric sequence is used to denote the consecutive inspection intervals. • The optimal inspection times and rejuvenation interval are found. • The new policy is capable of reducing average cost and improving system availability
A Geometric Approach to CP Violation: Applications to the MCPMFV SUSY Model
Ellis, John; Pilaftsis, Apostolos
2010-01-01
We analyze the constraints imposed by experimental upper limits on electric dipole moments (EDMs) within the Maximally CP- and Minimally Flavour-Violating (MCPMFV) version of the MSSM. Since the MCPMFV scenario has 6 non-standard CP-violating phases, in addition to the CP-odd QCD vacuum phase \\theta_QCD, cancellations may occur among the CP-violating contributions to the three measured EDMs, those of the Thallium, neutron and Mercury, leaving open the possibility of relatively large values of the other CP-violating observables. We develop a novel geometric method that uses the small-phase approximation as a starting point, takes the existing EDM constraints into account, and enables us to find maximal values of other CP-violating observables, such as the EDMs of the Deuteron and muon, the CP-violating asymmetry in b --> s \\gamma decay, and the B_s mixing phase. We apply this geometric method to provide upper limits on these observables within specific benchmark supersymmetric scenarios, including extensions t...
On geometrized gravitation theories
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
Kachalo, Së ma; Naveed, Hammad; Cao, Youfang; Zhao, Jieling; Liang, Jie
2015-01-01
development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating
Directory of Open Access Journals (Sweden)
Ingrid Paine
2016-04-01
Full Text Available Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB, the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.
Anatomically accurate, finite model eye for optical modeling.
Liou, H L; Brennan, N A
1997-08-01
There is a need for a schematic eye that models vision accurately under various conditions such as refractive surgical procedures, contact lens and spectacle wear, and near vision. Here we propose a new model eye close to anatomical, biometric, and optical realities. This is a finite model with four aspheric refracting surfaces and a gradient-index lens. It has an equivalent power of 60.35 D and an axial length of 23.95 mm. The new model eye provides spherical aberration values within the limits of empirical results and predicts chromatic aberration for wavelengths between 380 and 750 nm. It provides a model for calculating optical transfer functions and predicting optical performance of the eye.
International Nuclear Information System (INIS)
Iliadis, Georgios; Misailidou, Despina; Selviaridis, Panagiotis; Chatzisotiriou, Athanasios; Kalogera-Fountzila, Anna; Fragkoulidi, Anna; Fountzilas, George; Baltas, Dimos; Tselis, Nikolaos; Zamboglou, Nikolaos
2009-01-01
Background and purpose: the importance of tumor volume as a prognostic factor in high-grade gliomas is highly controversial and there are numerous methods estimating this parameter. In this study, a computer-based application was used in order to assess tumor volume from hard copies and a survival analysis was conducted in order to evaluate the prognostic significance of preoperative volumetric data in patients harboring glioblastomas. Patients and methods: 50 patients suffering from glioblastoma were analyzed retrospectively. Tumor volume was determined by the various geometric models as well as by an own specialized software (Volumio). Age, performance status, type of excision, and tumor location were also included in the multivariate analysis. Results: the spheroid and rectangular models overestimated tumor volume, while the ellipsoid model offered the best approximation. Volume failed to attain any statistical significance in prognosis, while age and performance status confirmed their importance in progression-free and overall survival of patients. Conclusion: geometric models provide a rough approximation of tumor volume and should not be used, as accurate determination of size is of paramount importance in order to draw safe conclusions in oncology. Although the significance of volumetry was not disclosed, further studies are definitely required. (orig.)
Advanced modelling of optical coherence tomography systems
International Nuclear Information System (INIS)
Andersen, Peter E; Thrane, Lars; Yura, Harold T; Tycho, Andreas; Joergensen, Thomas M; Frosz, Michael H
2004-01-01
Analytical and numerical models for describing and understanding the light propagation in samples imaged by optical coherence tomography (OCT) systems are presented. An analytical model for calculating the OCT signal based on the extended Huygens-Fresnel principle valid both for the single and multiple scattering regimes is reviewed. An advanced Monte Carlo model for calculating the OCT signal is also reviewed, and the validity of this model is shown through a mathematical proof based on the extended Huygens-Fresnel principle. Moreover, for the first time the model is verified experimentally. From the analytical model, an algorithm for enhancing OCT images is developed; the so-called true-reflection algorithm in which the OCT signal may be corrected for the attenuation caused by scattering. For the first time, the algorithm is demonstrated by using the Monte Carlo model as a numerical tissue phantom. Such algorithm holds promise for improving OCT imagery and to extend the possibility for functional imaging
A Thermo-Optic Propagation Modeling Capability.
Energy Technology Data Exchange (ETDEWEB)
Schrader, Karl; Akau, Ron
2014-10-01
A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developed for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.
Optical Imaging and Radiometric Modeling and Simulation
Ha, Kong Q.; Fitzmaurice, Michael W.; Moiser, Gary E.; Howard, Joseph M.; Le, Chi M.
2010-01-01
OPTOOL software is a general-purpose optical systems analysis tool that was developed to offer a solution to problems associated with computational programs written for the James Webb Space Telescope optical system. It integrates existing routines into coherent processes, and provides a structure with reusable capabilities that allow additional processes to be quickly developed and integrated. It has an extensive graphical user interface, which makes the tool more intuitive and friendly. OPTOOL is implemented using MATLAB with a Fourier optics-based approach for point spread function (PSF) calculations. It features parametric and Monte Carlo simulation capabilities, and uses a direct integration calculation to permit high spatial sampling of the PSF. Exit pupil optical path difference (OPD) maps can be generated using combinations of Zernike polynomials or shaped power spectral densities. The graphical user interface allows rapid creation of arbitrary pupil geometries, and entry of all other modeling parameters to support basic imaging and radiometric analyses. OPTOOL provides the capability to generate wavefront-error (WFE) maps for arbitrary grid sizes. These maps are 2D arrays containing digital sampled versions of functions ranging from Zernike polynomials to combination of sinusoidal wave functions in 2D, to functions generated from a spatial frequency power spectral distribution (PSD). It also can generate optical transfer functions (OTFs), which are incorporated into the PSF calculation. The user can specify radiometrics for the target and sky background, and key performance parameters for the instrument s focal plane array (FPA). This radiometric and detector model setup is fairly extensive, and includes parameters such as zodiacal background, thermal emission noise, read noise, and dark current. The setup also includes target spectral energy distribution as a function of wavelength for polychromatic sources, detector pixel size, and the FPA s charge
Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics
Directory of Open Access Journals (Sweden)
Antonia M. Frassino
2016-05-01
Full Text Available Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N-portrait beyond the semi-classical limit. We show that for a generic N this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.
Lower Bounds for Sorted Geometric Queries in the I/O Model
DEFF Research Database (Denmark)
Afshani, Peyman; Zeh, Norbert
2012-01-01
. This is highly relevant in an I/O context because storing a massive data set in a superlinear-space data structure is often infeasible. We also prove that answering queries using I/Os requires space, where N is the input size, B is the block size, and M is the size of the main memory. This bound is unlikely...... to be optimal and in fact we can show that, for a particular class of “persistence-based” data structures, the space lower bound can be improved to Ω(N2 / MO(1)). Both these lower bounds are a first step towards understanding the complexity of sorted geometric query problems. All our lower bounds assume...
1998-01-01
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Martin-Rojas, Ivan; Alfaro, Pedro; Estévez, Antonio
2014-05-01
We present a study that encompasses several software tools (iGIS©, ArcGIS©, Autocad©, etc.) and data (geological mapping, high resolution digital topographic data, high resolution aerial photographs, etc.) to create a detailed 3D geometric model of an active fault propagation growth fold. This 3D model clearly shows structural features of the analysed fold, as well as growth relationships and sedimentary patterns. The results obtained permit us to discuss the kinematics and structural evolution of the fold and the fault in time and space. The study fault propagation fold is the Crevillente syncline. This fold represents the northern limit of the Bajo Segura Basin, an intermontane basin in the Eastern Betic Cordillera (SE Spain) developed from upper Miocene on. 3D features of the Crevillente syncline, including growth pattern, indicate that limb rotation and, consequently, fault activity was higher during Messinian than during Tortonian; consequently, fault activity was also higher. From Pliocene on our data point that limb rotation and fault activity steadies or probably decreases. This in time evolution of the Crevillente syncline is not the same all along the structure; actually the 3D geometric model indicates that observed lateral heterogeneity is related to along strike variation of fault displacement.
Mao, Yujiang; Song, Jie; Wei, Jie; Wang, Manyi
2010-01-01
Unrecognized joint penetration (UJP) by screw penetration through the articular surface undetectable on routine anteroposterior (AP) and lateral radiographs can cause serious complications. We have developed a geometric model to analyze UJP, and methods for the prevention of the problem. A Steinmetz Solid (SS) is the overlapping portion between two identical, vertically intersecting cylinders. The AP and lateral radiographs of a femoral head (simplified as a sphere) are projections of two cylinder-shaped images. A screw that appears to be within the femoral head in fact only lies within the cylinder. A screw apparently within the femoral head on both AP and lateral images is only confined to the SS generated by two cylinders, but not necessarily confined to the femoral head itself. We have therefore analyzed UJP using a geometric model based on SS. The geometric basis of UJP lies in the fact that the SS is larger than the sphere (femoral head) with a volume ratio of 4: π. The theoretical risk of UJP for any screw therefore can be as high as 21.5% ((4-π)/4). In reality, screws are always carefully placed to ensure a distance between the screw's tip and the edge of femoral head (tip-to-edge distance, or TED). This TED effectively lowers the risk of UJP by reducing the size of the screw-confining SS. When the SS entirely fits into (internally tangential to) the femoral head, the risk of UJP approaches zero. A TED fulfilling this requirement can be regarded as safe (approximately 0.29 x femoral head radius). With a femoral head diameter of 5 cm, the safe TED is approximately 7 mm.
Green Network Planning Model for Optical Backbones
DEFF Research Database (Denmark)
Gutierrez Lopez, Jose Manuel; Riaz, M. Tahir; Jensen, Michael
2010-01-01
on the environment in general. In network planning there are existing planning models focused on QoS provisioning, investment minimization or combinations of both and other parameters. But there is a lack of a model for designing green optical backbones. This paper presents novel ideas to be able to define......Communication networks are becoming more essential for our daily lives and critically important for industry and governments. The intense growth in the backbone traffic implies an increment of the power demands of the transmission systems. This power usage might have a significant negative effect...
Directory of Open Access Journals (Sweden)
Xuan Yang
2015-01-01
Full Text Available This paper presents a geometric least square framework for deriving [0,1]-valued interval weights from interval fuzzy preference relations. By analyzing the relationship among [0,1]-valued interval weights, multiplicatively consistent interval judgments, and planes, a geometric least square model is developed to derive a normalized [0,1]-valued interval weight vector from an interval fuzzy preference relation. Based on the difference ratio between two interval fuzzy preference relations, a geometric average difference ratio between one interval fuzzy preference relation and the others is defined and employed to determine the relative importance weights for individual interval fuzzy preference relations. A geometric least square based approach is further put forward for solving group decision making problems. An individual decision numerical example and a group decision making problem with the selection of enterprise resource planning software products are furnished to illustrate the effectiveness and applicability of the proposed models.
Isik, Hakan
This study is premised on the fact that student conceptions of optics appear to be unrelated to student characteristics of gender, age, years since high school graduation, or previous academic experiences. This study investigated the relationships between student characteristics and student performance on image formation test items and the changes in student conceptions of optics after an introductory inquiry-based physics course. Data was collected from 39 college students who were involved in an inquiry-based physics course teaching topics of geometrical optics. Student data concerning characteristics and previous experiences with optics and mathematics were collected. Assessment of student understanding of optics knowledge for pinholes, plane mirrors, refraction, and convex lenses was collected with, the Test of Image Formation with Light-Ray Tracing instrument. Total scale and subscale scores representing the optics instrument content were derived from student pretest and posttest responses. The types of knowledge, needed to answer each optics item correctly, were categorized as situational, conceptual, procedural, and strategic knowledge. These types of knowledge were associated with student correct and incorrect responses to each item to explain the existences and changes in student scientific and naive conceptions. Correlation and stepwise multiple regression analyses were conducted to identify the student characteristics and academic experiences that significantly predicted scores on the subscales of the test. The results showed that student experience with calculus was a significant predictor of student performance on the total scale as well as on the refraction subscale of the Test of Image Formation with Light-Ray Tracing. A combination of student age and previous academic experience with precalculus was a significant predictor of student performance on the pretest pinhole subscale. Student characteristic of years since high school graduation
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
Directory of Open Access Journals (Sweden)
Rozilene Maria Cota Aroeira
2017-05-01
Full Text Available Abstract Introduction: Biomedical studies involve complex anatomical structures, which require specific methodology to generate their geometric models. The middle segment of the thoracic spine (T5-T10 is the site of the highest incidence of vertebral deformity in adolescents. Traditionally, its geometries are derived from computed tomography or magnetic resonance imaging data. However, this approach may restrict certain studies. The study aimed to generate two 3D geometric model of the T5-T10 thoracic spine segment, obtained from graphical images, and to create mesh for finite element studies. Methods A 3D geometric model of T5-T10 was generated using two anatomical images of T6 vertebra (side and top. The geometric model was created in Autodesk® Maya® 3D 2013, and the mesh process in HiperMesh and MeshMixer (v11.0.544 Autodesk. Results The T5-T10 thoracic segment model is presented with its passive components, bones, intervertebral discs and flavum, intertransverse and supraspinous ligaments, in different views, as well as the volumetric mesh. Conclusion The 3D geometric model generated from graphical images is suitable for application in non-patient-specific finite element model studies or, with restrictions, in the use of computed tomography or magnetic resonance imaging. This model may be useful for biomechanical studies related to the middle thoracic spine, the most vulnerable site for vertebral deformations.
Kokkalis, P.; Papayannis, A.; Amiridis, V.; Mamouri, R. E.; Veselovskii, I.; Kolgotin, A.; Tsaknakis, G.; Kristiansen, N. I.; Stohl, A.; Mona, L.
2013-09-01
Vertical profiles of the optical (extinction and backscatter coefficients, lidar ratio and Ångström exponent), microphysical (mean effective radius, mean refractive index, mean number concentration) and geometrical properties as well as the mass concentration of volcanic particles from the Eyjafjallajökull eruption were retrieved at selected heights over Athens, Greece, using multi-wavelength Raman lidar measurements performed during the period 21-24 April 2010. Aerosol Robotic Network (AERONET) particulate columnar measurements along with inversion schemes were initialized together with lidar observations to deliver the aforementioned products. The well-known FLEXPART (FLEXible PARTicle dispersion model) model used for volcanic dispersion simulations is initiated as well in order to estimate the horizontal and vertical distribution of volcanic particles. Compared with the lidar measurements within the planetary boundary layer over Athens, FLEXPART proved to be a useful tool for determining the state of mixing of ash with other, locally emitted aerosol types. The major findings presented in our work concern the identification of volcanic particles layers in the form of filaments after 7-day transport from the volcanic source (approximately 4000 km away from our site) from the surface and up to 10 km according to the lidar measurements. Mean hourly averaged lidar signals indicated that the layer thickness of volcanic particles ranged between 1.5 and 2.2 km. The corresponding aerosol optical depth was found to vary from 0.01 to 0.18 at 355 nm and from 0.02 up to 0.17 at 532 nm. Furthermore, the corresponding lidar ratios (S) ranged between 60 and 80 sr at 355 nm and 44 and 88 sr at 532 nm. The mean effective radius of the volcanic particles estimated by applying inversion scheme to the lidar data found to vary within the range 0.13-0.38 μm and the refractive index ranged from 1.39+0.009i to 1.48+0.006i. This high variability is most probably attributed to the
Modeling heading and path perception from optic flow in the case of independently moving objects
Raudies, Florian; Neumann, Heiko
2013-01-01
Humans are usually accurate when estimating heading or path from optic flow, even in the presence of independently moving objects (IMOs) in an otherwise rigid scene. To invoke significant biases in perceived heading, IMOs have to be large and obscure the focus of expansion (FOE) in the image plane, which is the point of approach. For the estimation of path during curvilinear self-motion no significant biases were found in the presence of IMOs. What makes humans robust in their estimation of heading or path using optic flow? We derive analytical models of optic flow for linear and curvilinear self-motion using geometric scene models. Heading biases of a linear least squares method, which builds upon these analytical models, are large, larger than those reported for humans. This motivated us to study segmentation cues that are available from optic flow. We derive models of accretion/deletion, expansion/contraction, acceleration/deceleration, local spatial curvature, and local temporal curvature, to be used as cues to segment an IMO from the background. Integrating these segmentation cues into our method of estimating heading or path now explains human psychophysical data and extends, as well as unifies, previous investigations. Our analysis suggests that various cues available from optic flow help to segment IMOs and, thus, make humans' heading and path perception robust in the presence of such IMOs. PMID:23554589
Modeling Heading and Path Perception from Optic Flow in the Case of Independently Moving Objects
Directory of Open Access Journals (Sweden)
Florian eRaudies
2013-04-01
Full Text Available Humans are usually accurate when estimating heading or path from optic flow, even in the presence of independently moving objects (IMO in an otherwise rigid scene. To invoke significant biases in perceived heading, IMOs have to be large and obscure the focus of expansion (FOE in the image plane, which is the point of approach. For the estimation of path during curvilinear self-motion no significant biases were found in the presence of IMOs. What makes humans robust in their estimation of heading or path using optic flow? We derive analytical models of optic flow for linear and curvilinear self-motion using geometric scene models. Heading biases of a linear least squares method, which builds upon these analytical models, are large, larger than those reported for humans. This motivated us to study segmentation cues that are available from optic flow. We derive models of accretion / deletion, expansion / contraction, acceleration / deceleration, local spatial curvature, and local temporal curvature, to be used as cues to segment an IMO from the background. Integrating these segmentation cues into our method of estimating heading or path now explains human psychophysical data and extends, as well as unifies, previous investigations. Our analysis suggests that various cues available from optic flow help to segment IMOs and, thus, make humans’ heading and path perception robust in the presence of such IMOs.
International Nuclear Information System (INIS)
Kotevski, Darko
2008-01-01
This paper is a resume of the master thesis made within my master studies at the Department for transmission and distribution systems at FEIT-Skopje. New methodology is presented for estimation of the rates of lightning strikes on power lines and substations with Monte Carlo simulation. Modeling is based on well known electro geometric model which states that protection zones of lightning protection devices are dependant with amplitude of the lighting current. Therefore, for a known configuration it is possible with application of simple numerical methods to evaluate efficiency of the protection devices. Data gained from the simulations can be used to design such devices, to correct existing lightning protection systems or to make analysis for improving reliability of power system elements in lightning incidence. (Author)
International Nuclear Information System (INIS)
Kotevski, Darko
2008-01-01
This paper is a resume of the master thesis made within my master studies at the Department for transmission and distribution systems at FEIT-Skopje. New methodology is presented for estimation of the rates of lightning strikes on power lines and substations with Monte Carlo simulation. Modeling is based on well known electro geometric model which states that protection zones of lightning protection devices are dependant with amplitude of the lighting current. Therefore, for a known configuration it is possible with application of simple numerical methods to evaluate efficiency of the protection devices. Data gained from the simulations can be used to design such devices, to correct existing lightning protection systems or to make analysis for improving reliability of power system elements in lightning incidence. (Author
Espinosa Moreno, Andres Santiago; Duque Daza, Carlos Alberto
2017-11-01
The effects of variation of two geometric parameters, such as bifurcation angle and carina rounding radius, during the respiratory inhalation process, are studied numerically using two synthetic models of lower human airways. Laminar flow simulations were performed for six angles and three rounding radius, for 500, 1000, 1500 and 2000 for Reynolds numbers. Numerical results showed the existence of a direct relationship between the deformation of the velocity profiles (effect produced by the bifurcation) and the vortical structures observed through the secondary flow patterns. It is observed that the location of the vortices (and their related saddle point) is associated with the displacement of the velocity peak. On the other hand, increasing the angle and the rounding radius seems to bring about a growth of the pressure drop, which in turn displaces the distribution and peaks of the maximum shear stresses of the carina, that is, of the bifurcation point. Some physiological effects associated with the phenomena produced by these geometric variations are also discussed.
International Nuclear Information System (INIS)
Craig, Tim; Battista, Jerry; Van Dyk, Jake
2003-01-01
Convolution methods have been used to model the effect of geometric uncertainties on dose delivery in radiation therapy. Convolution assumes shift invariance of the dose distribution. Internal inhomogeneities and surface curvature lead to violations of this assumption. The magnitude of the error resulting from violation of shift invariance is not well documented. This issue is addressed by comparing dose distributions calculated using the Convolution method with dose distributions obtained by Direct Simulation. A comparison of conventional Static dose distributions was also made with Direct Simulation. This analysis was performed for phantom geometries and several clinical tumor sites. A modification to the Convolution method to correct for some of the inherent errors is proposed and tested using example phantoms and patients. We refer to this modified method as the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over different beam arrangements in the various phantom examples) was 21% with the Static dose calculation, 9% with Convolution, and reduced to 5% with the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over four clinical examples) was 9% for the Static method, 13% for Convolution, and 3% for Corrected Convolution. While Convolution can provide a superior estimate of the dose delivered when geometric uncertainties are present, the violation of shift invariance can result in substantial errors near the surface of the patient. The proposed Corrected Convolution modification reduces errors near the surface to 3% or less
Hourdakis, E.; Casanova, A.; Larrieu, G.; Nassiopoulou, A. G.
2018-05-01
Three-dimensional (3D) Si surface nanostructuring is interesting towards increasing the capacitance density of a metal-oxidesemiconductor (MOS) capacitor, while keeping reduced footprint for miniaturization. Si nanowires (SiNWs) can be used in this respect. With the aim of understanding the electrical versus geometrical characteristics of such capacitors, we fabricated and studied a MOS capacitor with highly ordered arrays of vertical Si nanowires of different lengths and thermal silicon oxide dielectric, in comparison to similar flat MOS capacitors. The high homogeneity and ordering of the SiNWs allowed the determination of the single SiNW capacitance and intrinsic series resistance, as well as other electrical characteristics (density of interface states, flat-band voltage and leakage current) in relation to the geometrical characteristics of the SiNWs. The SiNW capacitors demonstrated increased capacitance density compared to the flat case, while maintaining a cutoff frequency above 1 MHz, much higher than in other reports in the literature. Finally, our model system has been shown to constitute an excellent platform for the study of SiNW capacitors with either grown or deposited dielectrics, as for example high-k dielectrics for further increasing the capacitance density. This will be the subject of future work.
Optical Model and Cross Section Uncertainties
Energy Technology Data Exchange (ETDEWEB)
Herman,M.W.; Pigni, M.T.; Dietrich, F.S.; Oblozinsky, P.
2009-10-05
Distinct minima and maxima in the neutron total cross section uncertainties were observed in model calculations using spherical optical potential. We found this oscillating structure to be a general feature of quantum mechanical wave scattering. Specifically, we analyzed neutron interaction with 56Fe from 1 keV up to 65 MeV, and investigated physical origin of the minima.We discuss their potential importance for practical applications as well as the implications for the uncertainties in total and absorption cross sections.
The forward tracking, an optical model method
Benayoun, M
2002-01-01
This Note describes the so-called Forward Tracking, and the underlying optical model, developed in the context of LHCb-Light studies. Starting from Velo tracks, cheated or found by real pattern recognition, the tracks are found in the ST1-3 chambers after the magnet. The main ingredient to the method is a parameterisation of the track in the ST1-3 region, based on the Velo track parameters and an X seed in one ST station. Performance with the LHCb-Minus and LHCb-Light setups is given.
Optical model representation of coupled channel effects
International Nuclear Information System (INIS)
Wall, N.S.; Cowley, A.A.; Johnson, R.C.; Kobas, A.M.
1977-01-01
A modification to the usual 6-parameter Woods-Saxon parameterization of the optical model for the scattering of composite particles is proposed. This additional real term reflects the effect of coupling other channels to the elastic scattering. The analyses favor a repulsive interaction for this term, especially for alpha particles. It is found that the repulsive term when combined with a Woods-Saxon term yields potentials with central values and volume integrals similar to those found by uncoupled elastic scattering calculations. These values are V(r = 0) approximately equal to 125 MeV and J/4A approximately equal to 300 MeV-fm 3
Optical modeling and simulation of thin-film photovoltaic devices
Krc, Janez
2013-01-01
In wafer-based and thin-film photovoltaic (PV) devices, the management of light is a crucial aspect of optimization since trapping sunlight in active parts of PV devices is essential for efficient energy conversions. Optical modeling and simulation enable efficient analysis and optimization of the optical situation in optoelectronic and PV devices. Optical Modeling and Simulation of Thin-Film Photovoltaic Devices provides readers with a thorough guide to performing optical modeling and simulations of thin-film solar cells and PV modules. It offers insight on examples of existing optical models
Directory of Open Access Journals (Sweden)
Alexander C. Ø. Jensen
2018-04-01
Full Text Available Models are increasingly used to estimate and pre-emptively calculate the occupational exposure of airborne released particulate matter. Typical two-box models assume instant and fully mixed air volumes, which can potentially cause issues in cases with fast processes, slow air mixing, and/or large volumes. In this study, we present an aerosol dispersion model and validate it by comparing the modelled concentrations with concentrations measured during chamber experiments. We investigated whether a better estimation of concentrations was possible by using different geometrical layouts rather than a typical two-box layout. A one-box, two-box, and two three-box layouts were used. The one box model was found to underestimate the concentrations close to the source, while overestimating the concentrations in the far field. The two-box model layout performed well based on comparisons from the chamber study in systems with a steady source concentration for both slow and fast mixing. The three-box layout was found to better estimate the concentrations and the timing of the peaks for fluctuating concentrations than the one-box or two-box layouts under relatively slow mixing conditions. This finding suggests that industry-relevant scaled volumes should be tested in practice to gain more knowledge about when to use the two-box or the three-box layout schemes for multi-box models.
Stress Measurement by Geometrical Optics
Robinson, R. S.; Rossnagel, S. M.
1986-01-01
Fast, simple technique measures stresses in thin films. Sample disk bowed by stress into approximately spherical shape. Reflected image of disk magnified by amount related to curvature and, therefore, stress. Method requires sample substrate, such as cheap microscope cover slide, two mirrors, laser light beam, and screen.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-01-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-06-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Bi, Lei; Yang, Ping
2016-07-01
The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles.
Stage-structured matrix models for organisms with non-geometric development times
Andrew Birt; Richard M. Feldman; David M. Cairns; Robert N. Coulson; Maria Tchakerian; Weimin Xi; James M. Guldin
2009-01-01
Matrix models have been used to model population growth of organisms for many decades. They are popular because of both their conceptual simplicity and their computational efficiency. For some types of organisms they are relatively accurate in predicting population growth; however, for others the matrix approach does not adequately model...
On the structure of the space of geometric product-form models
Bayer, Nimrod; Boucherie, Richardus J.
2002-01-01
This article deals with Markovian models defined on a finite-dimensional discrete state space and possess a stationary state distribution of a product-form. We view the space of such models as a mathematical object and explore its structure. We focus on models on an orthant [script Z]+n, which are
Helicopter Rotor Load Prediction Using a Geometrically Exact Beam with Multicomponent Model
DEFF Research Database (Denmark)
Lee, Hyun-Ku; Viswamurthy, S.R.; Park, Sang Chul
2010-01-01
In this paper, an accurate structural dynamic analysis was developed for a helicopter rotor system including rotor control components, which was coupled to various aerodynamic and wake models in order to predict an aeroelastic response and the loads acting on the rotor. Its blade analysis was based...... rotor-blade/control-system model was loosely coupled with various inflow and wake models in order to simulate both hover and forward-flight conditions. The resulting rotor blade response and pitch link loads are in good agreement with those predicted byCAMRADII. The present analysis features both model...... on an intrinsic formulation of moving beams implemented in the time domain. The rotor control system was modeled as a combination of rigid and elastic components. A multicomponent analysis was then developed by coupling the beam finite element model with the rotor control system model to obtain a complete rotor-blade/control...
A simple model for fibre optics: planar dielectric waveguides in rotation
International Nuclear Information System (INIS)
Perez-Ocon, F; Pena, A; Jimenez, J R; Diaz, J A
2006-01-01
In planar dielectric waveguides, there is only one type of propagated ray: the one that crosses the waveguide axis after each total internal reflection. According to the model of geometrical optics, there are two types of guided ray in fibre optics: meridional and skew. Each one is formulated by a suitable mathematical treatment. In this work, we demonstrate that the complex mathematical treatment for the skew rays can be avoided by considering a planar waveguide (with the same refractive index profile as the fibre and thickness equal to its diameter) that rotates around the direction of the axis with angular velocity ω. A section of this fibre is inscribed in the hypothetical slab. This model has been successfully introduced to students of engineering and physics
International Nuclear Information System (INIS)
Chang Yiren; Hsu Long; Chi Sien
2006-01-01
Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system
On equivalent radius of curvature for PWL geometrical modeling a loop antenna
CSIR Research Space (South Africa)
Lysko, AA
2012-11-01
Full Text Available A circular loop antenna is often numerically modeled using a regular polygon. This approach is simple and robust, yet it alters the circumference of the loop and may thus shift the resonance frequency in the numerical model. This letter introduces a...
International Nuclear Information System (INIS)
Kim Il Gon; Lee, Seong Su; Jang, Gi Wan
2012-07-01
This book indicates physical optics with properties and transmission of light, mathematical expression of wave like harmonic wave and cylindrical wave, electromagnetic theory and light, transmission of light with Fermat principle and Fresnel equation, geometrical optics I, geometrical optics II, optical instrument such as stops, glasses and camera, polarized light like double refraction by polarized light, interference, interference by multiple reflections, diffraction, solid optics, crystal optics such as Faraday rotation and Kerr effect and measurement of light. Each chapter has an exercise.
Energy Technology Data Exchange (ETDEWEB)
Kim Il Gon; Lee, Seong Su; Jang, Gi Wan
2012-07-15
This book indicates physical optics with properties and transmission of light, mathematical expression of wave like harmonic wave and cylindrical wave, electromagnetic theory and light, transmission of light with Fermat principle and Fresnel equation, geometrical optics I, geometrical optics II, optical instrument such as stops, glasses and camera, polarized light like double refraction by polarized light, interference, interference by multiple reflections, diffraction, solid optics, crystal optics such as Faraday rotation and Kerr effect and measurement of light. Each chapter has an exercise.
Patient specific dynamic geometric models from sequential volumetric time series image data.
Cameron, B M; Robb, R A
2004-01-01
Generating patient specific dynamic models is complicated by the complexity of the motion intrinsic and extrinsic to the anatomic structures being modeled. Using a physics-based sequentially deforming algorithm, an anatomically accurate dynamic four-dimensional model can be created from a sequence of 3-D volumetric time series data sets. While such algorithms may accurately track the cyclic non-linear motion of the heart, they generally fail to accurately track extrinsic structural and non-cyclic motion. To accurately model these motions, we have modified a physics-based deformation algorithm to use a meta-surface defining the temporal and spatial maxima of the anatomic structure as the base reference surface. A mass-spring physics-based deformable model, which can expand or shrink with the local intrinsic motion, is applied to the metasurface, deforming this base reference surface to the volumetric data at each time point. As the meta-surface encompasses the temporal maxima of the structure, any extrinsic motion is inherently encoded into the base reference surface and allows the computation of the time point surfaces to be performed in parallel. The resultant 4-D model can be interactively transformed and viewed from different angles, showing the spatial and temporal motion of the anatomic structure. Using texture maps and per-vertex coloring, additional data such as physiological and/or biomechanical variables (e.g., mapping electrical activation sequences onto contracting myocardial surfaces) can be associated with the dynamic model, producing a 5-D model. For acquisition systems that may capture only limited time series data (e.g., only images at end-diastole/end-systole or inhalation/exhalation), this algorithm can provide useful interpolated surfaces between the time points. Such models help minimize the number of time points required to usefully depict the motion of anatomic structures for quantitative assessment of regional dynamics.
Wang, Zhen-yu; Yu, Jian-cheng; Zhang, Ai-qun; Wang, Ya-xing; Zhao, Wen-tao
2017-12-01
Combining high precision numerical analysis methods with optimization algorithms to make a systematic exploration of a design space has become an important topic in the modern design methods. During the design process of an underwater glider's flying-wing structure, a surrogate model is introduced to decrease the computation time for a high precision analysis. By these means, the contradiction between precision and efficiency is solved effectively. Based on the parametric geometry modeling, mesh generation and computational fluid dynamics analysis, a surrogate model is constructed by adopting the design of experiment (DOE) theory to solve the multi-objects design optimization problem of the underwater glider. The procedure of a surrogate model construction is presented, and the Gaussian kernel function is specifically discussed. The Particle Swarm Optimization (PSO) algorithm is applied to hydrodynamic design optimization. The hydrodynamic performance of the optimized flying-wing structure underwater glider increases by 9.1%.
Directory of Open Access Journals (Sweden)
Nita H. SHAH
2010-07-01
Full Text Available This paper deals with the rigorous photogrammetric solution to model the uncertainty in the orientation parameters of Indian Remote Sensing Satellite IRS-P5 (Cartosat-1. Cartosat-1 is a three axis stabilized spacecraft launched into polar sun-synchronous circular orbit at an altitude of 618 km. The satellite has two panchromatic (PAN cameras with nominal resolution of ~2.5 m. The camera looking ahead is called FORE mounted with +26 deg angle and the other looking near nadir is called AFT mounted with -5 deg, in along track direction. Data Product Generation Software (DPGS system uses the rigorous photogrammetric Collinearity model in order to utilize the full system information, together with payload geometry & control points, for estimating the uncertainty in attitude parameters. The initial orbit, attitude knowledge is obtained from GPS bound orbit measurement, star tracker and gyros. The variations in satellite attitude with time are modelled using simple linear polynomial model. Also, based on this model, Kalman filter approach is studied and applied to improve the uncertainty in the orientation of spacecraft with high quality ground control points (GCPs. The sequential estimator (Kalman filter is used in an iterative process which corrects the parameters at each time of observation rather than at epoch time. Results are presented for three stereo data sets. The accuracy of model depends on the accuracy of the control points.
Energy Technology Data Exchange (ETDEWEB)
Dolly, S; Chen, H; Mutic, S; Anastasio, M; Li, H [Washington University School of Medicine, Saint Louis, MO (United States)
2016-06-15
Purpose: A persistent challenge for the quality assessment of radiation therapy treatments (e.g. contouring accuracy) is the absence of the known, ground truth for patient data. Moreover, assessment results are often patient-dependent. Computer simulation studies utilizing numerical phantoms can be performed for quality assessment with a known ground truth. However, previously reported numerical phantoms do not include the statistical properties of inter-patient variations, as their models are based on only one patient. In addition, these models do not incorporate tumor data. In this study, a methodology was developed for generating numerical phantoms which encapsulate the statistical variations of patients within radiation therapy, including tumors. Methods: Based on previous work in contouring assessment, geometric attribute distribution (GAD) models were employed to model both the deterministic and stochastic properties of individual organs via principle component analysis. Using pre-existing radiation therapy contour data, the GAD models are trained to model the shape and centroid distributions of each organ. Then, organs with different shapes and positions can be generated by assigning statistically sound weights to the GAD model parameters. Organ contour data from 20 retrospective prostate patient cases were manually extracted and utilized to train the GAD models. As a demonstration, computer-simulated CT images of generated numerical phantoms were calculated and assessed subjectively and objectively for realism. Results: A cohort of numerical phantoms of the male human pelvis was generated. CT images were deemed realistic both subjectively and objectively in terms of image noise power spectrum. Conclusion: A methodology has been developed to generate realistic numerical anthropomorphic phantoms using pre-existing radiation therapy data. The GAD models guarantee that generated organs span the statistical distribution of observed radiation therapy patients
International Nuclear Information System (INIS)
Dolly, S; Chen, H; Mutic, S; Anastasio, M; Li, H
2016-01-01
Purpose: A persistent challenge for the quality assessment of radiation therapy treatments (e.g. contouring accuracy) is the absence of the known, ground truth for patient data. Moreover, assessment results are often patient-dependent. Computer simulation studies utilizing numerical phantoms can be performed for quality assessment with a known ground truth. However, previously reported numerical phantoms do not include the statistical properties of inter-patient variations, as their models are based on only one patient. In addition, these models do not incorporate tumor data. In this study, a methodology was developed for generating numerical phantoms which encapsulate the statistical variations of patients within radiation therapy, including tumors. Methods: Based on previous work in contouring assessment, geometric attribute distribution (GAD) models were employed to model both the deterministic and stochastic properties of individual organs via principle component analysis. Using pre-existing radiation therapy contour data, the GAD models are trained to model the shape and centroid distributions of each organ. Then, organs with different shapes and positions can be generated by assigning statistically sound weights to the GAD model parameters. Organ contour data from 20 retrospective prostate patient cases were manually extracted and utilized to train the GAD models. As a demonstration, computer-simulated CT images of generated numerical phantoms were calculated and assessed subjectively and objectively for realism. Results: A cohort of numerical phantoms of the male human pelvis was generated. CT images were deemed realistic both subjectively and objectively in terms of image noise power spectrum. Conclusion: A methodology has been developed to generate realistic numerical anthropomorphic phantoms using pre-existing radiation therapy data. The GAD models guarantee that generated organs span the statistical distribution of observed radiation therapy patients