A library for computing the filtered and non-filtered 3D Green's tensor associated with infinite homogeneous space and surfaces

We describe a library to compute various types of Green's tensor for three-dimensional electromagnetic scattering calculations. This library includes the retarded and non-retarded (quasi-static) Green's tensors for infinite homogeneous space and the non-retarded Green's tensor associated with a surface. Both standard and filtered Green's tensor can be computed. Filtered Green's tensor can be used to accurately investigate high permittivity scatterers with the coupled-dipole approximation.     

Scattering of electromagnetic radiation by a multilayered sphere

The computer implementation of the algorithm for the calculation of electromagnetic radiation scattering by a multilayered sphere developed by Yang, is presented. It has been shown that the program is effective, resulting in very accurate values of scattering efficiencies for a wide range of size parameters, which is a considerable improvement over previous implementations of similar algorithms. The program, named scattnlay, would be the first of its kind to be publicly available.

Program summary

Program title: scattnlayCatalogue identifier: AEEY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEY_1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Gnu General Public License (GPL)No. of lines in distributed program, including test data, etc.: 8932No. of bytes in distributed program, including test data, etc.: 175 276Distribution format: tar.gzProgramming language: ANSI CComputer: Any with a C compilerOperating system: Linux (any), Windows, SolarisRAM: ∼1-100 MBClassification: 1.3Nature of problem: The scattering of electromagnetic (EM) radiation by a multilayered sphere is an interesting phenomenon to study for the application of such materials in several fields. Just to mention two examples, metal nanoshells (a dielectric core surrounded by a metallic shell) are a class of nanoparticles with tunable optical resonances that can be used, among others, in medicine for optical imaging and photothermal cancer therapy; while in the field of atmospheric sciences, light absorption by aerosols has a heating effect in the atmosphere that is of great interest to study several climatic effects. Although at first glance the expressions of the scattering coefficients seem simple and straightforward to implement, they involve several numerical difficulties which make most of the existent algorithms inapplicable to several extreme cases. More recently, Yang [1] has developed an improved recursive algorithm that circumvents most of the numerical problems present in previous algorithms, which is implemented in the current program.Solution method: Calculations of Mie scattering coefficients and efficiency factors for a multilayered sphere as described by Yang [1], combined with standard solutions of the scattering amplitude functions.Restrictions: Single scattering, permeability of the layers is always unity.Running time: Seconds to minutesReferences:

[1]

W. Yang, Appl. Opt. 42 (2003) 1710-1720.

     

Photofragment image analysis using the Onion-Peeling Algorithm

With the growing popularity of the velocity map imaging technique, a need for the analysis of photoion and photoelectron images arose. Here, a computer program is presented that allows for the analysis of cylindrically symmetric images. It permits the inversion of the projection of the 3D charged particle distribution using the Onion Peeling Algorithm. Further analysis includes the determination of radial and angular distributions, from which velocity distributions and spatial anisotropy parameters are obtained. Identification and quantification of the different photolysis channels is therefore straightforward. In addition, the program features geometry correction, centering, and multi-Gaussian fitting routines, as well as a user-friendly graphical interface and the possibility of generating synthetic images using either the fitted or user-defined parameters.

Program summary

Title of program: Glass OnionCatalogue identifier: ADRYProgram Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADRYProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer: IBM PCOperating system under which the program has been tested: Windows 98, Windows 2000, Windows NTProgramming language used: Delphi 4.0Memory required to execute with typical data: 18 MwordsNo. of bits in a word: 32No. of bytes in distributed program, including test data, etc.: 9 911 434Distribution format: zip fileKeywords: Photofragment image, onion peeling, anisotropy parametersNature of physical problem: Information about velocity and angular distributions of photofragments is the basis on which the analysis of the photolysis process resides. Reconstructing the three-dimensional distribution from the photofragment image is the first step, further processing involving angular and radial integration of the inverted image to obtain velocity and angular distributions. Provisions have to be made to correct for slight distortions of the image, and to verify the accuracy of the analysis process.Method of solution: The “Onion Peeling” algorithm described by Helm [Rev. Sci. Instrum. 67 (6) (1996)] is used to perform the image reconstruction. Angular integration with a subsequent multi-Gaussian fit supplies information about the velocity distribution of the photofragments, whereas radial integration with subsequent expansion of the angular distributions over Legendre Polynomials gives the spatial anisotropy parameters. Fitting algorithms have been developed to centre the image and to correct for image distortion.Restrictions on the complexity of the problem: The maximum image size (1280×1280) and resolution (16 bit) are restricted by available memory and can be changed in the source code. Initial centre coordinates within 5 pixels may be required for the correction and the centering algorithm to converge. Peaks on the velocity profile separated by less then the peak width may not be deconvolved. In the charged particle image reconstruction, it is assumed that the kinetic energy released in the dissociation process is small compared to the energy acquired in the electric field. For the fitting parameters to be physically meaningful, cylindrical symmetry of the image has to be assumed but the actual inversion algorithm is stable to distortions of such symmetry in experimental images.Typical running time: The analysis procedure can be divided into three parts: inversion, fitting, and geometry correction. The inversion time grows approx. as R³, where R is the radius of the region of interest: for R=200 pixels it is less than a minute, for R=400 pixels less then 6 min on a 400 MHz IBM personal computer. The time for the velocity fitting procedure to converge depends strongly on the number of peaks in the velocity profile and the convergence criterion. It ranges between less then a second for simple curves and a few minutes for profiles with up to twenty peaks. The time taken for the image correction scales as R² and depends on the curve profile. It is on the order of a few minutes for images with R=500 pixels.Unusual features of the program: Our centering and image correction algorithm is based on Fourier analysis of the radial distribution to insure the sharpest velocity profile and is insensitive to an uneven intensity distribution. There exists an angular averaging option to stabilize the inversion algorithm and not to loose the resolution at the same time.     

Determining star-image location: A new sub-pixel interpolation technique to process image centroids

We develop a theoretical methodology to estimate the location of star centroids in images recorded by CCD and active pixel sensors. The approach may be generalized to other applications were point-sources must be located with high accuracy. In contrast with other approaches, our technique is suitable for use with non-100% fill ratio sensors. The approach is applied experimentally to two camera systems employing sensors with fill-ratios of approximately 50%. We describe experimental approaches to implement the new paradigm and characterize centroid performance using laboratory targets and against real night-sky images. Applied to a conventional CCD camera, a centroid performance of 11.6 times the raw pixel resolution is achieved. Applied to a camera employing an active-pixel sensor a performance of 12.8 is demonstrated. The approach enables the rapid development of autonomous star-camera systems without the extensive characterizations required to derive polynomic fitting coefficients employed by traditional centroid algorithms.     

A comparable study of image approximations to the reaction field

The recently developed high-order accurate multiple image approximation to the reaction field for a charge inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846-864] is compared favorably to other commonly employed reaction field schemes. These methods are of particular interest because they are useful in the study of biological macromolecules by the Monte Carlo and Molecular Dynamics methods.     

New Versions of Image Approximations to the Ionic Solvent Induced Reaction Field

A recent article by Deng and Cai [Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields, J. Comput. Phys. (2007), doi: 10.1016/j.jcp.2007.09.001] introduced two fourth-order image approximations to the reaction field for a charge inside a dielectric sphere immersed in a solvent of low ionic strength. To represent such a reaction field, the image approximations employ a point charge at the classical Kelvin image point and two line charges that extend from this Kelvin image point along the radial direction to infinity, with one decaying to zero and the other growing to infinity. In this paper, alternative versions of the fourth-order image approximations are presented, using the same point charge but three different line charges, all decaying to zero along the radial direction. Similar discussions on how to approximate the line charges by discrete image charges and how to apply the resulting multiple discrete image approximations together with the fast multipole method are also included.     

Finite-difference time-domain simulation of electromagnetic propagation in magnetized plasma

The electromagnetic propagation through a homogeneous magnetized plasma slab is studied using the finite-difference time-domain method based on Z transforms. The reflection and transmission coefficients of the magnetized plasma layer for the right-hand circularly polarized wave are computed. The comparison of the numerical results of the Z transform and recursive convolution algorithms with analytic values indicates that the Z transform algorithm is more accurate than the recursive convolution algorithm. The dependence of the absorption coefficient on frequency is presented.     

Effects of external magnetic field on propagation of electromagnetic wave in uniform magnetized plasma slabs

A simple method is proposed to describe the propagation of electromagnetic waves in magnetized uniform plasma slabs. Using this method, the reflection, absorption and transmission coefficients of such plasmas for right-hand circularly waves are studied and the effects of the continuously changing external magnetic field on the power of the electromagnetic waves propagated in magnetized plasma slabs with fixed parameters are presented. Our method enables more detailed numerical analyses which are useful in practical applications pertaining to the control of the reflection or absorption coefficients of electromagnetic wave through a uniform magnetized plasma slab by adjusting the external magnetic field.     

A completely open source based computing system for computer generation of Fourier holograms

Computer generated holograms are usually generated using commercial software like MATLAB, MATHCAD, Mathematica, etc. This work is an approach in doing the same using freely distributed open source packages and Operating System. A Fourier hologram is generated using this method and tested for simulated and optical reconstruction. The reconstructed images are in good agreement with the objects chosen. The significance of using such a system is also discussed.

Program summary

Program title: FHOLOCatalogue identifier: AEDS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 176 336No. of bytes in distributed program, including test data, etc.: 4 294 872Distribution format: tar.gzProgramming language: C++Computer: any X86 micro computerOperating system: Linux (Debian Etch)RAM: 512 MBClassification: 18Nature of problem: To generate a Fourier Hologram in micro computer only by using open source operating system and packages.Running time: Depends on the matrix size. 10 sec for a matrix of size 256×256.     

An out-of-core high-resolution FFT algorithm for determining large-scale imperfections of surface potentials in crystals

We present a simple out-of-core algorithm for computing the Fast-Fourier Transform (FFT) needed to determine the two-dimensional potential of surface crystals with large-scale features, like faults, at ultra-high resolution, with around 10⁹ grid points. This algorithm represents a proof of concept that a simple and easy-to-code, out-of-core algorithm can be easily implemented and used to solve large-scale problems on low-cost hardware. The main novelties of our algorithm are: (1) elapsed and I/O times decrease with the number of single records (lines) being read; (2) only basic reading and writing routines is necessary for making the out-of-core access. Our method can be easily extended to 3D and be applied to many grand-challenge problems in science and engineering, such as fluid dynamics.     

Optimized evaluation of a large sum of functions using a three-grid approach

The efficient evaluation of numerous values of functions that vary rapidly only in a small part of the region of interest is presented. An optimized algorithm using a sequence of grids with increasing resolution is developed. The algorithm does not make any assumptions about special properties of the function to be evaluated, e.g., symmetry. An additional speed-up is obtained by exploiting the asymptotic behaviour of the functions to be summed. Two applications from high resolution atmospheric radiative transfer modelling in the infrared and microwave are presented. In a third example asymmetric Rautian line shapes important for high resolution molecular spectroscopy are considered. Computational gains by more than two orders of magnitude with relative errors less than 10⁻³ have been achieved.     

The Invar tensor package: Differential invariants of Riemann

The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6⋅¹⁰²³ objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than 6⋅¹⁰⁵ relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple).

Program summary

Program title:Invar Tensor Package v2.0Catalogue identifier:ADZK_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v2_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:3 243 249No. of bytes in distributed program, including test data, etc.:939Distribution format:tar.gzProgramming language:Mathematica and MapleComputer:Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11Operating system:Linux, Unix, Windows XP, MacOSRAM:100 MbWord size:64 or 32 bitsSupplementary material:The new database of relations is much larger than that for the previous version and therefore has not been included in the distribution. To obtain the Mathematica and Maple database files click on this link.Classification:1.5, 5Does the new version supersede the previous version?:Yes. The previous version (1.0) only handled algebraic invariants. The current version (2.0) has been extended to cover differential invariants as well.Nature of problem:Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives.Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor.Reasons for new version:With this new version, the user can manipulate differential invariants of the Riemann tensor. Differential invariants are required in many physical problems in classical and quantum gravity.Summary of revisions:The database of syzygies has been expanded by a factor of 30. New commands were added in order to deal with the enlarged database and to manipulate the covariant derivative.Restrictions:The present version only handles scalars, and not expressions with free indices.Additional comments:The distribution file for this program is over 53 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent.Running time:One second to fully reduce any monomial of the Riemann tensor up to degree 7 or order 10 in terms of independent invariants. The Mathematica notebook included in the distribution takes approximately 5 minutes to run.     

Motion4D - A library for lightrays and timelike worldlines in the theory of relativity

The Motion4D-library solves the geodesic equation as well as the parallel- and Fermi-Walker-transport in four-dimensional Lorentzian spacetimes numerically. Initial conditions are given with respect to natural local tetrads which are adapted to the symmetries or the coordinates of the spacetime. Beside some already implemented metrics like the Schwarzschild and Kerr metric, the object oriented structure of the library permits to implement other metrics or integrators in a straight forward manner.

Program summary

Program title: Motion4D-libraryCatalogue identifier: AEEX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 150 425No. of bytes in distributed program, including test data, etc.: 5 139 407Distribution format: tar.gzProgramming language: C++Computer: All platforms with a C++ compilerOperating system: Linux, Unix, WindowsRAM: 39 MBytesClassification: 1.5External routines: Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/)Nature of problem: Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes.Solution method: Integration of ordinary differential equationsRunning time: The test runs provided with the distribution require only a few seconds to run.     

GeodesicViewer - A tool for exploring geodesics in the theory of relativity

The GeodesicViewer realizes exocentric two- and three-dimensional illustrations of lightlike and timelike geodesics in the general theory of relativity. By means of an intuitive graphical user interface, all parameters of a spacetime as well as the initial conditions of the geodesics can be modified interactively. This makes the GeodesicViewer a useful instrument for the exploration of geodesics in four-dimensional Lorentzian spacetimes.

Program summary

Program title: GeodesicViewerCatalogue identifier: AEFP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 168 868No. of bytes in distributed program, including test data, etc.: 6 076 202Distribution format: tar.gzProgramming language: C++, Qt, Qwt, OpenGLComputer: All platforms with a C++ compiler, Qt, Qwt, OpenGLOperating system: Linux, Mac OS XRAM: 24 MbytesClassification: 1.5External routines:

•

Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/)

•

Motion4D (included in the package). The Motion4D library can also be downloaded from CPC. Catalogue identifier: AEEX

•

Qt (http://qt.nokia.com/downloads)

•

Qwt (http://qwt.sourceforge.net/)

•

OpenGL (http://www.opengl.org/)

Nature of problem: Illustrate geodesics in four-dimensional Lorentzian spacetimes.Solution method: Integration of ordinary differential equations. 3D-Rendering via OpenGL.Running time: Interactive. The examples given take milliseconds.     

球面全景影像自动测量路灯坐标的方法

目的 针对城市实施的路灯杆编码项目,即获取路灯坐标并依次编号,传统的测量方法耗费大量人力物力,且作业周期长,虽然激光测量精度高,但成本也高。为此本文提出一种将基于深度学习的目标检测与全景量测结合自动获取路灯坐标的方法。方法 通过Faster R-CNN（faster region convolutional neural network）训练检测模型,对全景图像中的路灯底座进行检测,同时输出检测框坐标,并与HOG（histogram of oriented gradient）特征结合SVM（support vector machine）的检测结果进行效果对比。再将检测框的对角线交点作为路灯脚点,采用核线匹配的方式找到两幅图像中一个或多个路灯相对应的同名像点并进行前方交会得到路灯的实际空间坐标,为路灯编码做好前期工作。结果 采用上述两种方法分别对100幅全景影像的路灯进行检测,结果显示Faster R-CNN具有明显优势,采用Faster R-CNN与全景量测结合自动获取路灯坐标。由于路灯底部到两成像中心的距离大小及3点构成的交会角大小对坐标量测精度具有较大影响,本文分别对距离约为7 m、11 m、18 m的点在交会角为0°180°的范围进行量测结果对比。经验证,交会角在30°150°时,距离越近,对量测精度的影响越小。基于上述规律,在自动量测的120个路灯坐标中筛选出交会角大于30°且小于150°,距离小于20 m的102个点进行精度验证,其空间坐标量测结果的误差最大不超过0.6 m,中误差小于0.3 m,满足路灯编码项目中路灯坐标精度在1 m以内的要求。结论 本文提出了一种自动获取路灯坐标的方法,将基于深度学习的目标检测应用于全景量测中,避免手动选取全景图像的同名像点进行双像量测,节省大量人力物力,具有一定的实践意义。本文方法适用于城市车流量较少的路段或时段,以免车辆遮挡造成过多干扰,对于路灯遮挡严重的街道全景,本文方法存在一定的局限性。     

Diffuse conditions for efficient solution of multislab radiation transport problems

In this article, we make use of recently developed spectral nodal methods for anisotropically scattering media and we derive mathematical conditions for the diffuse reflection and transmission of radiation in the discrete ordinates formulation of particle transport theory for plane-parallel applications. The conditions arise from a suitable reformulation of spatially discretized equations defined on the boundary layers of a multislab domain. As a result, the boundary layers can be removed from the radiation transport calculations and replaced with exact and numerically stable equivalent conditions. In order to illustrate the applicability and computational merit of our discrete ordinates conditions for diffuse reflection and transmission in radiation transport calculations, we perform numerical experiments with atmospheric radiative transfer and nuclear reactor core models.     

Application of simulated annealing for multispectral tomography

A new method based on simulated annealing is developed to obtain tomographic reconstructions based on multispectral absorption spectroscopy. The new method is able to exploit the spectral information content, to incorporate various a priori information, and to ameliorate the ill-posedness of the tomographic inversion problem. Numerical simulations are conducted to demonstrate the performance of this method for simultaneous temperature and species concentration imaging. This method is expected to enhance the practicality of multispectral tomography.     

A program for accurate solutions of two-electron atoms

We present a comprehensible computer program capable of treating non-relativistic ground and excited states for a two-electron atom having infinite nuclear mass. An iterative approach based on the implicitly restarted Arnoldi method (IRAM) is employed. The Hamiltonian matrix is never explicitly computed. Instead the action of the Hamiltonian operator on discrete pair functions is implemented. The finite difference method is applied and subsequent extrapolations gives the continuous grid result. The program is written in C and is highly optimized. All computations are made in double precision. Despite this relatively low degree of floating point precision (48 digits are not uncommon), the accuracy in the results can reach about 10 significant figures. Both serial and parallel versions are provided. The parallel program is particularly suitable for shared memory machines such as the Sun Starcat series. The serial version is simple to compile and should run on any platform.

Program summary

Title of program: corr2elCatalogue identifier: ADUXProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUXProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format: tar.gzComputer for which the program is designed and others on which it has been tested:Computers: Sun Fire 15K StarCat, Sun Ultra SPARC III, PCOperating systems or monitors under which the program has been tested: Sun Solaris 9, LinuxProgramming language used: ANSI CMemory required to execute with typical data: 3 Mwords or moreNo. bits in a word: 32No. processors used: arbitraryHas the code been vectorized or parallelized: parallelizedNumber of lines in distributed program, including test data, etc.:5885Number of bytes in distributed program, including test data, etc.: 26 199Nature of physical problem: The Schrödinger equation for two-electron atoms is solved using finite differences.Method of solution: An iterative eigenvalue-solver that requires only the action of the Hamiltonian on a trial function is applied. The two-electron wave function is expanded in a sum of partial waves. The finite difference method is then applied to approximate the derivatives of the pair functions. The total action of the Hamiltonian on the partial waves, including correlation effects, is computed using highly optimized routines.Restriction on the complexity of the problem: The Hamiltonian employed here does not take relativistic or finite nuclear mass effects into account. The amount of computing time may become unreasonable for excited states far above the ground state. The use of double precision puts a limit on the accuracy obtainable.Typical running time: This ranges from half a minute (to obtain 10 significant figures for the s-limit of the Helium ground state) to perhaps a day for advanced examples depending on the level of parallelization.Unusual features of the program: The implicitly restarted Arnoldi method used to obtain the eigenvalues is implemented by using the ARPACK/PARPACK program library [http://www.netlib.org/arpack]. This package also depends on the standard numerical libraries BLAS and LAPACK [http://www.netlib.org/lapack]. Good performance is obtained by using Sun's optimized performance libraries [http://www.sun.com]. By using a 64-bit environment (Ultra SPARC III and Solaris 9), memory limitations are non-problematic. Shared memory is used in the parallel version. Fast communication between the nodes is made over shared memory using Sun's implementation of MPI.