Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions
Institute of Scientific and Technical Information of China (English)
ZHU Meng-Hua; LIU Liang-Gang; QI Dong-Xu; YOU Zhong; XU Ao-Ao
2009-01-01
In this paper,the least square fitting method with the cubic B-spline basis hmctioas is derived to reduce the influence of statistical fluctuations in the gamma ray spectra.The derived procedure is simple and automatic.The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.
Cubic B-spline curve approximation by curve unclamping
Chen, Xiao-Diao; Ma, Weiyin; Paul, Jean-Claude
2010-01-01
International audience; A new approach for cubic B-spline curve approximation is presented. The method produces an approximation cubic B-spline curve tangent to a given curve at a set of selected positions, called tangent points, in a piecewise manner starting from a seed segment. A heuristic method is provided to select the tangent points. The first segment of the approximation cubic B-spline curve can be obtained using an inner point interpolation method, least-squares method or geometric H...
Cubic generalized B-splines for interpolation and nonlinear filtering of images
Tshughuryan, Heghine
1997-04-01
This paper presents the introduction and using of the generalized or parametric B-splines, namely the cubic generalized B-splines, in various signal processing applications. The theory of generalized B-splines is briefly reviewed and also some important properties of generalized B-splines are investigated. In this paper it is shown the use of generalized B-splines as a tool to solve the quasioptimal algorithm problem for nonlinear filtering. Finally, the experimental results are presented for oscillatory and other signals and images.
Application and Realization of the Computer Animation Design Based on Improved Cubic B-spline Curves
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Ni Na
2015-01-01
Full Text Available Based on the application of the cubic B-spline curves in the computer animation design, taking into account the security and confidentiality of the information, this paper improves the animation design techniques by the use of the improved cubic B-spline curves. Finally, this paper provides the relevant C language programs of the animation design.
三次均匀B样条与α-B样条的扩展%Extended Cubic Uniform B-spline and α-B-spline
Institute of Scientific and Technical Information of China (English)
徐岗; 汪国昭
2008-01-01
Spline curve and surface play an important role in CAD and computer graphics. In this paper, we propose several extensions of cubic uniform B-spline. Then, we present the ex- tensions of interpolating α-B-spline based on the new B-splines and the singular blending technique. The advantage of the ex- tensions is that they have global and local shape parameters. Furthermore, we also investigate their applications in data in- terpolation and polygonal shape deformation.
Xiaolong Wang; Yi Wang; Zhizhu Cao; Weizhong Zou; Liping Wang; Guojun Yu; Bo Yu; Jinjun Zhang
2013-01-01
In general, proper orthogonal decomposition (POD) method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified...
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Directory of Open Access Journals (Sweden)
Xiaolong Wang
2013-01-01
Full Text Available In general, proper orthogonal decomposition (POD method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified via two typical examples. Both results of the two methods are satisfying, and the results of cubic B-spline interpolation are more accurate than those of linear interpolation. The results are meaningful for guiding the application of the POD interpolation to complex multiparameter problems.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
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Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2015-01-01
Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
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H. S. Shukla
2014-11-01
Full Text Available In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Cubic Trigonometric B-spline Galerkin Methods for the Regularized Long Wave Equation
Irk, Dursun; Keskin, Pinar
2016-10-01
A numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on Crank Nicolson method for the time integration and cubic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves.
A new extension algorithm for cubic B-splines based on minimal strain energy
Institute of Scientific and Technical Information of China (English)
MO Guo-liang; ZHAO Ya-nan
2006-01-01
Extension ora B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC2 parameter to be zero and determining the second GC2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C2-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
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Muhammad Abbas
Full Text Available In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Abbas, Muhammad; Majid, Ahmad Abd; Md Ismail, Ahmad Izani; Rashid, Abdur
2014-01-01
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Modeling of type-2 fuzzy cubic B-spline surface for flood data problem in Malaysia
Bidin, Mohd Syafiq; Wahab, Abd. Fatah
2017-08-01
Malaysia possesses a low and sloping land areas which may cause flood. The flood phenomenon can be analyzed if the surface data of the study area can be modeled by geometric modeling. Type-2 fuzzy data for the flood data is defined using type-2 fuzzy set theory in order to solve the uncertainty of complex data. Then, cubic B-spline surface function is used to produce a smooth surface. Three main processes are carried out to find a solution to crisp type-2 fuzzy data which is fuzzification (α-cut operation), type-reduction and defuzzification. Upon conducting these processes, Type-2 Fuzzy Cubic B-Spline Surface Model is applied to visualize the surface data of the flood areas that are complex uncertainty.
Numerical Solution of One-dimensional Telegraph Equation using Cubic B-spline Collocation Method
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J. Rashidinia
2014-02-01
Full Text Available In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained by some existing methods to verify the accurate nature of our method.
A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements
A.A. Soliman
2012-01-01
Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.
A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements
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A. A. Soliman
2012-01-01
Full Text Available Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.
A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
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S. Battal Gazi Karakoç
2016-02-01
Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.
Certified Approximation of Parametric Space Curves with Cubic B-spline Curves
Shen, Liyong; Gao, Xiao-Shan
2012-01-01
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the topology, singular points, etc. The approximated curve is divided into segments called quasi-cubic B\\'{e}zier curve segments which have properties similar to a cubic rational B\\'{e}zier curve. And the approximate curve is naturally constructed as the associated cubic rational B\\'{e}zier curve of the control tetrahedron of a quasi-cubic curve. A novel optimization method is proposed to select proper weights in the cubic rational B\\'{e}zier curve to approximate the given curve. The error of the approximation is controlled by the size of its tetrahedron, which converges to zero by subdividing the curve segments. As an applic...
Extended cubic B-spline method for solving a linear system of second-order boundary value problems.
Heilat, Ahmed Salem; Hamid, Nur Nadiah Abd; Ismail, Ahmad Izani Md
2016-01-01
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The examples suggest that this method produces comparable or more accurate results than cubic B-spline and some other methods.
One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation
Institute of Scientific and Technical Information of China (English)
ZHANG Li; YANG Yan; LI Yuan-yuan; TAN Jie-qing
2014-01-01
A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation (WPIA for short) and consists of following steps:finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structure of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.
Csébfalvi, Balázs
2010-01-01
In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the nonseparable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a nonseparable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions, respectively.
A Cubic B-Spline Approach for Inter-Transformation Between Potential Field and Gradient Data
Wang, B.; Gao, S. S.
2008-12-01
Traditionally, algorithms involving Fast Fourier Transforms (FFT) are used to calculate gradients from field data and vise versa. Because the popular FFT differentiation algorithms are prone to noise, expensive field campaigns are increasingly utilized to obtain gradient data. In areas with both field and gradient data, transformation facilitates comparison. In areas with only one kind of data, transformation facilitates interpretation by transforming the measured data into another form of data. We advance unified formulae for interpolation, differentiation and integration using cubic B-splines, and propose new space-domain approaches for 2D and 3D transformations from potential field data to potential-field gradient data and vice versa. We also advance spline-based continuation techniques. In the spline-based algorithms, the spacing can be either regular or irregular. Analyses using synthetic and real gravity and magnetic data show that the new algorithms have higher accuracy, are more noise-tolerant and thus provide better insights into understanding the nature of the sources than the traditional FFT techniques.
Csébfalvi, Balázs
2013-09-01
In this paper, Cosine-Weighted B-spline (CWB) filters are proposed for interpolation on the optimal Body-Centered Cubic (BCC) lattice. We demonstrate that our CWB filters can well exploit the fast trilinear texture-fetching capability of modern GPUs, and outperform the state-of-the-art box-spline filters not just in terms of efficiency, but in terms of visual quality and numerical accuracy as well. Furthermore, we rigorously show that the CWB filters are better tailored to the BCC lattice than the previously proposed quasi-interpolating BCC B-spline filters, because they form a Riesz basis; exactly reproduce the original signal at the lattice points; but still provide the same approximation order.
Mittal, R. C.; Jain, R. K.
2012-12-01
In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.
Souto, Nelson; Thuillier, Sandrine; Andrade-Campos, A.
2016-10-01
Nowadays, full-field measurement methods are largely used to acquire the strain field developed by heterogeneous mechanical tests. Recent material parameters identification strategies based on a single heterogeneous test have been proposed considering that an inhomogeneous strain field can lead to a more complete mechanical characterization of the sheet metals. The purpose of this work is the design of a heterogeneous test promoting an enhanced mechanical behavior characterization of thin metallic sheets, under several strain paths and strain amplitudes. To achieve this goal, a design optimization strategy finding the appropriate specimen shape of the heterogeneous test by using either B-Splines or cubic splines was developed. The influence of using approximation or interpolation curves, respectively, was investigated in order to determine the most effective approach for achieving a better shape design. The optimization process is guided by an indicator criterion which evaluates, quantitatively, the strain field information provided by the mechanical test. Moreover, the design of the heterogeneous test is based on the resemblance with the experimental reality, since a rigid tool leading to uniaxial loading path is used for applying the displacement in a similar way as universal standard testing machines. The results obtained reveal that the optimization strategy using B-Splines curve approximation led to a heterogeneous test providing larger strain field information for characterizing the mechanical behavior of sheet metals.
A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines
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Canivar, Aynur [Cemal Mumtaz Teachers Training Anatolian High School, 26210 Eskisehir (Turkey); Sari, Murat, E-mail: msari@pau.edu.t [Department of Mathematics, Pamukkale University, Denizli 20070 (Turkey); Dag, Idris [Department of Computer Engineering, Eskisehir Osmangazi University, Eskisehir 26480 (Turkey)
2010-08-15
In this paper, to obtain accurate solutions of the Korteweg-de Vries (KdV) equation, a Taylor-Galerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L{sub 2} and L{sub {infinity} }error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.
Segmented Regression Based on B-Splines with Solved Examples
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Miloš Kaňka
2015-12-01
Full Text Available The subject of the paper is segmented linear, quadratic, and cubic regression based on B-spline basis functions. In this article we expose the formulas for the computation of B-splines of order one, two, and three that is needed to construct linear, quadratic, and cubic regression. We list some interesting properties of these functions. For a clearer understanding we give the solutions of a couple of elementary exercises regarding these functions.
GA Based Rational cubic B-Spline Representation for Still Image Interpolation
Samreen Abbas; Malik Zawwar Hussain; Misbah Irshad
2016-01-01
In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA). GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA) models with traditional one are hired for comparison with existing image interpolation schemes and perc...
GA Based Rational cubic B-Spline Representation for Still Image Interpolation
Directory of Open Access Journals (Sweden)
Samreen Abbas
2016-12-01
Full Text Available In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA. GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA models with traditional one are hired for comparison with existing image interpolation schemes and perceptual quality check of resulting images. The results show that the proposed scheme is better than the existing ones in comparison.
Directory of Open Access Journals (Sweden)
Zhiwei Pan
2016-05-01
Full Text Available Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton (IC-GN algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
Fillion-Gourdeau, F; Bandrauk, A D
2015-01-01
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
Energy Technology Data Exchange (ETDEWEB)
Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca [Université du Québec, INRS – Énergie, Matériaux et Télécommunications, Varennes, J3X 1S2 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Lorin, E., E-mail: elorin@math.carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Bandrauk, A.D., E-mail: andre.bandrauk@usherbrooke.ca [Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, J1K 2R1 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada)
2016-02-15
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
Institute of Scientific and Technical Information of China (English)
Zhang Yue-Xia; Meng Hui-Yan; Shi Ting-Yun
2008-01-01
The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and I/2 of a hydrogen atom in parallel electric and magnetic fields.The method can calculate the ground and higher excited resonances accurately and efficiently.The resonance parameters with accuracies of 10-9 - 10-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones.Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.
Zhiwei Pan; Wei Chen; Zhenyu Jiang; Liqun Tang; Yiping Liu; Zejia Liu
2016-01-01
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation effi...
Institute of Scientific and Technical Information of China (English)
梁锡坤
2011-01-01
为了丰富和发展B样条曲线理论,利用曲线线性组合的思想,将3次均匀B样条曲线进行了拓展,并讨论了拓展曲线的性质.研究表明,拓展曲线的基具有较简单的表达式;拓展曲线包含了原曲线的基本形式,比原曲线具有更强的描述能力,且保持曲线次数不变.利用曲线的形状因子可以调整曲线的局部形状;同时得到了一种闭曲线表示的新途径.%In order to develop the theory of B-spline curve, the representation of cubic uniform B-spline curve is extended to a general form based on linear combination of curves.Moreover, some properties of the extended curve are discussed in details.The research shows that the basis of the generalized curve is relative simple, and the extended curve includes the original B-spline curve and shows much better shape-control capability than the original curve.Meanwhile, the extended curve keeps the same degree of original one.It is easy to find that the curve can be reshape by adjusting the shape factor.Also, a new method of the representation of closed curve is given.
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
Application of Piecewise Cubic B-Spline%过两端点分段三次 B 样条方法应用研究*
Institute of Scientific and Technical Information of China (English)
王争争
2015-01-01
通过引入约束点 P0和常量 r，构建过两端点分段三次B样条曲线并推出衔接点光滑衔接条件。应用过两端点分段三次B样条方法可以构建直线、三角形、四边形及蛋形画法，并通过消齿光顺得到理想效果。实现图形的平移、缩放和旋转，通过逆时针、顺时针旋转计算消除偏差，保形效果理想。按顺时针方向生成闭曲线并记录轨迹点位置数据，方便平面上闭曲线对象间关系的计算，并得到布尔运算结果。应用该方法可以构建空间图形，实现颜色渐变效果理想。%By introducing the constraint point P0 and constant r ,two endpoints piecewise cubic B spline curve is built and some smooth cohesion terms are introduced .Application of two endpoints piecewise cubic B spline method can build straight lines ,triangles ,quadrilateral and egg painting .Through the elimination of tooth smoothing ,ideal effect is got . Translation ,scaling and rotation of graphics are achieved and eliminated by counterclockwise ,clockwise calculation devia‐tion ,conformal effect is ideal .Clockwise to generate closed curve trajectory point location and record data ,convenient plane closed curve calculation of relations between objects ,Boolean calculation results are obtained .The method can build space graphics ,make color gradient effect ideal .
The structure of uniform B-spline curves with parameters
Institute of Scientific and Technical Information of China (English)
Juan Cao; Guozhao Wang
2008-01-01
The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.
Indhumathi, C; Cai, Y Y; Guan, Y Q; Opas, M; Zheng, J
2012-01-01
Confocal laser scanning microscopy has become a most powerful tool to visualize and analyze the dynamic behavior of cellular molecules. Photobleaching of fluorochromes is a major problem with confocal image acquisition that will lead to intensity attenuation. Photobleaching effect can be reduced by optimizing the collection efficiency of the confocal image by fast z-scanning. However, such images suffer from distortions, particularly in the z dimension, which causes disparities in the x, y, and z directions of the voxels with the original image stacks. As a result, reliable segmentation and feature extraction of these images may be difficult or even impossible. Image interpolation is especially needed for the correction of undersampling artifact in the axial plane of three-dimensional images generated by a confocal microscope to obtain cubic voxels. In this work, we present an adaptive cubic B-spline-based interpolation with the aid of lookup tables by deriving adaptive weights based on local gradients for the sampling nodes in the interpolation formulae. Thus, the proposed method enhances the axial resolution of confocal images by improving the accuracy of the interpolated value simultaneously with great reduction in computational cost. Numerical experimental results confirm the effectiveness of the proposed interpolation approach and demonstrate its superiority both in terms of accuracy and speed compared to other interpolation algorithms.
Institute of Scientific and Technical Information of China (English)
冯健; 叶伯生; 周向东
2012-01-01
针对FPGA的特点对三次B样条曲线插补算法进行优化,使用VHDL语言实现了三次B样条插补算法,并在FPGA中进行实际验证.%The paper optimizes the cubic B -spline interpolation algorithm based on the characteristics of the FPGA,and verify the algorithm implemented by VHDL language on FPGA.
Directory of Open Access Journals (Sweden)
Xiaogang Ji
2014-01-01
Full Text Available In the process of curves and surfaces fairing with multiresolution analysis, fairing accuracy will be determined by final fairing scale. On the basis of Dyadic wavelet fairing algorithm (DWFA, arbitrary resolution wavelet fairing algorithm (ARWFA, and corresponding software, accuracy control of multiresolution fairing was studied for the uncertainty of fairing scale. Firstly, using the idea of inverse problem for reference, linear hypothesis was adopted to predict the corresponding wavelet scale for any given fairing error. Although linear hypothesis has error, it can be eliminated by multiple iterations. So faired curves can be determined by a minimum number of control vertexes and have the best faring effect under the requirement of accuracy. Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting. With the increase of order of curves, inverse calculation accuracy becomes higher and higher. Verification results show that inverse calculation scale can meet the accuracy requirement when fitting curve is sextic. In the whole fairing process, because there is no approximation algorithm such as interpolation and approximation, faired curves can be reconstructed again exactly. This algorithm meets the idea and essence of wavelet analysis well.
Institute of Scientific and Technical Information of China (English)
QIAO Hao-Xue; LI Bai-Wen
2002-01-01
A B-spline method has been used to calculate the electron structure of cndohedrally confined hydrogenlike atoms.The boundary conditions were conveniently satisfied with such the method.The evolution of the energy spectrum,as function of the depth of the confining well,exhibits a "mirror collapse".Ions with higher ionicity have more "collapse lines",the energies change more sharply at "collapse points",and the oscillator strengths change more violently with the depth of the confining well.
三次B样条曲线拟合的虹膜定位%Iris Localization Algorithm Based on Cubic B-spline Curve Fitting
Institute of Scientific and Technical Information of China (English)
叶永强; 沈建新; 周啸; 张敏
2011-01-01
采用圆检测定位虹膜内外边界的方法是当前虹膜定位的主流算法.当虹膜图像分辨率很高时,圆曲线不能准确地拟合虹膜真实边界,特别是受瞳孔收缩影响很大的内边界.而采用三次B样条曲线能够很好地拟合内边界.为了提高定位效率,首先运用质心探测方法分割出瞳孔区域,然后在瞳孔区域中搜索内边界点,采用三次B样条曲线精确拟合内边界；最后利用Canny算子检测外边界,并采用圆曲线的最小二乘拟合外边界.运用Bath大学虹膜库中的1000幅虹膜图像对该定位算法进行测试,内边界定位时间0.0203s、准确率99.2％；外边界定位时间2.0277s,准确率98.9％,满足准确、高效的定位要求.%The current important methods of iris localization are based on circle detection. But they could not fit the real boundary well when iris images are high-resolution, especially the inner boundary under the influence of pupil constriction. Proposed method based on cubic B-spline curve can figure out this problem. It locates the inner boundary area first, and then the outer boundary. To improve the efficiency and robustness for inner boundary localization, this paper has proposed a method to segment the pupil area first based centroid detection, then search inner edge in the segmented area. The outer boundary area is then determined by using Ihe parameter relations between inner and outer boundary. Finally, using canny operator delects the outer edge, and the outer boundary is fitted in the Least-square circle sense. The Experiment results based on the iris database of Bath University, with 99.2% accuracy and 0.022s positioning time of inner boundary, 98.9% and 2.027s of outer show that the proposed approach is efficient and robust.
非均匀三次B样条曲线插值的GS-PIA算法%Non-uniform Cubic B-spline Curve Interpolation Algorithm of GS-PIA
Institute of Scientific and Technical Information of China (English)
刘晓艳; 邓重阳
2015-01-01
提出了非均匀三次B样条曲线插值的GS-PIA算法。该算法与解线性方程组的高斯－赛德尔迭代法有同样的优点，即把已经更新的点参与到迭代过程来优化迭代过程；同时也具有渐进迭代逼近方法的优点，即有明确的几何意义，并能得到一系列逐次逼近插值点的非均匀三次 B样条曲线。%This paper presents a non-uniform cubic B-spline curve interpolation algorithm of GS-PIA.The algorithm and the Gauss-Seidel iterative method of solving linear equations have the same advantages , namely the points involved in the iterative process which has been updated to optimize the iterative process .At the same time, the algorithm also has the advantage of progressive iterative approximation method , namely, there is a clear geometric significance , and can make a series of non-uniform cubic B-spline curve approximation interpolation points .
Vibration Analysis of Rectangular Plates with One or More Guided Edges via Bicubic B-Spline Method
Directory of Open Access Journals (Sweden)
W.J. Si
2005-01-01
Full Text Available A simple and accurate method is proposed for the vibration analysis of rectangular plates with one or more guided edges, in which bicubic B-spline interpolation in combination with a new type of basis cubic B-spline functions is used to approximate the plate deflection. This type of basis cubic B-spline functions can satisfy simply supported, clamped, free, and guided edge conditions with easy numerical manipulation. The frequency characteristic equation is formulated based on classical thin plate theory by performing Hamilton's principle. The present solutions are verified with the analytical ones. Fast convergence, high accuracy and computational efficiency have been demonstrated from the comparisons. Frequency parameters for 13 cases of rectangular plates with at least one guided edge, which are possible by approximate or numerical methods only, are presented. These results are new in literature.
Trigonometric polynomial B-spline with shape parameter
Institute of Scientific and Technical Information of China (English)
WANG Wentao; WANG Guozhao
2004-01-01
The basis function of n order trigonometric polynomial B-spline with shape parameter is constructed by an integral approach. The shape of the constructed curve can be adjusted by changing the shape parameter and it has most of the properties of B-spline. The ellipse and circle can be accurately represented by this basis function.
带有切线多边形的三次B样条的α扩展曲线%α extension of the cubic B-spline curve with given tangent polygon
Institute of Scientific and Technical Information of China (English)
王成伟
2011-01-01
为了使三次均匀B样条的α扩展曲线与给定多边形相切,构造了一种与给定多边形相切的三次均匀B样条曲线的α扩展的算法.在算法中,所有的三次均匀B样条的α扩展曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改.最后给出了2个算例.%In order to a expansion of the cubic uniform B-spline curve tangent to the given polygon,in this paper, an algorithm for constructing α extension of the cubic uniform B-spine curve which is tangent to the given polygon is described. The control points of α extension of the cubic uniform B-spine curve to be constructed are computed simply by the vertices of the given polygon. The constructed curve is shape-preserving to the polygon. The local modification to a extension of the cubic uniform B-spine curve can be completed by simply adjusting the corresponding control parameters. Two examples are included.
基于三次B样条的曲线逼近算法及其收敛性%Approximate algorithm of curves and its convergence based on cubic B-spline
Institute of Scientific and Technical Information of China (English)
蒋勇; 李玉梅
2013-01-01
为了改进传统的插值样条曲线算法不易于后期处理和实时局部修改、B样条算法不能满足精度要求的缺点,提出了一种基于三次B样条的曲线逼近算法[1].该算法以三次B样条为基础对曲线的逼近领域进行了研究,通过大量的数值实验证明了该算法的可行性及高效性.该算法通过结合插值样条与B样条的各种优点,有效避免了传统算法的不足.同时,对该算法的收敛性进行了理论证明.数值实验表明了该算法具有收敛速度快、精度高且编程易实现等优点,为曲线研究提供了可供参考的有效算法.%In order to improve the shortcomings of the traditional interpolation spline that is not easy to solve the problems at the post-processing and to do the local modification in time,and to improve the disadvantage of the approximate spline which can not meet the accuracy requirements,the approximate algorithm based on the cubic B-Spline is put forward[1].The algorithm is based on the cubic B-Spline and makes some research on the area of the curve approximate.A large number of numerical experiments are made to illustrate the feasibility and the efficiency of the algorithm.The algrithm combines the advantages of the interpolation spline and the B-Spline.The shortcomings of the traditional algrithrn are prevented effectively.At the same time,the theoretical proof is put forward to demonstrate the convergence of the algorithm.And the numerical experiments show that this algorithm has fast convergence speed and high precision.And its programming is easy to implement.A effective algorithm is put forward for the curve research which can be use as a reference.
带多个形状参数的三次均匀B样条曲线的扩展%Extension of Uniform Cubic B-Spline Curves withMultiple Shape Parameters
Institute of Scientific and Technical Information of China (English)
夏成林; 邬弘毅; 郑兴国; 彭凯军
2011-01-01
通过构造两类带多个形状参数的调配函数,生成三次均匀B样条基函数的扩展.基于给出的调配函数定义了两类带多个形状参数的分段多项式曲线.这些曲线具有三次均匀B样条曲线的绝大多数重要性质,能达到GC1或GC2连续.改变形状参数的值可以独立地调控各子段的端点的位置及其切矢的长度,对曲线进行整体或局部调整,甚至直接插值任何所需的控制点.%Two classes of blending functions with multiple shape parameters are presented in this paper. They are the extension of uniform cubic B-spline basic functions. Based on the given blending functions, the piecewise polynomial curves with shape parameters are defined. These curves inherit the most properties of uniform cubic B-spline curves with GCl or GC2 continuity.The position and the length of tangent vector at the end points of curve segments can be independently controlled by changing the values of the shape parameters. These curves can be adjusted totally or locally and interpolated by any given control points.
基于误差控制的自适应3次B样条曲线插值%Adaptive curve interpolation of cubic B-spline based on error control
Institute of Scientific and Technical Information of China (English)
叶铁丽; 李学艺; 曾庆良
2013-01-01
Aiming at the problem of the existing curve interpolation algorithm on data compression, an adaptive curve interpolation algorithm of cubic B-spline is presented. An initial cubic B-spline curve is interpolated by selected minimum data points. Based on the presented algorithm for calculating the minimum distance from point to a curve, all the interpolation errors corresponding to remaining data points are calculated, and the maximum interpolation error is obtained. If the maximum error is greater than the threshold value, the point with the maximum error is added to the data points to interpolate a new curve. The process continues until the maximum interpolation error is less than the threshold value. Comparing to the current curve interpolation methods, the proposed algorithm can compress data points greatly with the same precision.%针对现有曲线插值算法不能有效压缩型值点的缺陷,研究了一种自适应三次B样条曲线插值算法.从型值点序列中选用最少的点插值一条初始曲线,基于提出的点到曲线的最小距离计算方法,分别计算各非插值点对应的插值误差,并从中提取最大插值误差.若最大误差大于给定的误差阈值,则将其对应的型值点加入插值型值点序列,重新插值曲线,直到最大插值误差满足误差要求.与现有曲线插值算法相比,该算法可以在保证插值精度的前提下有效压缩数据量.
Institute of Scientific and Technical Information of China (English)
苏世栋; 刘鹏飞
2012-01-01
为了增强关节式工业机器人加工不规则工件的能力,将三次均匀B样条曲线应用于关节式机器人轨迹插补算法中,使机器人末端以三次B样条的曲线轨迹通过各加工点.在分析了三次均匀B样条曲线特性的基础上,给出了三次均匀B样条曲线的一般表达式.在增加曲线自由端点条件后,使用追赶算法快速反算出控制点.使用预估校正的方法推导出插补算法,该算法能使机器人末端遵循抛物线过渡型的加速-匀速-减速变化规律,给出了预测减速点的方法.对一个类花瓣型的加工对象进行仿真,证明文中方法的可行性.%To enhance capability of industry joint robot to machine irregular shape workpiece, the cubic uniform B - spline curve is introduced to manipulator trajectory interpolation. After reviewing characteristics of cubic uniform B-spline curve, the general expressions of such curve are proposed. A chasing method is used to calculate the control points,while conditions of two free endpoints are added to the solutions. A predict-correct method is used to derive the interpolation algorithm, which directs the velocity of end-effecter to follow a parabolic curve-accelerating, uniform and decelerating, and the prediction of deceleration point is presented. A simulation is tested in a flower-shaped workpiece and feasibility of manipulator trajectory interpolation algorithm is verified.
Bi-cubic non-uniform B-spline surface reconstruction for slice contours%断层轮廓的双三次非均匀B样条曲面重构
Institute of Scientific and Technical Information of China (English)
王瑜; 郑津津; 周洪军; 沈连婠
2011-01-01
A surface reconstruction method from the slice contours was proposed. First, feature points were extracted based on curvature feature, and they were resampled in order to get a unification of sampling points in each line (column). Then, the sampling points were interpolated to get a bi-cubic non-uniform B-spline surface. Finally, nodes were inserted on the surface based on distance feature at a certain control accuracy, and the new control points through the least-squares approximation method were calculated to get approximate surface within the permissible range error. Based on the characteristics of slice contours, B-spline cycle and non-cycle B-spline combined, and the calculation of closed and non-closed surface was discussed. It was found that the combination of interpolation and approximation makes the algorithm more rapid and practical.%针对断层图像数据,提出了一种曲面重构的方法.依据曲率特征首先提取各层特征点,对其重采样使每行(列)获得统一的采样点数;再对采样点插值得到非均匀双三次B样条曲面;最后,在一定控制精度下对曲面依据距离特征进行节点插入,通过最小二乘逼近法算出新的控制顶点,从而得到误差在容许范围内的逼近曲面.根据断层轮廓的特点,本算法综合运用了周期B样条和非周期B样条,讨论了封闭曲面和非封闭曲面的计算方法.另外插值和逼近的结合应用使该算法更快速、实用.
Institute of Scientific and Technical Information of China (English)
A. Zerarka; O. Haif-Khaif; K. Libarir; A. Attaf
2011-01-01
This research concerns with the development of a linear three-dimensional numerical model in a quantum environment. We use the semi inverse variational method together with B-spline bases to extract the structures of bound states of the Schr(o)dinger equation. The model performances are demonstrated for the Coulomb type problem. From realistic examples, some state configurations are presented to illustrate the effectiveness and the exactitude of the proposed method.
Bejancu, Aurelian
2006-12-01
This paper considers the problem of interpolation on a semi-plane grid from a space of box-splines on the three-direction mesh. Building on a new treatment of univariate semi-cardinal interpolation for natural cubic splines, the solution is obtained as a Lagrange series with suitable localization and polynomial reproduction properties. It is proved that the extension of the natural boundary conditions to box-spline semi-cardinal interpolation attains half of the approximation order of the cardinal case.
Institute of Scientific and Technical Information of China (English)
祝恒佳; 严思杰; 刘学伟
2011-01-01
A method of modifying glass - shape curve based on cubic B - spline curve is studied. An algorithm of screening the effective data points in processing the sampling points is putted forward. As a result, the glass - shape curve can be generated by calculating the control points and interpolation. The curve can be modified directly by dragging the control point. And then calculate the space curve of the glass,and control the three axis linkage for molding movement. The algorithm effectively simplify the calculating process of modifying the glass - shape curve, and make the modifying convenience.%研究了一种基于三次B样条来进行镜框曲线修调策略.提出对镜框采样数据的有效型值点筛选算法,通过反求控制点、插值生成镜框平面曲线.直接通过拖动控制点来对平面曲线进行修调.进而计算镜框空间曲线,控制三轴联动来完成镜框成型运动.该算法能够有效简化曲线修调的计算过程,并使修调操作方便.
Spatially variant convolution with scaled B-splines.
Muñoz-Barrutia, Arrate; Artaechevarria, Xabier; Ortiz-de-Solorzano, Carlos
2010-01-01
We present an efficient algorithm to compute multidimensional spatially variant convolutions--or inner products--between N-dimensional signals and B-splines--or their derivatives--of any order and arbitrary sizes. The multidimensional B-splines are computed as tensor products of 1-D B-splines, and the input signal is expressed in a B-spline basis. The convolution is then computed by using an adequate combination of integration and scaled finite differences as to have, for moderate and large scale values, a computational complexity that does not depend on the scaling factor. To show in practice the benefit of using our spatially variant convolution approach, we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector.
Institute of Scientific and Technical Information of China (English)
蔡利栋
2001-01-01
The profit-and-loss revision technique may improve the accuracy of approximation to raw image data undergone a cubic B-spline smoothing. Comments are made on this technique from the viewpoint of image smoothing and restoration, giving highlights on the equivalence between spline smoothing and diffusion smoothing, and between profit-and-loss revision and inverse diffusion restoration; formulating the revision operators into a series of renewal recursions together with an estimation to the order of their deviations from the raw data; and exposing the numerical instability of both simple and renewal recursion of the profit and loss revision. Finally, a discussion is further made on the feasibility of applying the profit-and-loss revision to edge detection for images in the presence of noise.%以三阶B-样条作数据磨光时，引入盈亏修正可以在磨光的同时提高逼近原始数据的精度.通过从图象的平滑与恢复处理的角度出发来对盈亏修正技术进行评注，并进一步阐明了样条磨光与扩散平滑、盈亏修正与反扩散恢复在离散条件下的等价关系，给出了用于修正的更新迭代算子序列以及相应的偏差阶数估计，并且指出了盈亏修正的简单迭代和更新迭代都是数值上绝对不稳定的计算；最后讨论了盈亏修正技术在图象边缘探测中的适用性.
Numerical Methods Using B-Splines
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES
Institute of Scientific and Technical Information of China (English)
ZHU Weidong; KE Yinglin
2007-01-01
A method to reconstruct Symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using Symmetric knot vector and Symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a Symmetric knot vector is selected in order to get Symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be Symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.
Regional Ionosphere Mapping with Kriging and B-spline Methods
Grynyshyna-Poliuga, O.; Stanislawska, I. M.
2013-12-01
This work demonstrates the concept and practical examples of mapping of regional ionosphere, based on GPS observations from the EGNOS Ranging and Integrity Monitoring Stations (RIMS) network and permanent stations near to them. Interpolation/prediction techniques, such as kriging (KR) and the cubic B-spline, which are suitable for handling multi-scale phenomena and unevenly distributed data, were used to create total electron content (TEC) maps. Their computational efficiency (especially the B-spline) and the ability to handle undersampled data (especially kriging) are particularly attractive. The data sets have been collect into seasonal bins representing June, December solstices and equinox (March, September). TEC maps have a spatial resolution of 2.50 and 2.50 in latitude and longitude, respectively, and a 15-minutes temporal resolution. The time series of the TEC maps can be used to derive average monthly maps describing major ionospheric trends as a function of time, season, and spatial location.
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.
Hou, Fei; He, Ying; Qin, Hong; Hao, Aimin
2017-09-01
Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.
Uniform trigonometric polynomial B-spline curves
Institute of Scientific and Technical Information of China (English)
吕勇刚; 汪国昭; 杨勋年
2002-01-01
This paper presents a new kind of uniform spline curve, named trigonometric polynomialB-splines, over space Ω = span{sint, cost, tk-3,tk-4,…,t,1} of which k is an arbitrary integerlarger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similarV properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.
A B-spline method used to calculate added resistance in waves
Zangeneh, Razieh; Ghiasi, Mahmood
2017-01-01
Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green's formula. The Kochin function is applied to compute added resistance using Maruo's far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss-Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.
Mautz, R.; Ping, J.; Heki, K.; Schaffrin, B.; Shum, C.; Potts, L.
2005-05-01
Wavelet expansion has been demonstrated to be suitable for the representation of spatial functions. Here we propose the so-called B-spline wavelets to represent spatial time-series of GPS-derived global ionosphere maps (GIMs) of the vertical total electron content (TEC) from the Earth’s surface to the mean altitudes of GPS satellites, over Japan. The scalar-valued B-spline wavelets can be defined in a two-dimensional, but not necessarily planar, domain. Generated by a sequence of knots, different degrees of B-splines can be implemented: degree 1 represents the Haar wavelet; degree 2, the linear B-spline wavelet, or degree 4, the cubic B-spline wavelet. A non-uniform version of these wavelets allows us to handle data on a bounded domain without any edge effects. B-splines are easily extended with great computational efficiency to domains of arbitrary dimensions, while preserving their properties. This generalization employs tensor products of B-splines, defined as linear superposition of products of univariate B-splines in different directions. The data and model may be identical at the locations of the data points if the number of wavelet coefficients is equal to the number of grid points. In addition, data compression is made efficient by eliminating the wavelet coefficients with negligible magnitudes, thereby reducing the observational noise. We applied the developed methodology to the representation of the spatial and temporal variations of GIM from an extremely dense GPS network, the GPS Earth Observation Network (GEONET) in Japan. Since the sampling of the TEC is registered regularly in time, we use a two-dimensional B-spline wavelet representation in space and a one-dimensional spline interpolation in time. Over the Japan region, the B-spline wavelet method can overcome the problem of bias for the spherical harmonic model at the boundary, caused by the non-compact support. The hierarchical decomposition not only allows an inexpensive calculation, but also
Ng-Thow-Hing, Victor; Agur, Anne; Ball, Kevin A.; Fiume, Eugene; McKee, Nancy
1998-05-01
We introduce a mathematical primitive called the B-spline solid that can be used to create deformable models of muscle shape. B-spline solids can be used to model skeletal muscle for the purpose of building a data library of reusable, deformable muscles that are reconstructed from actual muscle data. Algorithms are provided for minimizing shape distortions that may be caused when fitting discrete sampled data to a continuous B-spline solid model. Visible Human image data provides a good indication of the perimeter of a muscle, but is not suitable for providing internal muscle fiber bundle arrangements which are important for physical simulation of muscle function. To obtain these fiber bundle orientations, we obtain 3-D muscle fiber bundle coordinates by triangulating optical images taken from three different camera views of serially dissected human soleus specimens. B-spline solids are represented as mathematical three-dimensional vector functions which can parameterize an enclosed volume as well as its boundary surface. They are based on B-spline basis functions, allowing local deformations via adjustable control points and smooth continuity of shape. After the B-spline solid muscle model is fitted with its external surface and internal volume arrangements, we can subsequently deform its shape to allow simulation of animated muscle tissue.
Variational B-spline level-set: a linear filtering approach for fast deformable model evolution.
Bernard, Olivier; Friboulet, Denis; Thévenaz, Philippe; Unser, Michael
2009-06-01
In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.
Conformal interpolating algorithm based on B-spline for aspheric ultra-precision machining
Li, Chenggui; Sun, Dan; Wang, Min
2006-02-01
Numeric control machining and on-line compensation for aspheric surface are key techniques for ultra-precision machining. In this paper, conformal cubic B-spline interpolating curve is first applied to fit the character curve of aspheric surface. Its algorithm and process are also proposed and imitated by Matlab7.0 software. To evaluate the performance of the conformal B-spline interpolation, comparison was made between linear and circular interpolations. The result verifies this method can ensure smoothness of interpolating spline curve and preserve original shape characters. The surface quality interpolated by B-spline is higher than by line and by circle arc. The algorithm is benefit to increasing the surface form precision of workpiece during ultra-precision machining.
Quadrotor system identification using the multivariate multiplex b-spline
Visser, T.; De Visser, C.C.; Van Kampen, E.J.
2015-01-01
A novel method for aircraft system identification is presented that is based on a new multivariate spline type; the multivariate multiplex B-spline. The multivariate multiplex B-spline is a generalization of the recently introduced tensor-simplex B-spline. Multivariate multiplex splines obtain simil
Adaptive Parametrization of Multivariate B-splines for Image Registration
DEFF Research Database (Denmark)
Hansen, Michael Sass; Glocker, Benjamin; Navab, Nassir;
2008-01-01
cost function. In the current work we introduce multivariate B-splines as a novel alternative to the widely used tensor B-splines enabling us to make efficient use of the derived measure.The multivariate B-splines of order n are Cn- 1 smooth and are based on Delaunay configurations of arbitrary 2D or 3......D control point sets. Efficient algorithms for finding the configurations are presented, and B-splines are through their flexibility shown to feature several advantages over the tensor B-splines. In spite of efforts to make the tensor product B-splines more flexible, the knots are still bound...... to reside on a regular grid. In contrast, by efficient non- constrained placement of the knots, the multivariate B- splines are shown to give a good representation of inho- mogeneous objects in natural settings. The wide applicability of the method is illustrated through its application on medical data...
Short-Term Wind Speed Forecast Based on B-Spline Neural Network Optimized by PSO
Directory of Open Access Journals (Sweden)
Zhongqiang Wu
2015-01-01
Full Text Available Considering the randomness and volatility of wind, a method based on B-spline neural network optimized by particle swarm optimization is proposed to predict the short-term wind speed. The B-spline neural network can change the division of input space and the definition of basis function flexibly. For any input, only a few outputs of hidden layers are nonzero, the outputs are simple, and the convergence speed is fast, but it is easy to fall into local minimum. The traditional method to divide the input space is thoughtless and it will influence the final prediction accuracy. Particle swarm optimization is adopted to solve the problem by optimizing the nodes. Simulated results show that it has higher prediction accuracy than traditional B-spline neural network and BP neural network.
Multiple products of B-splines used in CAD system
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The function upgrade of computer aided design (CAD) system requested that the multiple product of B-spline functions should be represented as a linear combination of some suitable (usually higher-degree) B-splines. In this paper, we apply the theory of spline space and discrete B-splines to deduce the representation of the coefficients of all terms of the linear combination, which can be directly applied to software coding in system development.
Harmening, Corinna; Neuner, Hans
2017-03-01
Freeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis. A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures. In [10] the problem of finding an alternative to these trial-and-error-procedures was addressed for the case of B-spline curves: The task of choosing the optimal number of control points was interpreted as a model selection problem. Two model selection criteria, the Akaike and the Bayesian Information Criterion, were used to identify the B-spline curve with the optimal number of control points from a set of candidate B-spline models. In order to overcome the drawbacks of the information criteria, an alternative approach based on statistical learning theory was developed. The criteria were evaluated by means of simulated data sets. The present paper continues these investigations. If necessary, the methods proposed in [10] are extended to areal approaches so that they can be used to determine the optimal number of B-spline surface control points. Furthermore, the methods are evaluated by means of real laser scanner data sets rather than by simulated ones. The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.
Optimization and dynamics of protein-protein complexes using B-splines.
Gillilan, Richard E; Lilien, Ryan H
2004-10-01
A moving-grid approach for optimization and dynamics of protein-protein complexes is introduced, which utilizes cubic B-spline interpolation for rapid energy and force evaluation. The method allows for the efficient use of full electrostatic potentials joined smoothly to multipoles at long distance so that multiprotein simulation is possible. Using a recently published benchmark of 58 protein complexes, we examine the performance and quality of the grid approximation, refining cocrystallized complexes to within 0.68 A RMSD of interface atoms, close to the optimum 0.63 A produced by the underlying MMFF94 force field. We quantify the theoretical statistical advantage of using minimization in a stochastic search in the case of two rigid bodies, and contrast it with the underlying cost of conjugate gradient minimization using B-splines. The volumes of conjugate gradient minimization basins of attraction in cocrystallized systems are generally orders of magnitude larger than well volumes based on energy thresholds needed to discriminate native from nonnative states; nonetheless, computational cost is significant. Molecular dynamics using B-splines is doubly efficient due to the combined advantages of rapid force evaluation and large simulation step sizes. Large basins localized around the native state and other possible binding sites are identifiable during simulations of protein-protein motion. In addition to providing increased modeling detail, B-splines offer new algorithmic possibilities that should be valuable in refining docking candidates and studying global complex behavior.
B-spline image model for energy minimization-based optical flow estimation.
Le Besnerais, Guy; Champagnat, Frédéric
2006-10-01
Robust estimation of the optical flow is addressed through a multiresolution energy minimization. It involves repeated evaluation of spatial and temporal gradients of image intensity which rely usually on bilinear interpolation and image filtering. We propose to base both computations on a single pyramidal cubic B-spline model of image intensity. We show empirically improvements in convergence speed and estimation error and validate the resulting algorithm on real test sequences.
A B-spline Galerkin method for the Dirac equation
Froese Fischer, Charlotte; Zatsarinny, Oleg
2009-06-01
The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.
Calculations of Electron Structure of Endohedrally Confined Helium Atom with B-Spline Type Functions
Institute of Scientific and Technical Information of China (English)
QIAO HaoXue; SHI TingYun; LI BaiWen
2002-01-01
The B-spline basis set method is used to study the properties of helium confined endohedrally at thegeometrical centre of a fullerene. The boundary conditions of the wavefunctions can be simply satisfied with thismethod. From our results, the phenomenon of "mirror collapse" is found in the case of confining helium. The interestingbehaviors of confining helium are also discussed.
Understanding recurrence relations for Chebyshevian B-splines via blossoms
Mazure, Marie-Laurence
2008-10-01
The purpose of this article is to show how naturally recurrence relations for most general Chebyshevian B-splines emerge from blossoms. In particular, this work gives a new insight into previous results by Lyche [A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155-178], the importance of which it underlines.
Exponential B-splines and the partition of unity property
DEFF Research Database (Denmark)
Christensen, Ole; Massopust, Peter
2012-01-01
We provide an explicit formula for a large class of exponential B-splines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant. As an application of this result we construct explicitly given pairs of dual...
A Unified Representation Scheme for Solid Geometric Objects Using B-splines (extended Abstract)
Bahler, D.
1985-01-01
A geometric representation scheme called the B-spline cylinder, which consists of interpolation between pairs of uniform periodic cubic B-spline curves is discussed. This approach carries a number of interesting implications. For one, a single relatively simple database schema can be used to represent a reasonably large class of objects, since the spline representation is flexible enough to allow a large domain of representable objects at very little cost in data complexity. The model is thus very storage-efficient. A second feature of such a system is that it reduces to one the number of routines which the system must support to perform a given operation on objects. Third, the scheme enables easy conversion to and from other representations. The formal definition of the cylinder entity is given. In the geometric properties of the entity are explored and several operations on such objects are defined. Some general purpose criteria for evaluating any geometric representation scheme are introduced and the B-spline cylinder scheme according to these criteria is evaluated.
Micropolar Fluids Using B-spline Divergence Conforming Spaces
Sarmiento, Adel
2014-06-06
We discretized the two-dimensional linear momentum, microrotation, energy and mass conservation equations from micropolar fluids theory, with the finite element method, creating divergence conforming spaces based on B-spline basis functions to obtain pointwise divergence free solutions [8]. Weak boundary conditions were imposed using Nitsche\\'s method for tangential conditions, while normal conditions were imposed strongly. Once the exact mass conservation was provided by the divergence free formulation, we focused on evaluating the differences between micropolar fluids and conventional fluids, to show the advantages of using the micropolar fluid model to capture the features of complex fluids. A square and an arc heat driven cavities were solved as test cases. A variation of the parameters of the model, along with the variation of Rayleigh number were performed for a better understanding of the system. The divergence free formulation was used to guarantee an accurate solution of the flow. This formulation was implemented using the framework PetIGA as a basis, using its parallel stuctures to achieve high scalability. The results of the square heat driven cavity test case are in good agreement with those reported earlier.
Use of B-Spline in the Finite Element Analysis: Comparison with ANCF Geometry
2011-02-04
formulations developed in this paper. 15. SUBJECT TERMS Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS 16. SECURITY...Keywords: Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS . UNCLAS: Dist A. Approved for public release 3 1...developed by computational geometry methods such as B- spline and NURBS (Non-Uniform Rational B-Splines) representations. This fact has motivated
Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors.
Okaniwa, Shoichi; Nasri, Ahmad; Lin, Hongwei; Abbas, Abdulwahed; Kineri, Yuki; Maekawa, Takashi
2012-09-01
This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.
A new wavelet-based thin plate element using B-spline wavelet on the interval
Jiawei, Xiang; Xuefeng, Chen; Zhengjia, He; Yinghong, Zhang
2008-01-01
By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.
Fingerprint Representation Methods Based on B-Spline Functions
Institute of Scientific and Technical Information of China (English)
Ruan Ke; Xia De-lin; Yan Pu-liu
2004-01-01
The global characteristics of a fingerprint image such as the ridge shape and ridge topology are often ignored in most automatic fingerprint verification system. In this paper, a new representative method based on B-Spline curve is proposed to address this problem. The resultant B-Spline curves can represent the global characteristics completely and the curves are analyzable and precise. An algorithm is also proposed to extract the curves from the fingerprint image. In addition to preserve the most information of the fingerprint image, the knot-points number of the B-Spline curve is reduced to minimum in this algorithm. At the same time, the influence of the fingerprint image noise is discussed. In the end, an example is given to demonstrate the effectiveness of the representation method.
Construction of generalized magnetic coordinates by B-spline expansion
Energy Technology Data Exchange (ETDEWEB)
Kurata, Michinari [Dept. of Energy Engineering and Science, Graduate School of Engineering, Nagoya Univ., Nagoya, Aichi (Japan); Todoroki, Jiro [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-06-01
Generalized Magnetic Coordinates (GMC) are curvilinear coordinates ({xi},{eta},{zeta}) in which the magnetic field is expressed in the form B={nabla}{psi}({xi},{eta},{zeta}) x {nabla}{zeta} + H{sup {zeta}}({xi},{eta}){nabla}{xi} x {nabla}{eta}. The coordinates are expanded in Fourier series in the toroidal direction and the B-spline function in other two dimensions to treat the aperiodic model magnetic field. The coordinates are well constructed, but are influenced by the boundary condition in the B-spline expansion. (author)
Color management with a hammer: the B-spline fitter
Bell, Ian E.; Liu, Bonny H. P.
2003-01-01
To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.
An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals
Directory of Open Access Journals (Sweden)
Hongyi Li
2015-01-01
Full Text Available A B-spline empirical mode decomposition (BEMD method is proposed to improve the celebrated empirical mode decomposition (EMD method. The improvement of BEMD on EMD mainly concentrates on the sifting process. First, instead of the curve that resulted from computing the average of upper and lower envelopes, the curve interpolated by the midpoints of local maximal and minimal points is used as the mean curve, which can reduce the cost of computation. Second, the cubic spline interpolation is replaced with cubic B-spline interpolation on account of the advantages of B-spline over polynomial spline. The effectiveness of BEMD compared with EMD is validated by numerical simulations and an application to find the basis functions of EMI signals.
3-D Design of Free-Form B-Spline Surfaces
1974-09-01
a Mathematical Representation 5 11.2 Coons and Bezier Formulations 7 Coons Patches 7 Bözler Patches U 11.3 Local Basis Formulations 15 B-splines...lt|aa|^|MM|aM^|[ia|J|||.ai|h. j : ’ ^-*^ 16 Figure 2.4 Bezier Surface and Control Point Array. mmägmgft mm ^i^i_...isoparametric curvas (rendered as collections of straight line segments) in the surface and emphasized dots to represent the control points. Figure 3.G shows
Energy Spectra of the Confined Atoms Obtained by Using B-Splines
Institute of Scientific and Technical Information of China (English)
SHI Ting-Yun; BAO Cheng-Guang; LI Bai-Wen
2001-01-01
We have calculated the energy spectra of one- and two-electron atoms (ions) centered in an impenetrable spherical box by variational method with B-splines as basis functions. Accurate results are obtained for both large and small radii of confinement. The critical box radius of confined hydrogen atom is also calculated to show the usefulness of our method. A partial energy degeneracy in confined hydrogen atom is found when the radius of spherical box is equal to the distance at which a node of single-node wavefunctions of free hydrogen atom is located.
A matrix method for degree-raising of B-spline curves
Institute of Scientific and Technical Information of China (English)
秦开怀
1997-01-01
A new identity is proved that represents the kth order B-splines as linear combinations of the (k + 1) th order B-splines A new method for degree-raising of B-spline curves is presented based on the identity. The new method can be used for all kinds of B-spline curves, that is, both uniform and arbitrarily nonuniform B-spline curves. When used for degree-raising of a segment of a uniform B-spline curve of degree k - 1, it can help obtain a segment of curve of degree k that is still a uniform B-spline curve without raising the multiplicity of any knot. The method for degree-raising of Bezier curves can be regarded as the special case of the new method presented. Moreover, the conventional theory for degree-raising, whose shortcoming has been found, is discussed.
B-spline parameterization of spatial response in a monolithic scintillation camera
Solovov, V; Chepel, V; Domingos, V; Martins, R
2016-01-01
A framework for parameterization of the light response functions (LRFs) in a scintillation camera was developed. It is based on approximation of the measured or simulated photosensor response with weighted sums of uniform cubic B-splines or their tensor products. The LRFs represented in this way are smooth, computationally inexpensive to evaluate and require much less memory than non-parametric alternatives. The parameters are found in a straightforward way by the linear least squares method. The use of linear fit makes the fitting process stable and predictable enough to be used in non-supervised mode. Several techniques that allow to reduce the storage and processing power requirements were developed. A software library for fitting simulated and measured light response with spline functions was developed and integrated into an open source software package ANTS2 designed for simulation and data processing for Anger camera-type detectors.
Directory of Open Access Journals (Sweden)
T Nikbakht
2012-12-01
Full Text Available Effects of quantum size and potential shape on the spectra of an electron and a hydrogenic-donor at the center of a permeable spherical cavity have been calculated, using linear variational method. B-splines have been used as basis functions. By extensive convergence tests and comparing with other results given in the literature, the validity and efficiency of the method were confirmed.
RANCANG BANGUN PROGRAM PENGEDITAN KURVA B-SPLINE MULTIRESOLUSI BERBASIS WAVELETS
Directory of Open Access Journals (Sweden)
Nanik Suciati
2002-07-01
Full Text Available Penelitian ini menyusun representasi multiresolusi untuk kurva B-spline kubik yang menginterpolasi titik-titik ujung dengan basis wavelets. Representasi multiresolusi ini digunakan untuk mendukung beberapa tipe pengeditan kurva, yaitu penghalusan kurva dengan tingkat resolusi kontinyu untuk menghilangkan detail-detail kurva yang tidak diinginkan, pengeditan bentuk keseluruhan kurva dengan tetap mempertahankan detaildetailnya, perubahan detail-detail kurva tanpa mempengaruhi bentuk keseluruhannya, dan pengeditan satubagian tertentu dari kurva melalui manipulasi secara langsung terhadap titik-titik kontrolnya. Untuk menguji kemampuan representasi multiresolusi dalam mendukung empat tipe manipulasi kurva tersebut, disusun program pengeditan kurva dengan menggunakan bahasa pemrograman Visual C++ pada komputer Pentium 133 MHz, memori 16 Mbyte, sistem operasi Windows 95, lingkungan pengembangan Microsoft DevelopmentStudio 97 dan pustaka Microsoft Foundation Class. Dari hasil uji coba program diketahui bahwa representasi multiresolusi memberikan dukungan yang sangat baik terhadap tipe-tipe pengeditan seperti yang disebutkan di atas. Representasi multiresolusi tidak membutuhkan memori penyimpan ekstra selain dari yang digunakan untuk menyimpan titik kontrol. Dari hasil uji coba program menggunakan ratusan titik kontrol, algoritma berjalan cukup cepat dan memadai berkaitan dengan tuntutan komunikasi interaktif antara user dan program.Kata kunci: B-Spline, Wavelet, Multiresolusi
B-splines on 3-D tetrahedron partition in four-directional mesh
Institute of Scientific and Technical Information of China (English)
SUN; Jiachang
2001-01-01
［1］ de Boor, C., Hllig, K., Riemannschneider, S. D., Box Splines, New York: Springer-Verlag, 1993.［2］ Dahmen, W., Micchelli, C. A., Recent Process in Multivariate Splines, Interpolating Cardinal Splines as Their Degree Tends to Infinity (ed. Ward, J.), New York: Academic Press, 1983, 27.［3］ de Boor, C., Topics in multivariate approximation theory, in Topics in Numerical Analysis, Lecture Notes in Mathematics (ed. Turner, P. R.), Vol. 965, New York: Springer-Verlag, 1982, 39.［4］ de Boor, C., B-form basics, in Geometric Modelling (ed. Farin, G.), Philadephia: SIAM, 1987, 131.［5］ Chui, C. K., Wang, R. H., Spaces of bivariate cubic and quartic splines on type-1 triangulations, J. Math. Anal. Appl., 1984, 101: 540.［6］ Jia, R. Q., Approximation order from certain spaces of smooth bivariate splines on a three-direction mesh, Trans. AMS, 1986, 295: 199.［7］ Dahmen, W., On multivariate B-splines, SIAM J. Numer. Anal., 1980, 17: 179.［8］ Sun Jiachang, The B-net structure and recurrence algorithms for B-splines on a three direction mesh, Mathematica Numerica Sinica, 1990, 12: 365.［9］ Sun Jiachang, Some results on the field of spline theory and its applications, Contemporary Mathematics, 1994, 163: 127.［10］ Sun Jiachang, Dual bases and quasi-interpolation of B-splines on S13 with three direction meshes, Acta Mathematicae Applicatae Sinica, 1991, 14: 170.［11］ Wang, R. H., He, T. X., Liu, X. Y. Et al., An integral method for constructing bivariate spline functions, J. Comp. Math., 1989, 7: 244.［12］ Wang, R. H., Shi, X. Q., A kind of C interpolation in the n-dimensional finite element method, J. Math. Res. And Exp., 1989, 9: 173.［13］ Shi, X. Q., Wang, R. H., The existence conditions of space S12(Δn), Chinese Science Bulletin, 1989, 34: 2015.
Hodograph computation and bound estimation for rational B-spline curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is necessary to compute the derivative and estimate the bound of rational B-spline curves in design system, which has not been studied to date. To improve the function of computer aided design (CAD) system, and to enhance the efficiency of different algorithms of rational B-spline curves, the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational B-spline curves are derived by applying Dir function, which indicates the direction of Cartesian vector between homogeneous points, discrete B-spline theory and the formula of translating the product into a summation of B-spline functions. As an application of the result above,upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.
A fast direct point-by-point generating algorithm for B Spline curves and surfaces
Institute of Scientific and Technical Information of China (English)
LI Zhong; HAN Dan-fu
2005-01-01
Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix transformation from B Spline representation to Bezier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.
Automatic Shape Control of Triangular B-Splines of Arbitrary Topology
Institute of Scientific and Technical Information of China (English)
Ying He; Xian-Feng Gu; Hong Qin
2006-01-01
Triangular B-splines are powerful and flexible in modeling a broader class of geometric objects defined over arbitrary, non-rectangular domains. Despite their great potential and advantages in theory, practical techniques and computational tools with triangular B-splines are less-developed. This is mainly because users have to handle a large number of irregularly distributed control points over arbitrary triangulation. In this paper, an automatic and efficient method is proposed to generate visually pleasing, high-quality triangular B-splines of arbitrary topology. The experimental results on several real datasets show that triangular B-splines are powerful and effective in both theory and practice.
Fast Selection of Spectral Variables with B-Spline Compression
Rossi, Fabrice; Wertz, Vincent; Meurens, Marc; Verleysen, Michel
2007-01-01
The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual infor...
C-B样条曲线的分割和拼接%Arbitrary Subdivision Algorithm and Joining of C-B-Spline
Institute of Scientific and Technical Information of China (English)
宋丽平
2011-01-01
曲线曲面造型中设计复杂的自由曲线时,单段曲线已不能满足外形设计的要求,因而在实际造型中,经常采用曲线的分割和拼接.C-B样条理论是曲线曲面造型的一项重要内容.在对C-B样条基函数及曲线端点特性分析的基础上,提出了C-B样条曲线的任意分割算法,并对C-B样条曲线间进行了G1拼接.给出了 B样条曲线和C-B样条曲线G1和G2光滑拼接的几何条件.采用分割和拼接技术会增加C-B样条曲线的灵活性,所得结论具有明确的几何意义,并可以进一步推广到C-B样条曲面造型中.%The single curve already can' t satisfy the requirements of shape design when designing complex free curve in curve/surface modeling. Thus in the actual modeling, C-B-spline theory is an important content of curve/surface modeling. Propose the algorithm of arbitrarily divided when analysing C-B-spline basis functions,then splicing between two C-B-spline. In addition,give geometry conditions about B-spline curves and C-B-spline curves. The results are benefit for the shape modification, and they can also be extended to surface modeling with C-B-spline.
Soldea, Octavian; Elber, Gershon; Rivlin, Ehud
2006-02-01
This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.
Büchmann, Bjarne
2000-05-01
An analysis is given for the accuracy and stability of some perturbation-based time-domain boundary element models (BEMs) with B-spline basis functions, solving hydrodynamic free-surface problems, including forward speed effects. The spatial convergence rate is found as a function of the order of the B-spline basis. It is shown that for all the models examined the mixed implicit-explicit Euler time integration scheme is correct to second order. Stability diagrams are found for models based on B-splines of orders third through to sixth for two different time integration schemes. The stability analysis can be regarded as an extension of the analysis by Vada and Nakos [Vada T, Nakos DE. Time marching schemes for ship motion simulations. In Proceedings of the 8th International Workshop on Water Waves and Floating Bodies, St. John's, Newfoundland, Canada, 1993; 155-158] to include B-splines of orders higher than three (piecewise quadratic polynomials) and to include finite water depth and a current at an oblique angle to the model grid. Copyright
Regional Densification of a Global VTEC Model Based on B-Spline Representations
Erdogan, Eren; Schmidt, Michael; Dettmering, Denise; Goss, Andreas; Seitz, Florian; Börger, Klaus; Brandert, Sylvia; Görres, Barbara; Kersten, Wilhelm F.; Bothmer, Volker; Hinrichs, Johannes; Mrotzek, Niclas
2017-04-01
both directions. The spectral resolution of both model parts is defined by the number of B-spline basis functions introduced for longitude and latitude directions related to appropriate coordinate systems. Furthermore, the TLVM has to be developed under the postulation that the global model part will be computed continuously in near real-time (NRT) and routinely predicted into the future by an algorithm based on deterministic and statistical forecast models. Thus, the additional regional densification model part, which will be computed also in NRT, but possibly only for a specified time duration, must be estimated independently from the global one. For that purpose a data separation procedure has to be developed in order to estimate the unknown series coefficients of both model parts independently. This procedure must also consider additional technique-dependent unknowns such as the Differential Code Biases (DCBs) within GNSS and intersystem biases. In this contribution we will present the concept to set up the TLVM including the data combination and the Kalman filtering procedure; first numerical results will be presented.
Symmetric alteration of four knots of B-spline and NURBS surfaces
Institute of Scientific and Technical Information of China (English)
LI Ya-juan; WANG Guo-zhao
2006-01-01
Modifying the knots ofa B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface,the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.
B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration
Institute of Scientific and Technical Information of China (English)
雷桂媛
2002-01-01
The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O(N-1) is regained by using the B-splines smoothed rejection method in importance sampling.
B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration
Institute of Scientific and Technical Information of China (English)
雷桂媛
2002-01-01
The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.
Institute of Scientific and Technical Information of China (English)
温伟斌; 蹇开林; 骆少明
2013-01-01
A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven-tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin-ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.
B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy
Directory of Open Access Journals (Sweden)
Shilpa Dilipkumar
2015-03-01
Full Text Available An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy. A comparative study of the proposed technique with the state-of-art maximum likelihood (ML and maximum-a-posteriori (MAP with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED.
Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations
2012-04-01
geometrical mapping meeting our criteria could be defined utilizing B-splines or Non- Uniform Rational B-Splines ( NURBS ) on the coarsest mesh Mh0 . For...examples of such mappings, see Chapter 2 of [13]. NURBS mappings are especially useful as they can represent many geometries of scientific and...complications that are beyond the scope of this work. We would like to note that all four assumptions hold if we employ a conforming NURBS multi-patch
B-SPLINE-BASED SVM MODEL AND ITS APPLICATIONS TO OIL WATER-FLOODED STATUS IDENTIFICATION
Institute of Scientific and Technical Information of China (English)
Shang Fuhua; Zhao Tiejun; Yi Xiongying
2007-01-01
A method of B-spline transform for signal feature extraction is developed. With the B-spline,the log-signal space is mapped into the vector space. An efficient algorithm based on Support Vector Machine (SVM) to automatically identify the water-flooded status of oil-saturated stratum is described.The experiments show that this algorithm can improve the performances for the identification and the generalization in the case of a limited set of samples.
Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data
Garcia-Capulin, C. H.; F. J. Cuevas; Trejo-Caballero, G.; Rostro-Gonzalez, H.
2014-01-01
B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor pro...
A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images
Directory of Open Access Journals (Sweden)
Xiaogang Du
2016-01-01
Full Text Available The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU.
A class of compactly supported symmetric/antisymmetric B-spline wavelets
Institute of Scientific and Technical Information of China (English)
YANG Shouzhi; LOU Zengjian
2005-01-01
An algorithm for constructing a class of compactly supported symmetric/antisymmetric B-spline wavelets is presented.For any m th order and k th order cardinal B-spline Nm (x), Nk (x), if m + k is an even integer, the corresponding m th order B-spline wavelets ψkm (x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψkm (x), m ＞ 1 is m th Bspline wavelet associated with two spline functions Nm (x) and Nk (x), then (ψkm (x))′( x ) is m - 1th B-spline wavelet associated with Nm-1(x) and Nk+1(x), i.e. (ψkm(x))′(x) =22ψk+1m-1(x). Similarly, ∫x0 ψkm(t)dt, k ＞1 is m + 1th B-spline wavelet associated with Nm + 1 (x) and Nk-1 (x). Using this method, we recovered Chui and Wang' s spline wavelets. Since a class of B-spline wavelets are symmetric/antisymmetric, their linear phase property is assured. Several examples are also presented.
BSR: B-spline atomic R-matrix codes
Zatsarinny, Oleg
2006-02-01
BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput
Energy Technology Data Exchange (ETDEWEB)
Vasconcelos, Geovane Vitor; Dantas, Carlos Costa, E-mail: geovitor@bol.com.b, E-mail: ccd@ufpe.b [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Dept. de Energia Nuclear. Grupo de Radioquimica; Melo, Silvio de Barros; Pires, Renan Ferraz, E-mail: sbm@cin.ufpe.b, E-mail: rfp@cin.ufpe.b [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Centro de Informatica
2009-07-01
The 3D tomography reconstruction has been a profitable alternative in the analysis of the FCC-type- riser (Fluid Catalytic Cracking), for appropriately keeping track of the sectional catalyst concentration distribution in the process of oil refining. The method of tomography reconstruction proposed by M. Azzi and colleagues (1991) uses a relatively small amount of trajectories (from 3 to 5) and projections (from 5 to 7) of gamma rays, a desirable feature in the industrial process tomography. Compared to more popular methods, such as the FBP (Filtered Back Projection), which demands a much higher amount of gamma rays projections, the method by Azzi et al. is more appropriate for the industrial process, where the physical limitations and the cost of the process require more economical arrangements. The use of few projections and trajectories facilitates the diagnosis in the flow dynamical process. This article proposes an improvement in the basis functions introduced by Azzi et al., through the use of quadratic B-splines functions. The use of B-splines functions makes possible a smoother surface reconstruction of the density distribution, since the functions are continuous and smooth. This work describes how the modeling can be done. (author)
N-dimensional non uniform rational B-splines for metamodeling
Energy Technology Data Exchange (ETDEWEB)
Turner, Cameron J [Los Alamos National Laboratory; Crawford, Richard H [UT - AUSTIN
2008-01-01
Non Uniform Rational B-splines (NURBs) have unique properties that make them attractive for engineering metamodeling applications. NURBs are known to accurately model many different continuous curve and surface topologies in 1-and 2-variate spaces. However, engineering metamodels of the design space often require hypervariate representations of multidimensional outputs. In essence, design space metamodels are hyperdimensional constructs with a dimensionality determined by their input and output variables. To use NURBs as the basis for a metamodel in a hyperdimensional space, traditional geometric fitting techniques must be adapted to hypervariate and hyperdimensional spaces composed of both continuous and discontinuous variable types. In this paper, we describe the necessary adaptations for the development of a NURBs-based metamodel called a Hyperdimensional Performance Model or HyPerModel. HyPerModels are capable of accurately and reliably modeling nonlinear hyperdimensional objects defined by both continuous and discontinuous variables of a wide variety of topologies, such as those that define typical engineering design spaces. We demonstrate this ability by successfully generating accurate HyPerModels of 10 trial functions laying the foundation for future work with N-dimensional NURBs in design space applications.
n-dimensional non uniform rational b-splines for metamodeling
Energy Technology Data Exchange (ETDEWEB)
Turner, Cameron J [Los Alamos National Laboratory; Crawford, Richard H [UT-AUSTIN
2008-01-01
Non Uniform Rational B-splines (NURBs) have unique properties that make them attractive for engineering metamodeling applications. NURBs are known to accurately model many different continuous curve and surface topologies in 1- and 2-variate spaces. However, engineering metamodels of the design space often require hypervariate representations of multidimensional outputs. In essence, design space metamodels are hyperdimensional constructs with a dimensionality determined by their input and output variables. To use NURBs as the basis for a metamodel in a hyperdimensional space, traditional geometric fitting techniques must be adapted to hypervariate and hyperdimensional spaces composed of both continuous and discontinuous variable types. In this paper, they describe the necessary adaptations for the development of a NURBs-based metamodel called a Hyperdimensional Performance Model or HyPerModel. HyPerModels are capable of accurately and reliably modeling nonlinear hyperdimensional objects defined by both continuous and discontinuous variables of a wide variety of topologies, such as those that define typical engineering design spaces. They demonstrate this ability by successfully generating accurate HyPerModels of 10 trial functions laying the foundation for future work with N-dimensional NURBs in design space applications.
Online estimation of B-spline mixture models from TOF-PET list-mode data
Energy Technology Data Exchange (ETDEWEB)
Schretter, Colas; Kobbelt, Leif [RWTH Aachen Univ. (Germany). Computer Graphics Group; Sun, Jianyong [Nottingham Univ. (United Kingdom). Intelligent Modelling and Analysis Research Group
2011-07-01
In emission tomography, images are usually represented by regular grids of voxels or overlapping smooth image elements (blobs). Few other image models have been proposed like tetrahedral meshes or point clouds that are adapted to an anatomical image. This work proposes a practical sparse and continuous image model inspired from the field of parametric density estimation for Gaussian mixture models. The position, size, aspect ratio and orientation of each image element is optimized as well as its weight with a very fast online estimation method. Furthermore, the number of mixture components, hence the image resolution, is locally adapted according to the available data. The system model is represented in the same basis as image elements and captures time of flight and positron range effects in an exact way. Computations use apodized B-spline approximations of Gaussians and simple closed-form analytical expressions without any sampling or interpolation. In consequence, the reconstructed image never suffers from spurious aliasing artifacts. Noiseless images of the XCAT brain phantom were reconstructed from simulated data. (orig.)
基于C-B样条的三角形和四边形曲面生成%Triangular and quadrilateral surface construction using C-B spline
Institute of Scientific and Technical Information of China (English)
李薇; 吴卓奇; 荻原一郎
2012-01-01
This paper provides a different solution to represent basic smooth elements like triangular and quadrilateral surface patches from mesh using C-B spline curves. C-B spline curves are developed by the basis {sin t, cos t, t, 1}, and it overcomes some shortcomings of the B-spline and non-uniform rational B-splines (NURBS) model, for example, they have to increase unnecessary control point in order to satisfy the data grid topology, their derivative and integral are complex and tedious, their degrees are too high, and it is difficult to discuss their continuous conditions. How to develop C-B spline curves into surface becomes an important problem. In this paper, the interpolation operators are constructed by using side-vertex method and a convex combination of these operators is achieved. The C-B spline curves are developed into triangular and quadrilateral surface patches which can be used in reverse engineering of CAD.%文章给出了基于C-B样条的由网格数据产生三角形和四边形曲面片的方法,C-B样条是由基底函数{sin t,cos t,t,1}导出的一种新型样条曲线,它可以克服现在正在使用的B样条和有理B样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就成为一个重要问题.作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将C-B样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD的逆向工程中散乱数据的曲面重构.
Energy Technology Data Exchange (ETDEWEB)
Linsen, L; Pascucci, V; Duchaineau, M A; Hamann, B; Joy, K I
2002-11-19
Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on 4{radical}2 subdivision. The n{radical}2-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lighting scheme based on n{radical}2 subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.
Dominant point detecting based non-uniform B-spline approximation for grain contour
Institute of Scientific and Technical Information of China (English)
ZHAO XiuYang; YIN YanSheng; YANG Bo
2007-01-01
Three-dimension reconstruction from serial sections has been used in the last decade to obtain information concerning three-dimensional microstructural geometry. One of the crucial steps of three-dimension reconstruction is getting compact and fairing grain contours. Based on the achievement of closed raw contours of ceramic composite grains by using wavelet and level set, an adaptive method is adopted for the polygonal approximation of the digitized raw contours. Instead of setting a fixed length of support region in advance, the novel method computes the suitable length of support region for each point to find the best estimated curvature. The dominant points are identified as the points with local maximum estimated curvatures. Periodic closed B-spline approximation is used to find the most compact B-spline grain boundary contours within the given tolerance. A flexible distance selection approach is adopted to obtain the common knot vector of serial contours consisting of less knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Finally, a B-spline surface interpolating the serial contours is generated via B-spline surface skinning.
Dominant point detecting based non-uniform B-spline approximation for grain contour
Institute of Scientific and Technical Information of China (English)
2007-01-01
Three-dimension reconstruction from serial sections has been used in the last decade to obtain information concerning three-dimensional microstructural ge-ometry. One of the crucial steps of three-dimension reconstruction is getting compact and fairing grain contours. Based on the achievement of closed raw con-tours of ceramic composite grains by using wavelet and level set, an adaptive method is adopted for the polygonal approximation of the digitized raw contours. Instead of setting a fixed length of support region in advance, the novel method computes the suitable length of support region for each point to find the best es-timated curvature. The dominant points are identified as the points with local maximum estimated curvatures. Periodic closed B-spline approximation is used to find the most compact B-spline grain boundary contours within the given tolerance. A flexible distance selection approach is adopted to obtain the common knot vector of serial contours consisting of less knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Finally, a B-spline surface interpolating the serial contours is generated via B-spline surface skinning.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
B-Spline with Symplectic Algorithm Method for Solution of Time-Dependent Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
BIAN Xue-Bin; QIAO Hao-Xue; SHI Ting-Yun
2006-01-01
@@ A B-spline with the symplectic algorithm method for the solution of time-dependent Schr(o)dinger equations(TDSEs) is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is given in a symplectic scheme.
A few remarks on recurrence relations for geometrically continuous piecewise Chebyshevian B-splines
Mazure, Marie-Laurence
2009-08-01
This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457-470, 2008) in which we showed that T. Lyche's recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155-178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences, T. Lyche's approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots. Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603-624, 2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35-78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller supports involved in the recurrence relations.
Shape Parameterization in Aircraft Design: A Novel Method, Based on B-Splines
Straathof, M.H.
2012-01-01
This thesis introduces a new parameterization technique based on the Class-Shape-Transformation (CST) method. The new technique consists of an extension to the CST method in the form of a refinement function based on B-splines. This Class-Shape-Refinement-Transformation (CSRT) method has the same ad
Study of Microwave Multiphoton Transition of Rydberg Potassium Atom by Using B-Spline
Institute of Scientific and Technical Information of China (English)
JIN Cheng; ZHOU Xiao-Xin; ZHAO Song-Feng
2005-01-01
The B-spline expansion technique and time-dependent two-level approach are applied to study the interaction between the microwave field and potassium atoms in a static electric field. We obtain theoretical multiphoton resonance spectra that can be compared with the experimental data. We also obtain the time evolution of the final state in different microwave fields.
Constructing iterative non-uniform B-spline curve and surface to fit data points
Institute of Scientific and Technical Information of China (English)
LIN Hongwei; WANG Guojin; DONG Chenshi
2004-01-01
In this paper, based on the idea of profit and loss modification, we present the iterative non-uniform B-spline curve and surface to settle a key problem in computer aided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We start with a piece of initial non-uniform B-spline curve (surface) which takes the given point set as its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higher precision. In this paper, using modern matrix theory, we strictly prove that the limit curve (surface) of the iteration interpolates the given point set. The non-uniform B-spline curves (surfaces) generated with the iteration have many advantages, such as satisfying the NURBS standard, having explicit expression, gaining locality, and convexity preserving,etc.
The use of B-splines in the assessment of strain levels associated with plain dents
Energy Technology Data Exchange (ETDEWEB)
Noronha Junior, Dauro B.; Martins, Ricardo R. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES); Jacob, Breno P.; Souza, Eduardo [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Civil. Lab. de Metodos Computacionais e Sistemas Offshore (LAMCSO)
2005-07-01
Most international pipeline codes consider plain dents injurious if they exceed a depth of 6% of the nominal pipe diameter. ASME B31.8 - Gas Transmission and Distribution Piping Systems - 2003 Edition gives an alternative to the above mentioned limit. According to this edition of the code, plain dents of any depth are acceptable provided strain levels associated with the deformation do not exceed 6% strain. In order to use the method for estimating strain in dents proposed in Appendix R of B31.8 Code, interpolation or other mathematical technique is usually necessary to develop surface contour information from in-line inspections (ILI) tools or direct information data. This paper describes the application of a piece-wise interpolating technique that makes use of fourth-order B-spline curves to approximating the dent profile in both longitudinal and circumferential directions. The results obtained using B-splines were tested against nonlinear finite analyses of dented pipelines and a distinct methodology proposed by Rosenfeld et al. (1998). The results obtained with the use of B-splines compared well with both techniques. Furthermore, the extension of the proposed methodology to the description of the topology of dents with more general shapes using B-spline surfaces is very promising. (author)
Numerical solution of Poisson equation by quintic B-spline interpolation%均匀二型剖分下的二元五次B样条基函数及其应用
Institute of Scientific and Technical Information of China (English)
张胜刚; 宋明威; 王仁宏; 李国荣; 唐晓; 刘启贵
2012-01-01
1975年王仁宏建立了任意剖分下多元样条函数的基本理论框架,即所谓光滑余因子方法.多元样条在函数逼近、计算机辅助几何设计、有限元及小波等领域中均有重要的应用.由于某些特殊剖分如均匀剖分的可研究性,1984年王仁宏给出均匀二型剖分下的二元三次一阶光滑样条空间S1((△(2)mn))的维数及其B样条基函数,在计算机辅助几何设计,微分方程数值解等方面应用广泛.在研究光滑余因子方法的基础上,分析均匀二型剖分下的二元五次三阶光滑样条空间(S35)((△(2)mn))函数空间,给出了(S35)((△(2)mn))的维数及其B样条基函数,满足曲面拟合和微分方程数值解等应用中对更高阶光滑性的要求.基于该组基函数,提出一种Poisson方程的数值解方法,通过数值实例检验该方法的精度.%Multivariate splines have wide applications in approximation theory, computer aided geometric design(CAGD) and finite element method. In 1975, Ren-Hong Wang established a new approach to study the basic theory on multivariate spline functions on arbitrary partition by presenting the so called Smoothing cofactor-conformality method. As the large applications in CAGD et al. , Ren-Hong Wang discussed the dimension and B-spline basis of the C1 cubic spline spaces on type-2 triangulation partition, which is denoted by S31(△(2)mn). Accordingly we analyze the C3 quintic spline spaces on type-2 triangulation partition S53 (△(2)mn). The dimension and one group of B spline basis of S53(△(2)mn)are given. High derivatives is satisfied in applications. Based on the basis one numerical scheme is proposed to simulate the Poisson equation. Numerical examples are given to show the validity of the scheme.
均匀B样条曲线曲面的小波表示%Wavelets-Based Representation of Uniform B-Spline Curves and Surfaces
Institute of Scientific and Technical Information of China (English)
赵罡; 穆国旺; 闫光荣; 朱心雄
2001-01-01
Wavelets-based representation provides a more flexible method for expressing curves and surfaces in different resolution levels. For uniform B-spline curves and surfaces, a unified expression can be adopted after decomposition to describe the wavelets for the interior and boundaries of the domain defined, and hence the multiplication is the only operation be needed to wavelets reconstruction. This results in high efficiency for the computation. The paper describes, from the point of geometry view, the principles and methods of realizing wavelets-based multiresolution representation of uniform cubic B-spline curves and surfaces.%小波基为曲线曲面带来了更为灵活的表达方式。均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式，在进行小波重构时仅需作乘法运算，计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。
Durmaz, Murat; Karslioglu, Mahmut Onur
2015-04-01
There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.
Geometry Modeling of Ship Hull Based on Non-uniform B-spline
Institute of Scientific and Technical Information of China (English)
WANG Hu; ZOU Zao-jian
2008-01-01
In order to generate the three-dimensional (3-D) hull surface accurately and smoothly, a mixed method which is made up of non-uniform B-spline together with an iterative procedure was developed. By using the iterative method the data points on each section curve are calculated and the generalized waterlines and transverse section curves are determined. Then using the non-uniform B-spline expression, the control vertex net of the hull is calculated based on the generalized waterlines and section curves. A ship with tunnel stern was taken as test case. The numerical results prove that the proposed approach for geometry modeling of 3-D ship hull surface is accurate and effective.
Non-Rigid Image Registration Algorithm Based on B-Splines Approximation
Institute of Scientific and Technical Information of China (English)
ZHANG Hongying; ZHANG Jiawan; SUN Jizhou; SUN Yigang
2007-01-01
An intensity-based non-rigid registration algorithm is discussed, which uses Gaussian smoothing to constrain the transformation to be smooth, and thus preserves the topology of images. In view of the insufficiency of the uniform Gaussian filtering of the deformation field, an automatic and accurate non-rigid image registration method based on B-splines approximation is proposed. The regularization strategy is adopted by using multi-level B-splines approximation to regularize the dis-placement fields in a coarse-to-fine manner. Moreover, it assigns the different weights to the estimated displacements according to their reliabilities. In this way, the level of regularity can be adapted locally. Experiments were performed on both synthetic and real medical images of brain, and the results show that the proposed method improves the registration accuracy and robustness.
Left ventricular motion reconstruction with a prolate spheroidal B-spline model
Energy Technology Data Exchange (ETDEWEB)
Li Jin; Denney, Thomas S Jr [Electrical and Computer Engineering Department, 200 Broun Hall, Auburn University, AL 36849-5201 (United States)
2006-02-07
Tagged cardiac magnetic resonance (MR) imaging can non-invasively image deformation of the left ventricular (LV) wall. Three-dimensional (3D) analysis of tag data requires fitting a deformation model to tag lines in the image data. In this paper, we present a 3D myocardial displacement and strain reconstruction method based on a B-spline deformation model defined in prolate spheroidal coordinates, which more closely matches the shape of the LV wall than existing Cartesian or cylindrical coordinate models. The prolate spheroidal B-spline (PSB) deformation model also enforces smoothness across and can compute strain at the apex. The PSB reconstruction algorithm was evaluated on a previously published data set to allow head-to-head comparison of the PSB model with existing LV deformation reconstruction methods. We conclude that the PSB method can accurately reconstruct deformation and strain in the LV wall from tagged MR images and has several advantages relative to existing techniques.
Left ventricular motion reconstruction with a prolate spheroidal B-spline model
Li, Jin; Denney, Thomas S., Jr.
2006-02-01
Tagged cardiac magnetic resonance (MR) imaging can non-invasively image deformation of the left ventricular (LV) wall. Three-dimensional (3D) analysis of tag data requires fitting a deformation model to tag lines in the image data. In this paper, we present a 3D myocardial displacement and strain reconstruction method based on a B-spline deformation model defined in prolate spheroidal coordinates, which more closely matches the shape of the LV wall than existing Cartesian or cylindrical coordinate models. The prolate spheroidal B-spline (PSB) deformation model also enforces smoothness across and can compute strain at the apex. The PSB reconstruction algorithm was evaluated on a previously published data set to allow head-to-head comparison of the PSB model with existing LV deformation reconstruction methods. We conclude that the PSB method can accurately reconstruct deformation and strain in the LV wall from tagged MR images and has several advantages relative to existing techniques.
Ship hull plate processing surface fairing with constraints based on B-spline
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.
B-Spline Active Contour with Handling of Topology Changes for Fast Video Segmentation
Directory of Open Access Journals (Sweden)
Frederic Precioso
2002-06-01
Full Text Available This paper deals with video segmentation for MPEG-4 and MPEG-7 applications. Region-based active contour is a powerful technique for segmentation. However most of these methods are implemented using level sets. Although level-set methods provide accurate segmentation, they suffer from large computational cost. We propose to use a regular B-spline parametric method to provide a fast and accurate segmentation. Our B-spline interpolation is based on a fixed number of points 2j depending on the level of the desired details. Through this spatial multiresolution approach, the computational cost of the segmentation is reduced. We introduce a length penalty. This results in improving both smoothness and accuracy. Then we show some experiments on real-video sequences.
River Flow Lane Detection and Kalman Filtering-Based B-Spline Lane Tracking
Directory of Open Access Journals (Sweden)
King Hann Lim
2012-01-01
Full Text Available A novel lane detection technique using adaptive line segment and river flow method is proposed in this paper to estimate driving lane edges. A Kalman filtering-based B-spline tracking model is also presented to quickly predict lane boundaries in consecutive frames. Firstly, sky region and road shadows are removed by applying a regional dividing method and road region analysis, respectively. Next, the change of lane orientation is monitored in order to define an adaptive line segment separating the region into near and far fields. In the near field, a 1D Hough transform is used to approximate a pair of lane boundaries. Subsequently, river flow method is applied to obtain lane curvature in the far field. Once the lane boundaries are detected, a B-spline mathematical model is updated using a Kalman filter to continuously track the road edges. Simulation results show that the proposed lane detection and tracking method has good performance with low complexity.
Introduction of b-splines to trajectory planning for robot manipulators
Directory of Open Access Journals (Sweden)
Per E. Koch
1988-04-01
Full Text Available This paper describes how B-splines can be used to construct joint trajectories for robot manipulators. The motion is specified by a sequence of Cartesian knots, i.e., positions and orientations of the end effector of a robot manipulator. For a six joint robot manipulator, these Cartesian knots are transformed into six sets of joint variables, with each set corresponding to a joint. Splines, represented as linear combinations of B-splines, are used to fit the sequence of joint variables for each of the six joints. A computationally very simple, recurrence formula is used to generate the 8-splines. This approach is used for the first time to establish the mathematical model of trajectory generation for robot manipulators, and offers flexibility, computational efficiency, and a compact representation.
双二次B-样条插值图像缩放%Image resizing via bi-quadratic B-spline interpolation
Institute of Scientific and Technical Information of China (English)
李英明; 夏海宏
2011-01-01
双线性和各种双三次插值方法是图像缩放中常用方法,但是双二次插值函数却很少被人提起.本文提出了一种基于双二次B-样条局部插值的图像缩放方法,该算法在图像局部重构过程中对称地采用了4×4采样点,并通过对该函数进行重采样来实现图像的缩放,避免了二次函数在图像重构与采样中的相位失真问题,此算法是一个局部性算法,易于扩展.实验结果表明,本文算法得到的图像的峰值信噪比(PSNR)、MISSIM值比双线性插值、双三次卷积、Catmull-Rom三次插值、Dodgson插值算法都要好,接近于最好的双三次B-样条算法,视觉效果虽然不如双三次B-样条插值算法,但优于Dodgson方法,计算时间比双三次B-样条减少了近三分之一.由于该算法没有对图像边缘特征进行特殊处理,对于一些细节纹理比较丰富的图像,将进一步研究.%Bilinear interpolation and various bi-cubic interpolations are frequently adopted in image resizing. However the biquadratic function is rarely considered due to its phase distortion problem. In this paper, we propose an image resizing method via bi-quadratic B-spline interpolation, where 4x4 pixels are sampled symmetrically in the local image. The proposed algorithm is a local algorithm and can be easily extended. According to our experiment results, the proposed bi-quadratic B-spline interpolation algorithm has better image peak signal-to-noise ratio ( PSNR) and MISSIM than bi-linear interpolation, bi-cubic convolution, Catmull-Rom cubic interpolation, or the Dodgson interpolation algorithm. The results are comparable to the bi-cubic B-spline interpolation algorithm, though the visual effects are not as good as that, but still better than the Dodgson algorithm. The computing time is reduced by nearly one-third compared to the bi-cubic B-spline interpolation algorithm. Since the algorithm has not carried on the special handling to the image edge features
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
An efficient active B-spline/nurbs model for virtual sculpting
Moore, Patricia
2013-01-01
This thesis presents an Efficient Active B-Spline/Nurbs Model for Virtual Sculpting. In spite of the on-going rapid development of computer graphics and computer-aided design tools, 3D graphics designers still rely on non-intuitive modelling procedures for the creation and manipulation of freeform virtual content. The ’Virtual Sculpting' paradigm is a well-established mechanism for shielding designers from the complex mathematics that underpin freeform shape design. The premise is to emulate ...
B-spline soliton solution of the fifth order KdV type equations
Zahra, W. K.; Ouf, W. A.; El-Azab, M. S.
2013-10-01
In this paper, we develop a numerical solution based on sextic B-spline collocation method for solving the generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.
Generalized b-spline subdivision-surface wavelets and lossless compression
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Duchaineau, M A; Hamann, B; Joy, K I
1999-11-24
We present a new construction of wavelets on arbitrary two-manifold topology for geometry compression. The constructed wavelets generalize symmetric tensor product wavelets with associated B-spline scaling functions to irregular polygonal base mesh domains. The wavelets and scaling functions are tensor products almost everywhere, except in the neighborhoods of some extraordinary points (points of valence unequal four) in the base mesh that defines the topology. The compression of arbitrary polygonal meshes representing isosurfaces of scalar-valued trivariate functions is a primary application. The main contribution of this paper is the generalization of lifted symmetric tensor product B-spline wavelets to two-manifold geometries. Surfaces composed of B-spline patches can easily be converted to this scheme. We present a lossless compression method for geometries with or without associated functions like color, texture, or normals. The new wavelet transform is highly efficient and can represent surfaces at any level of resolution with high degrees of continuity, except at a finite number of extraordinary points in the base mesh. In the neighborhoods of these points detail can be added to the surface to approximate any degree of continuity.
Geometric Hermite Interpolation for Space Curves by B-Spline%空间曲线几何Hermite插值的B样条方法
Institute of Scientific and Technical Information of China (English)
朱春钢; 王仁宏
2005-01-01
在给定的GC2插值条件,利用de Boor的构造平面曲线的GC2-Hermite插值方法,构造了一条具有两个自由度的三次B样条插值曲线,并证明插值曲线是局部存在的且具有4阶精度.%This paper considers the space GC2 Hermite interpolation by cubic B-spline curve which is based on de Boor's idea for constructing the planar GC2 Hermite interpolation. In addition to position and tangent direction, the curvature vector is interpolated at each point. It is proved that under appropriate assumptions the interpolant exists locally with two degrees of freedom and the 4th order accuracy.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
M. D. Landon; R. W. Johnson
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Johnson, Richard Wayne; Landon, Mark Dee
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
Energy Technology Data Exchange (ETDEWEB)
McCurdy, C. William; Horner, Daniel A.; Rescigno, Thomas N.; Martin, Fernando
2004-02-19
Calculations of absolute triple differential and single differential cross sections for helium double photoionization are performed using an implementation of exterior complex scaling in B-splines. Results for cross sections, well-converged in partial waves, are presented and compared with both experiment and earlier theoretical calculations. These calculations establish the practicality and effectiveness of the complex B-spline approach to calculations of double ionization of atomic and molecular systems.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Johnson, Richard Wayne; Landon, Mark Dee
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
M. D. Landon; R. W. Johnson
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
Local-basis-function approach to computed tomography
Hanson, K. M.; Wecksung, G. W.
1985-12-01
In the local basis-function approach, a reconstruction is represented as a linear expansion of basis functions, which are arranged on a rectangular grid and possess a local region of support. The basis functions considered here are positive and may overlap. It is found that basis functions based on cubic B-splines offer significant improvements in the calculational accuracy that can be achieved with iterative tomographic reconstruction algorithms. By employing repetitive basis functions, the computational effort involved in these algorithms can be minimized through the use of tabulated values for the line or strip integrals over a single-basis function. The local nature of the basis functions reduces the difficulties associated with applying local constraints on reconstruction values, such as upper and lower limits. Since a reconstruction is specified everywhere by a set of coefficients, display of a coarsely represented image does not require an arbitrary choice of an interpolation function.
PREDICTION AND CALCULATION OF AZEOTROPIC’S BEHAVIOURS ON THE BASIS OF CUBIC EQUATION OF STATE
Троценко, А. В.
2015-01-01
The azeotropic binary mixtures are effective working substances for various refrigerators, including low-temperature ones. Their experimental finding and investigation is the complicated and labour-intensive problem. That problemrestrains more practical application of azeotropic mixtures in cooling systems. The problems of prediction and modeling of azeotropic behaviours with the help of two-parametric cubic equations of a state are considered. Using the maxwell line method, the conditions of...
Data assimilation using Bayesian filters and B-spline geological models
Duan, Lian
2011-04-01
This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir.
Two kinds of quadratic trigonometric B-spline curves with uniform knot vectors%均匀结点情形下的两类二阶三角B-样条曲线
Institute of Scientific and Technical Information of China (English)
王晶昕; 王迪
2014-01-01
Two kinds of quadratic trigonometric B-spline basis functions with uniform knot vectors are presented in this paper ,their constructions and properties are analyzed .These two kinds of functions can be used to construct trigonometric B-spline functions and trigonometric B-spline curves .Every segment of the first kind of curves is determined by three control points w hen every segment of the second kind of curves is determined by four control points .The properties of the two kinds of curves and the relationship between them are discussed .The cases of multiple knots of the first kind of basis functions are defined ,and we show how the curves like in this situation .The comparisons of the one order trigonometric B-spline curves and the quadratic trigonometric spline curves are presented in this paper .We came to a conclusion that the quadratic trigonometric B-spline curves are closer to the con-trol polygon than the one order trigonometric B-spline curves .%给出两类均匀结点情形下二阶三角B-样条基函数的定义，分析它们的构造过程，性质，并分别用其生成二阶三角B-样条函数和二阶三角B-样条曲线。其中第一类曲线是三点分段的，即由前后相继3个控制点决定一段曲线，与二阶B-样条曲线类似，第二类曲线是四点分段的，即由前后相继4个控制点决定一段曲线，与三阶B-样条曲线类似。讨论这两类曲线的性质及它们之间的关系。针对第一类曲线，还给出了重结点情形下基函数的定义并分析了这种情形下曲线的情况。将第一类二阶三角B-样条曲线与一阶三角B-样条曲线进行了对比，得出相同结点向量下，二阶三角B-样条曲线更加接近控制多边形的结论。
B-Spline Filtering for Automatic Detection of Calcification Lesions in Mammograms
Bueno, G.; Sánchez, S.; Ruiz, M.
2006-10-01
Breast cancer continues to be an important health problem between women population. Early detection is the only way to improve breast cancer prognosis and significantly reduce women mortality. It is by using CAD systems that radiologist can improve their ability to detect, and classify lesions in mammograms. In this study the usefulness of using B-spline based on a gradient scheme and compared to wavelet and adaptative filtering has been investigated for calcification lesion detection and as part of CAD systems. The technique has been applied to different density tissues. A qualitative validation shows the success of the method.
System identification of Wiener systems with B-spline functions using De Boor recursion
Hong, X.; Mitchell, R. J.; Chen, S.
2013-09-01
In this article a simple and effective algorithm is introduced for the system identification of the Wiener system using observational input/output data. The nonlinear static function in the Wiener system is modelled using a B-spline neural network. The Gauss-Newton algorithm is combined with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialisation scheme. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.
Energy Technology Data Exchange (ETDEWEB)
Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael
2000-04-11
A common problem in signal processing is to estimate the structure of an object from noisy measurements linearly related to the desired image. These problems are broadly known as inverse problems. A key feature which complicates the solution to such problems is their ill-posedness. That is, small perturbations in the data arising e.g. from noise can and do lead to severe, non-physical artifacts in the recovered image. The process of stabilizing these problems is known as regularization of which Tikhonov regularization is one of the most common. While this approach leads to a simple linear least squares problem to solve for generating the reconstruction, it has the unfortunate side effect of producing smooth images thereby obscuring important features such as edges. Therefore, over the past decade there has been much work in the development of edge-preserving regularizers. This technique leads to image estimates in which the important features are retained, but computationally the y require the solution of a nonlinear least squares problem, a daunting task in many practical multi-dimensional applications. In this thesis we explore low-order models for reducing the complexity of the re-construction process. Specifically, B-Splines are used to approximate the object. If a ''proper'' collection B-Splines are chosen that the object can be efficiently represented using a few basis functions, the dimensionality of the underlying problem will be significantly decreased. Consequently, an optimum distribution of splines needs to be determined. Here, an adaptive refining and pruning algorithm is developed to solve the problem. The refining part is based on curvature information, in which the intuition is that a relatively dense set of fine scale basis elements should cluster near regions of high curvature while a spares collection of basis vectors are required to adequately represent the object over spatially smooth areas. The pruning part is a greedy
An Improved Method for Airfoil Parameterization by B-Spline%一种改进的B样条翼型参数化方法
Institute of Scientific and Technical Information of China (English)
张骥; 朱春钢; 冯仁忠; 刘明明; 张恒洋
2016-01-01
翼型设计是空气动力学研究的一项重要内容，翼型的参数化结果将影响翼型的优化设计。为了减少翼型优化中的设计变量，保证优化结果的光滑性与C2连续，在优化过程中控制翼型几何特性的变化范围，提出了一种改进的B样条参数化方法。用一条三次非均匀B样条曲线表示翼型，翼型数据的参数化过程中主要运用了B样条曲线拟合算法，并且在一般的B样条曲线拟合算法的基础上加入了对曲线的法向约束，通过迭代得到最终的参数化结果。实验结果表明，该方法可以很好的拟合典型的翼型数据，得到的翼型参数化结果不仅光滑，满足 C2条件，而且所得翼型函数的参数个数比传统的参数化方法有了进一步的减少，更有利于之后翼型的优化设计。%Airfoil design is a crucial issue of aerodynamic research, the parameterization of airfoil will affect the airfoil optimization design. In order to reduce the number of variables in the airfoil optimization, eliminate the unfairness phenomenon, preserve theC2 continuity condition, and control the geometric characteristics of the airfoil in the optimization process, in this paper, we present an improved method for airfoil parameterization by B-spline. The method represents airfoil by a cubic non-uniform B-spline curve. Fitting of airfoil data by B-spline curve is mainly by least square method and the normal constraints. And the final result is obtained by iteration. Experiments show that the proposed method can be well fitted to the typical airfoil data, the resulting curve is fair andC2 continuity, and has few parameters of airfoil function compared with the classical airfoil parametric methods.
Harmening, Corinna; Neuner, Hans
2016-09-01
Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.
B-splines as a Tool to Solve Constraints in Non-Hydrostatic Forecast Model
Subias, Alvaro
2016-01-01
Finite elements has been proven to be an useful tool to discretize the vertical coordinate in the hydrostatic forecast models allowing to define model variables in full levels so that no staggering is needed. In the non-hydrostatic case a constraint in the vertical operators appears (called C1) that does not allow to reduce the set of semi-implicit linear equations to a single equation in one variable as in the analytic case. Recently vertical finite elements based in B-splines have been used with an iterative method to relax the C1 constraint. In this paper we want to develop properly some representations of vertical operators in terms of B-splines in order to keep the C1-constraint. An invertibility relation between integral and derivative operators between vertical velocity and vertical divergence is also presented. The final scope of this paper is to provide a theoretical framework of development of finite element vertical operators to be implemented in the nh-Harmonie model
Marghany, Maged
2014-06-01
A critical challenges in urban aeras is slums. In fact, they are considered a source of crime and disease due to poor-quality housing, unsanitary conditions, poor infrastructures and occupancy security. The poor in the dense urban slums are the most vulnerable to infection due to (i) inadequate and restricted access to safety, drinking water and sufficient quantities of water for personal hygiene; (ii) the lack of removal and treatment of excreta; and (iii) the lack of removal of solid waste. This study aims to investigate the capability of ENVISAT ASAR satellite and Google Earth data for three-dimensional (3-D) slum urban reconstruction in developed countries such as Egypt. The main objective of this work is to utilize some 3-D automatic detection algorithm for urban slum in ENVISAT ASAR and Google Erath images were acquired in Cairo, Egypt using Fuzzy B-spline algorithm. The results show that the fuzzy algorithm is the best indicator for chaotic urban slum as it can discriminate between them from its surrounding environment. The combination of Fuzzy and B-spline then used to reconstruct 3-D of urban slum. The results show that urban slums, road network, and infrastructures are perfectly discriminated. It can therefore be concluded that the fuzzy algorithm is an appropriate algorithm for chaotic urban slum automatic detection in ENVSIAT ASAR and Google Earth data.
Non-Stationary Hydrologic Frequency Analysis using B-Splines Quantile Regression
Nasri, B.; St-Hilaire, A.; Bouezmarni, T.; Ouarda, T.
2015-12-01
Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic structures and water resources system under the assumption of stationarity. However, with increasing evidence of changing climate, it is possible that the assumption of stationarity would no longer be valid and the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extreme flows based on B-Splines quantile regression, which allows to model non-stationary data that have a dependence on covariates. Such covariates may have linear or nonlinear dependence. A Markov Chain Monte Carlo (MCMC) algorithm is used to estimate quantiles and their posterior distributions. A coefficient of determination for quantiles regression is proposed to evaluate the estimation of the proposed model for each quantile level. The method is applied on annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in these variables and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for annual maximum and minimum discharge with high annual non-exceedance probabilities. Keywords: Quantile regression, B-Splines functions, MCMC, Streamflow, Climate indices, non-stationarity.
Adaptive sampling for real-time rendering of large terrain based on B-spline wavelet
Kalem, Sid Ali; Kourgli, Assia
2017-05-01
This paper describes a central processing unit (CPU)-based technique for terrain geometry rendering that could relieve graphics processing unit (GPU) from processing the appropriate level of detail (LOD) of the geometric surface. The proposed approach alleviates the computational load on the CPU and approaches GPU-based efficiency. As the datasets of realistic terrains are usually huge for real-time rendering, we suggest using a training stage to handle large tiled QuadTree terrain representation. The training stage is based on multiresolution wavelet decomposition and is used to limit the region of error control inside the tile. Maximum approximation errors are then calculated for each tile at different resolutions. Maximum world-space errors of the tile at different resolutions permit selection of the appropriate resolution of downsampling that will represent the tile at the run time. Tests and experiments demonstrate that B-spline 0 and B-spline 1 wavelets, well known for their properties of localization and their compact support, are suitable for fast and accurate localization of the maximum approximation error. The experimental results demonstrate that the proposed approach drastically reduces computation time in the CPU. Such a technique should also be used on low/medium end PCs, and embedded systems that are not equipped with the latest models of graphic hardware.
Generalized B-spline subdivision-surface wavelets for geometry compression.
Bertram, Martin; Duchaineau, Mark A; Hamann, Bernd; Joy, Kenneth I
2004-01-01
We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail can be expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-Spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform can be computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
G1 Continuity Conditions of B-spline Surfaces%B样条曲面间的G1连续条件
Institute of Scientific and Technical Information of China (English)
车翔玖; 梁学章
2002-01-01
According to the B-spline theory and Boehm algorithm, this paper presents severalnecessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In orderto meet the need of application, a kind of sufficient conditions of G1 continuity are developed, anda kind of sufficient conditions of G1 continuity among N(N ＞ 2) patch B-spline surfaces meetingat a common corner are given at the end.
Analysis of a Gyroscope's Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM
Institute of Scientific and Technical Information of China (English)
LIU Jian-feng; YUAN Gan-nan; HUANG Xu; YU Li
2005-01-01
A supported framework of a gyroscope′s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedron. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.
Likhachev, Dmitriy V.
2017-06-01
Johs and Hale developed the Kramers-Kronig consistent B-spline formulation for the dielectric function modeling in spectroscopic ellipsometry data analysis. In this article we use popular Akaike, corrected Akaike and Bayesian Information Criteria (AIC, AICc and BIC, respectively) to determine an optimal number of knots for B-spline model. These criteria allow finding a compromise between under- and overfitting of experimental data since they penalize for increasing number of knots and select representation which achieves the best fit with minimal number of knots. Proposed approach provides objective and practical guidance, as opposite to empirically driven or "gut feeling" decisions, for selecting the right number of knots for B-spline models in spectroscopic ellipsometry. AIC, AICc and BIC selection criteria work remarkably well as we demonstrated in several real-data applications. This approach formalizes selection of the optimal knot number and may be useful in practical perspective of spectroscopic ellipsometry data analysis.
AHT Bézier Curves and NUAHT B-Spline Curves
Institute of Scientific and Technical Information of China (English)
Gang Xu; Guo-Zhao Wang
2007-01-01
In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric ( AHT) Bézier curves and non-uniform algebraic hyperbolic trigonometric ( NUAHT) B-sptine curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., tn-5}, n ≥ 5. The two kinds of curves share most of the properties as those of the Bézier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method
Directory of Open Access Journals (Sweden)
Zhibo Yang
2014-01-01
Full Text Available A B-spline wavelet on interval (BSWI finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.
Frequency-modulated excitation of Rydberg potassium atoms by using B-spline
Institute of Scientific and Technical Information of China (English)
Li Xiao-Yong; Wang Guo-Li; Zhou Xiao-Xin
2012-01-01
By using the B-spline expansion technique and a model potential of the alkali atoms,the properties of frequencymodulated excitation of Rydberg potassium atoms in a static electric field and a microwave field are investigated by using the time-dependent two-level approach.We successfully reproduce the square wave oscillations in the low frequency,the stair step population oscillations in the intermediate frequency,and the multiphoton transitions in the high frequency with respect to the unmodulated Rabi frequency,which have been observed experimentally by Noel et al.[Phys.Rev.A 58 2265 (1998)].Furthermore,we also numerically obtain the discretized Rabi oscillations predicted in the Landau-Zener accumulation model.
Collocation method with quintic b-spline method for solving hirota-satsuma coupled KDV equation
Directory of Open Access Journals (Sweden)
K. R. Raslan
2016-05-01
Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled system of KdV (CKdV equation with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms, are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.
Vibration analysis of composite pipes using the finite element method with B-spline wavelets
Energy Technology Data Exchange (ETDEWEB)
Oke, Wasiu A.; Khulief, Yehia A. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2016-02-15
A finite element formulation using the B-spline wavelets on the interval is developed for modeling the free vibrations of composite pipes. The composite FRP pipe element is treated as a beam element. The finite pipe element is constructed in the wavelet space and then transformed to the physical space. Detailed expressions of the mass and stiffness matrices are derived for the composite pipe using the Bspline scaling and wavelet functions. Both Euler-Bernoulli and Timoshenko beam theories are considered. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the composite pipe. The developed wavelet-based finite element discretization scheme utilizes significantly less elements compared to the conventional finite element method for modeling composite pipes. Numerical solutions are obtained to demonstrate the accuracy of the developed element, which is verified by comparisons with some available results in the literature.
Magnetotelluric (MT) data smoothing based on B-Spline algorithm and qualitative spectral analysis
Handyarso, Accep; Grandis, Hendra
2017-07-01
Data processing is one of the essential steps to obtain optimum response function of the Earth's subsurface. The MT Data processing is based on the Fast Fourier Transform (FFT) algorithm which converts the time series data into its frequency domain counterpart. The FFT combined with statistical algorithm constitute the Robust Processing algorithm which is widely implemented in MT data processing software. The Robust Processing has three variants, i.e. No Weight (NW), Rho Variance (RV), and Ordinary Coherency (OC). The RV and OC options allow for denoising the data but in many cases the Robust Processing still results in not so smooth sounding curve due to strong noise presence during measurement, such that the Crosspower (XPR) analysis must be conducted in the data processing. The XPR analysis is very time consuming step within the data processing. The collaboration of B-Spline algorithm and Qualitative Spectral Analysis in the frequency domain could be of advantages as an alternative for these steps. The technique is started by using the best coherency from the Robust Processing results. In the Qualitative Spectral Analysis one can determine which part of the data based on frequency that is more or less reliable, then the next process invokes B-Spline algorithm for data smoothing. This algorithm would select the best fit of the data trend in the frequency domain. The smooth apparent resistivity and phase sounding curves can be considered as more appropriate to represent the subsurface. This algorithm has been applied to the real MT data from several survey and give satisfactory results.
A family of quasi-cubic blended splines and applications
Institute of Scientific and Technical Information of China (English)
SU Ben-yue; TAN Jie-qing
2006-01-01
A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter α, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter α, where dpi(α,t) is linear with respect to dα for the fixed t. With the shape parameter chosen properly,the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
A cubic interpolation pipeline for fast computation of 3D deformation fields modeled using B-splines
Castro-Pareja, Carlos R.; Shekhar, Raj
2006-02-01
Fast computation of 3D deformation fields is critical to bringing the application of automated elastic image registration algorithms to routine clinical practice. However, it lies beyond the computational power of current microprocessors; therefore requiring implementations using either massively parallel computers or application-specific hardware accelerators. The use of massively parallel computers in a clinical setting is not practical or cost-effective, therefore making the use of hardware accelerators necessary. We present a hardware pipeline that allows accelerating the computation of 3D deformation fields to speeds up to two orders of magnitude faster than software implementations on current workstations and about 64 times faster than other previously reported architectures. The pipeline implements a version of the free-form deformation calculation algorithm, which is optimized to minimize the number of arithmetic operations required to calculate the transformation of a given set of neighboring voxels, thereby achieving an efficient and compact implementation in hardware which allows its use as part of a larger system.
Directory of Open Access Journals (Sweden)
Shanshan He
2015-10-01
Full Text Available Piecewise linear (G01-based tool paths generated by CAM systems lack G1 and G2 continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1 an improved technique for initial control point determination over Dominant Point Method, (2 an algorithm that updates foot point parameters as needed, (3 analysis of the degrees of freedom of control points to insert new control points only when needed, (4 chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution.
基于B样条空间等距线的机器人轨迹优化算法%Robot Trajectory Optimization Algorithm Based on Spatial Offset B-Spline
Institute of Scientific and Technical Information of China (English)
胡绳荪; 庹宇鲲; 申俊琦; 陈昌亮; 谷文; 李坚
2015-01-01
针对J形坡口焊接机器人轨迹示教中理论轨迹与实际轨迹偏差较大的问题,利用实际轨迹的空间等距线逼近下一道焊接轨迹,并设计了相贯线轨迹等距线的B样条逼近算法. 算法主要包括:基于等曲线弧长准则对原B样条曲线取样;利用向心算法计算取样点的等距点;计算插值于该等距点的3次B样条曲线;在给定的全局误差限内去除多余控制顶点. 试验结果表明:等距点的向心算法可以有效解决相贯线曲线局部修改后主法向量发散的问题;全局插值方法可以保留原曲线修改特征;全局误差限下去除多余控制顶点可以减少B样条曲线控制顶点数目.%For the problem of the large deviation between the theoretical trajectory and the real trajectory of the J-groove joint welding robot during trajectory teaching, a solution is proposed using the offset spline of the real trajec-tory to approximate the next welding trajectory. An approximation algorithm for offset B-spline of intersecting splines is designed, which includes the following steps: sampling the original B-spline with the uniform curve arc length crite-rion; calculating the offset points of the sample points with the centripetal algorithm; fitting a cubic B-spline with global interpolation; removing most control points under the global error bound. The experimental results are as fol-lows: the centripetal algorithm could solve the problem of the divergence of the principal normal vectors after local modification on the intersecting curve; the algorithm of global interpolating could retain the modification features of the original trajectory; the algorithm of removing control points under global error bound could remove most control points effectively and reduce the number of control points of B-spline.
基于小波的B样条曲线多分辨表示及编辑%Wavelets-Based Multiresolution Representation and Edit of B-Spline Curves
Institute of Scientific and Technical Information of China (English)
赵罡; 朱心雄
2001-01-01
Multiresolution representation provides a more flexible approach to edit curves and surfaces in different resolution levels. The paper describes, from the viewpoint of geometry, the principles and methods of realizing wavelets-based multiresolution representation of quasi-uniform cubic B-spline curves. An example is given to illustrate the editing of B-spline curves in multiresolution level.%多分辨表示方法为曲线提供了更为灵活的表达方式，使得我们可以在不同分辨率下对曲线进行编辑.小波技术是实现曲线多分辨表示的一种新颖方法，已有许多论文从理论上论述了这项技术.文中从几何概念出发,由浅入深地论述了基于小波的准均匀三次B样条曲线多分辨表示的原理及其实现，并通过实例描述了B样条曲线的多分辨编辑.
Hardy, David J; Wolff, Matthew A; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D
2016-03-21
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.
CT segmentation of dental shapes by anatomy-driven reformation imaging and B-spline modelling.
Barone, S; Paoli, A; Razionale, A V
2016-06-01
Dedicated imaging methods are among the most important tools of modern computer-aided medical applications. In the last few years, cone beam computed tomography (CBCT) has gained popularity in digital dentistry for 3D imaging of jawbones and teeth. However, the anatomy of a maxillofacial region complicates the assessment of tooth geometry and anatomical location when using standard orthogonal views of the CT data set. In particular, a tooth is defined by a sub-region, which cannot be easily separated from surrounding tissues by only considering pixel grey-intensity values. For this reason, an image enhancement is usually necessary in order to properly segment tooth geometries. In this paper, an anatomy-driven methodology to reconstruct individual 3D tooth anatomies by processing CBCT data is presented. The main concept is to generate a small set of multi-planar reformation images along significant views for each target tooth, driven by the individual anatomical geometry of a specific patient. The reformation images greatly enhance the clearness of the target tooth contours. A set of meaningful 2D tooth contours is extracted and used to automatically model the overall 3D tooth shape through a B-spline representation. The effectiveness of the methodology has been verified by comparing some anatomy-driven reconstructions of anterior and premolar teeth with those obtained by using standard tooth segmentation tools. Copyright © 2015 John Wiley & Sons, Ltd.
Bayesian discharge rating curves based on B-spline smoothing functions
Directory of Open Access Journals (Sweden)
K. M. Ingimarsson
2010-05-01
Full Text Available Discharge in rivers is commonly estimated by the use of a rating curve constructed from pairs of measured water elevations and discharges at a specific location. The Bayesian approach has been successfully applied to estimate discharge rating curves that are based on the standard power-law. In this paper the standard power-law model is extended by adding a B-spline function. The extended model is compared to the standard power-law model by applying the models to discharge data sets from sixty one different rivers. In addition four rivers are analyzed in detail to demonstrate the benefit of the extended model. The models are compared using two measures, the Deviance Information Criterion (DIC and Bayes factor. The former provides robust comparison of fit adjusting for the different complexity of the models and the latter measures the evidence of one model against the other. The extended model captures deviations in the data from the standard power-law but reduces to the standard power-law when that model is adequate. The extended model provides substantially better fit than the standard power-law model for about 30% of the rivers and performs better for 60% of the rivers when extrapolating large discharge values.
Quartic B-spline collocation method applied to Korteweg de Vries equation
Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md
2014-07-01
The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+ɛuux+μuxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L∞-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L∞-norm are also increase.
Estimating kinetic parameters in TGA using B-spline smoothing and the Friedman method
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xiaojie; Preto, Fernando [CANMET Energy Technology Centre (CETC), Natural Resources (Canada); de Jong, Wiebren [Faculty 3mE, Department of Process and Energy, ET Section, Delft University of Technology, Leeghwaterstraat 44, 2628 CD Delft (Netherlands)
2009-10-15
The pyrolysis of biomass occurs via several parallel/serial decomposition reactions. The kinetic parameters, namely the activation energy (E) and the pre-exponential factor (k{sub o}), do not remain constant during the pyrolysis process. A modified empirical method is introduced for calculating the activation energy (E) and the pre-exponential factor (k{sub 0}) based on the Friedman analysis [Friedman HL. Kinetics of thermal degradation of char-forming plastics from thermogravimetry - application to a phenolic plastic. [J Polym Sci C 1963;6: 183-95]. The kinetic parameters are expressed as a function of the conversion (x) during the biomass pyrolysis process. The reactions are assumed to be of first order. At least three data sets obtained at different dynamic heating rates are required. From the Friedman analysis, the conversion (x) related functions E = E(x) and k{sub o} = k{sub o}(x) can be obtained by a B-spline regression method. The pyrolysis can hence be described as: dx/ dt=k(1-x)=k{sub o}(x). exp (-E(x)/RT)(1-x). In this paper, the adapted method is applied to pyrolysis of cellulose and two biomass fuels (meat and bone meal, chicken litter). Experiments were carried out at 2, 10 and 50 K min{sup -1} by thermogravimetric analysis. A good fit of the calculated conversion with experimental data was found. (author)
Edge detection of molten pool and weld line for CO2 welding based on B-spline wavelet
Institute of Scientific and Technical Information of China (English)
薛家祥; 贾林; 李海宝; 张丽玲
2004-01-01
Due to the disturbances of spatters, dusts and strong arc light, it is difficult to detect the molten pool edge and the weld line location in CO2 welding processes. The median filtering and self-multiplication was employed to preprocess the image of the CO2 welding in order to detect effectively the edge of molten pool and the location of weld line. The B-spline wavelet algorithm has been investigated, the influence of different scales and thresholds on the results of the edge detection have been compared and analyzed. The experimental results show that better performance to extract the edge of the molten pool and the location of weld line can be obtained by using the B-spline wavelet transform. The proposed edge detection approach can be further applied to the control of molten depth and the seam tracking.
Kanai, Takayuki; Kadoya, Noriyuki; Ito, Kengo; Onozato, Yusuke; Cho, Sang Yong; Kishi, Kazuma; Dobashi, Suguru; Umezawa, Rei; Matsushita, Haruo; Takeda, Ken; Jingu, Keiichi
2014-01-01
Deformable image registration (DIR) is fundamental technique for adaptive radiotherapy and image-guided radiotherapy. However, further improvement of DIR is still needed. We evaluated the accuracy of B-spline transformation-based DIR implemented in elastix. This registration package is largely based on the Insight Segmentation and Registration Toolkit (ITK), and several new functions were implemented to achieve high DIR accuracy. The purpose of this study was to clarify whether new functions ...
2013-04-01
surfaces consisting of Bezier curves and Nonuniform Rational B-spline Surfaces ( NURBS ). There are many times however, when both modeling approaches...have allowed the integration of free-form objects in CSG systems. This presentation will discuss the development and integration of NURBS into the...Ballistics Research Laboratory CSG modeling system. 15. SUBJECT TERMS NURBS , BSpline, raytracing, CSG, BRL-CAD 16. SECURITY CLASSIFICATION OF: 17
Geometric Construction of Algebraic Hyperbolic B-Spline%代数双曲B-样条的几何构造
Institute of Scientific and Technical Information of China (English)
朱平; 汪国昭
2009-01-01
样条曲线的升阶是CAD系统相互沟通必不可少的手段之一.由于双阶样条的升阶算法具有割角性质,因此具有鲜明的几何意义.以代数双曲B-样条为例,证明了样条曲线经过不断升阶之后,其控制多边形序列会像Bézier曲线一样收敛到初始的代数双曲B-样条曲线.利用文中得到的结果,就可以像Bézier曲线一样,通过几何割角法生成B-样条曲线﹑双曲线﹑悬链线等常用曲线.%Degree elevation of spline curves is an essential technique for communication between CAD systems. Since degree elevation algorithm by bi-order Spline can be interpreted as corner cutting process, degree elevation of Spline curve has obvious geometric meaning. Taking algebraic hyperbolic B-spline curve as an example, it is proved that Spline curve's control polygon sequence will converge to the initial algebraic hyperbolic B-spline curve after degree elevation continually. By this conclusion, common curves including B-spline, hyperbola and catenary curves can be obtained by geometric corner cutting as Bézier curves.
Chen, Jian; Tustison, Nicholas J.; Amini, Amir A.
2006-03-01
In this paper, an improved framework for estimation of 3-D left-ventricular deformations from tagged MRI is presented. Contiguous short- and long-axis tagged MR images are collected and are used within a 4-D B-Spline based deformable model to determine 4-D displacements and strains. An initial 4-D B-spline model fitted to sparse tag line data is first constructed by minimizing a 4-D Chamfer distance potential-based energy function for aligning isoparametric planes of the model with tag line locations; subsequently, dense virtual tag lines based on 2-D phase-based displacement estimates and the initial model are created. A final 4-D B-spline model with increased knots is fitted to the virtual tag lines. From the final model, we can extract accurate 3-D myocardial deformation fields and corresponding strain maps which are local measures of non-rigid deformation. Lagrangian strains in simulated data are derived which show improvement over our previous work. The method is also applied to 3-D tagged MRI data collected in a canine.
Directory of Open Access Journals (Sweden)
Sandra P Mateus
2010-01-01
Full Text Available Dentro de las técnicas existentes de Inteligencia Artificial, se escogieron y adaptaron dos Redes Neuronales Artificiales (RNA para realizar el ajuste de uno de los elementos que definen una B-Spline Racional No Uniforme (NURBS y con ello obtener un modelado adecuado de la NURBS. Los elementos escogidos fueron los puntos de control. Las RNA utilizadas son las de Función de Base Radial y las de Kohonen o Mapas Auto-organizativos. Con base en el análisis de resultados y la caracterización de las RNA, la Función de Base Radial tuvo un desempeño más adecuado y óptimo para un número elevado de datos, lo cual es una desventaja de los Mapas Auto-organizativos. En este modelo se tiene que realizar procesos extras para determinar la neurona ganadora y realizar el reajuste de los pesos.In the existing techniques of Artificial Intelligence, two Artificial Neural Networks (ANN were selected and adapted to fit one of the elements that define a Non-Uniform Rational B-Spline (NURBS and thus obtaining an appropriate modeling of the NURBS. The selected elements were the checkpoints. The ANN used were the Radial Basis Function and the Kohonen model or Self-Organizing Maps. Based on the analysis of the results and characterization of the ANN the Radial Basis Function had a more appropriate and optimum performance for a large number of data, which is a disadvantage of the Self-Organizing Maps. In this model, additional processes must be done to determine the winning neuron and the weights must be refitted.
Börger, Klaus; Schmidt, Michael; Dettmering, Denise; Limberger, Marco; Erdogan, Eren; Seitz, Florian; Brandert, Sylvia; Görres, Barbara; Kersten, Wilhelm; Bothmer, Volker; Hinrichs, Johannes; Venzmer, Malte; Mrotzek, Niclas
2016-04-01
Today, the observations of space geodetic techniques are usually available with a rather low latency which applies to space missions observing the solar terrestrial environment, too. Therefore, we can use all these measurements in near real-time to compute and to provide ionosphere information, e.g. the vertical total electron content (VTEC). GSSAC and BGIC support a project aiming at a service for providing ionosphere information. This project is called OPTIMAP, meaning "Operational Tool for Ionosphere Mapping and Prediction"; the scientific work is mainly done by the German Geodetic Research Institute of the Technical University Munich (DGFI-TUM) and the Institute for Astrophysics of the University of Goettingen (IAG). The OPTIMAP strategy for providing ionosphere target quantities of high quality, such as VTEC or the electron density, includes mathematical approaches and tools allowing for the model adaptation to the real observational scenario as a significant improvement w.r.t. the traditional well-established methods. For example, OPTIMAP combines different observation types such as GNSS (GPS, GLONASS), Satellite Altimetry (Jason-2), DORIS as well as radio-occultation measurements (FORMOSAT#3/COSMIC). All these observations run into a Kalman-filter to compute global ionosphere maps, i.e. VTEC, for the current instant of time and as a forecast for a couple of subsequent days. Mathematically, the global VTEC is set up as a series expansion in terms of two-dimensional basis functions defined as tensor products of trigonometric B-splines for longitude and polynomial B-splines for latitude. Compared to the classical spherical harmonics, B-splines have a localizing character and, therefore, can handle an inhomogeneous data distribution properly. Finally, B-splines enable a so-called multi-resolution-representation (MRR) enabling the combination of global and regional modelling approaches. In addition to the geodetic measurements, Sun observations are pre
Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.
2017-03-01
An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.
Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.
2016-11-01
An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.
Institute of Scientific and Technical Information of China (English)
XIONG Lei; LI haijiao; ZHANG Lewen
2008-01-01
The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.
2014-01-01
Este documento de tesis tiene el propósito de describir una metodología para obtener nubes de puntos que representen a superficies (o parches de geometría compleja) de piezas mecánicas que pueden ser replicadas en la industria. Estos puntos se obtuvieron utilizando el método de interpolación superficial B-Spline que deben cumplir un margen de error conocido y controlado de acuerdo a las tolerancias de fabricación utilizados en estos procesos de fabricación. En primer lugar e...
PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces
Sarmiento, A.F.
2016-10-01
We describe a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, an open-source library we have built and developed over the last decade, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.
B-Spline Variational Method for Shape Reconstruction from Shading%由单幅图像重构表面形状的B样条变分法研究
Institute of Scientific and Technical Information of China (English)
熊汉伟; 张湘伟
2001-01-01
B-spline approach is used to solve shape from shading problem, removing the smoothness and integrability restrictions from the objective functional formulation. A new B-spline hierarchical basis function is introduced to accelerate the algorithm. Simulation results show the efficiency of new approach.%针对SFS(Shape From Shading)问题中的Lagrange乘子难题，经过B样条插值，将SFS问题的可积性、光滑性限制隐含，消除Lagrange乘子的不利影响，采用B样条变分法解决了SFS问题；并根据B样条特殊结构，设计了SFS问题变分格式的层次基变换共轭梯度加速算法.初步的计算实例表明，此方法在精度、速度上有所提高，效果令人满意.
Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves
Directory of Open Access Journals (Sweden)
Hatice Kuşak Samancı
2017-01-01
Full Text Available The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.
Institute of Scientific and Technical Information of China (English)
Xiang Jiawei; He Zhengjia; Chen Xuefeng
2006-01-01
Based on B-spline wavelet on the interval (BSWI), two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based lements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.
Almeida, Nuno; Friboulet, Denis; Sarvari, Sebastian Imre; Bernard, Olivier; Barbosa, Daniel; Samset, Eigil; Dhooge, Jan
2016-02-01
Segmentation of the left atrium (LA) of the heart allows quantification of LA volume dynamics which can give insight into cardiac function. However, very little attention has been given to LA segmentation from three-dimensional (3-D) ultrasound (US), most efforts being focused on the segmentation of the left ventricle (LV). The B-spline explicit active surfaces (BEAS) framework has been shown to be a very robust and efficient methodology to perform LV segmentation. In this study, we propose an extension of the BEAS framework, introducing B-splines with uncoupled scaling. This formulation improves the shape support for less regular and more variable structures, by giving independent control over smoothness and number of control points. Semiautomatic segmentation of the LA endocardium using this framework was tested in a setup requiring little user input, on 20 volumetric sequences of echocardiographic data from healthy subjects. The segmentation results were evaluated against manual reference delineations of the LA. Relevant LA morphological and functional parameters were derived from the segmented surfaces, in order to assess the performance of the proposed method on its clinical usage. The results showed that the modified BEAS framework is capable of accurate semiautomatic LA segmentation in 3-D transthoracic US, providing reliable quantification of the LA morphology and function.
Côrtes, A.M.A.
2016-10-01
The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf−supinf−sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.
使用B样条无单元法进行梯形盖板受力分析%Stress Analysis of Trapezoidal Slabs by Using B-spline Meshless Method
Institute of Scientific and Technical Information of China (English)
李彬
2013-01-01
To meet the needs of stress analysis and evaluation of trapezoidal slabs of skew culvert,this paper puts forward a B-spline meshless method based on moderately thick slab theory.By using dual quartic and dual cubic B-spline to make interpolation for the deflection and the turning angle respectively,this paper deduces the stiffness matrix and equivalent load formulations,introduces the method of setting boundary condition by using penalty function,enumerates the key points of using both Matlab and Spline Toolbox in order to achieve this method,and gives numerical verification result.The results from research and calculation show that this method proposed has advantages such as concise formulation,simple post-processing,high precision and efficiency,and can facilitate the development of relevant specialized analysis program.%为满足对斜交涵洞梯形盖板进行受力分析与评估的需要,提出基于中厚板理论的B样条无单元方法.实现中对挠度和转角分别采用双四次和双三次B样条进行插值,使用变分原理推导相应的刚度矩阵和等效荷载列式,介绍利用罚函数施加边界条件的方法,列举使用Matlab及Spline Toolbox实现该方法时的一些要点,提供了数值验证结果.研究及计算结果表明,该方法列式简洁、后处理方便、精度好、效率高,为相关专用分析程序的开发提供一条方便的途径.
Institute of Scientific and Technical Information of China (English)
Joong-Hyun Rhim; Doo-Yeoun Cho; Kyu-Yeul Lee; Tae-Wan Kim
2006-01-01
We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and "reference curves". The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing "virtual" isoparametric curves. Finally, a discrete G1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.
Duddu, Ravindra
2011-10-05
We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.
Jaume-i-Capó, Antoni; Varona, Javier; González-Hidalgo, Manuel; Mas, Ramon; Perales, Francisco J.
2012-02-01
Human motion capture has a wide variety of applications, and in vision-based motion capture systems a major issue is the human body model and its initialization. We present a computer vision algorithm for building a human body model skeleton in an automatic way. The algorithm is based on the analysis of the human shape. We decompose the body into its main parts by computing the curvature of a B-spline parameterization of the human contour. This algorithm has been applied in a context where the user is standing in front of a camera stereo pair. The process is completed after the user assumes a predefined initial posture so as to identify the main joints and construct the human model. Using this model, the initialization problem of a vision-based markerless motion capture system of the human body is solved.
Kanai, Takayuki; Kadoya, Noriyuki; Ito, Kengo; Onozato, Yusuke; Cho, Sang Yong; Kishi, Kazuma; Dobashi, Suguru; Umezawa, Rei; Matsushita, Haruo; Takeda, Ken; Jingu, Keiichi
2014-11-01
Deformable image registration (DIR) is fundamental technique for adaptive radiotherapy and image-guided radiotherapy. However, further improvement of DIR is still needed. We evaluated the accuracy of B-spline transformation-based DIR implemented in elastix. This registration package is largely based on the Insight Segmentation and Registration Toolkit (ITK), and several new functions were implemented to achieve high DIR accuracy. The purpose of this study was to clarify whether new functions implemented in elastix are useful for improving DIR accuracy. Thoracic 4D computed tomography images of ten patients with esophageal or lung cancer were studied. Datasets for these patients were provided by DIR-lab (dir-lab.com) and included a coordinate list of anatomical landmarks that had been manually identified. DIR between peak-inhale and peak-exhale images was performed with four types of parameter settings. The first one represents original ITK (Parameter 1). The second employs the new function of elastix (Parameter 2), and the third was created to verify whether new functions improve DIR accuracy while keeping computational time (Parameter 3). The last one partially employs a new function (Parameter 4). Registration errors for these parameter settings were calculated using the manually determined landmark pairs. 3D registration errors with standard deviation over all cases were 1.78 (1.57), 1.28 (1.10), 1.44 (1.09) and 1.36 (1.35) mm for Parameter 1, 2, 3 and 4, respectively, indicating that the new functions are useful for improving DIR accuracy, even while maintaining the computational time, and this B-spline-based DIR could be used clinically to achieve high-accuracy adaptive radiotherapy. © The Author 2014. Published by Oxford University Press on behalf of The Japan Radiation Research Society and Japanese Society for Radiation Oncology.
B-spline goal-oriented error estimators for geometrically nonlinear rods
2011-04-01
approximation space is the same as the one used to represent the geometry and which can be represented by B–splines, NURBS (Non–Uniform Rational B... NURBS basis) and the related advantages in the context of analysis, we refer the reader to [7] and [15] (and to the references therein indicated). We...Publications, 2000. [26] T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs. Isogeometric analysis: Cad, finite el- ements, nurbs , exact geometry and mesh
Maltsev, I A; Tupitsyn, I I; Shabaev, V M; Kozhedub, Y S; Plunien, G; Stoehlker, Th
2013-01-01
A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are calculated for different values of the impact parameter. The obtained results are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime.
Metz, C T; Klein, S; Schaap, M; van Walsum, T; Niessen, W J
2011-04-01
A registration method for motion estimation in dynamic medical imaging data is proposed. Registration is performed directly on the dynamic image, thus avoiding a bias towards a specifically chosen reference time point. Both spatial and temporal smoothness of the transformations are taken into account. Optionally, cyclic motion can be imposed, which can be useful for visualization (viewing the segmentation sequentially) or model building purposes. The method is based on a 3D (2D+time) or 4D (3D+time) free-form B-spline deformation model, a similarity metric that minimizes the intensity variances over time and constrained optimization using a stochastic gradient descent method with adaptive step size estimation. The method was quantitatively compared with existing registration techniques on synthetic data and 3D+t computed tomography data of the lungs. This showed subvoxel accuracy while delivering smooth transformations, and high consistency of the registration results. Furthermore, the accuracy of semi-automatic derivation of left ventricular volume curves from 3D+t computed tomography angiography data of the heart was evaluated. On average, the deviation from the curves derived from the manual annotations was approximately 3%. The potential of the method for other imaging modalities was shown on 2D+t ultrasound and 2D+t magnetic resonance images. The software is publicly available as an extension to the registration package elastix. Copyright © 2010 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Verónica S. Martínez
2015-12-01
Full Text Available Metabolic flux analysis (MFA is widely used to estimate intracellular fluxes. Conventional MFA, however, is limited to continuous cultures and the mid-exponential growth phase of batch cultures. Dynamic MFA (DMFA has emerged to characterize time-resolved metabolic fluxes for the entire culture period. Here, the linear DMFA approach was extended using B-spline fitting (B-DMFA to estimate mass balanced fluxes. Smoother fits were achieved using reduced number of knots and parameters. Additionally, computation time was greatly reduced using a new heuristic algorithm for knot placement. B-DMFA revealed that Chinese hamster ovary cells shifted from 37 °C to 32 °C maintained a constant IgG volume-specific productivity, whereas the productivity for the controls peaked during mid-exponential growth phase and declined afterward. The observed 42% increase in product titer at 32 °C was explained by a prolonged cell growth with high cell viability, a larger cell volume and a more stable volume-specific productivity.
Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong
2015-07-01
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
Energy Technology Data Exchange (ETDEWEB)
Shao, Chenxi, E-mail: cxshao@ustc.edu.cn; Xue, Yong; Fang, Fang; Bai, Fangzhou [Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Yin, Peifeng [Department of Computer Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16801 (United States); Wang, Binghong [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2015-07-15
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
Côrtes, A.M.A.
2015-02-20
The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.
Oliver, Todd; Ulerich, Rhys; Topalian, Victor; Malaya, Nick; Moser, Robert
2013-11-01
A discretization of the Navier-Stokes equations appropriate for efficient DNS of compressible, reacting, wall-bounded flows is developed and applied. The spatial discretization uses a Fourier-Galerkin/B-spline collocation approach. Because of the algebraic complexity of the constitutive models involved, a flux-based approach is used where the viscous terms are evaluated using repeated application of the first derivative operator. In such an approach, a filter is required to achieve appropriate dissipation at high wavenumbers. We formulate a new filter source operator based on the viscous operator. Temporal discretization is achieved using the SMR91 hybrid implicit/explicit scheme. The linear implicit operator is chosen to eliminate wall-normal acoustics from the CFL constraint while also decoupling the species equations from the remaining flow equations, which minimizes the cost of the required linear algebra. Results will be shown for a mildly supersonic, multispecies boundary layer case inspired by the flow over the ablating surface of a space capsule entering Earth's atmosphere. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].
2012-01-01
In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using particle swarmoptimization (PSO) procedure. ...
Energy Technology Data Exchange (ETDEWEB)
Soares Filho, Djalma Manoel; Eckhardt, Wietze; Braganca, Ricardo Silva Nunes de [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas. Setor de Geofisica e Estratigrafia
1997-07-01
A gauss-Newton type method for seismic crosswell traveltime tomography based on B-splines products linear combinations for velocity field representation is presented. Knot points and order are established through Dierckx approximation technique according to the initial guess model parameters. The Frechet derivatives are contour integrations along the rays and the regularization factor is estimated using the concepts of condition number and Backus-Gilbert spread factor for normalized resolution matrices. A numerical example demonstrates the robustness of the method. (author)
Pandithevan, Ponnusamy
2015-02-01
In tissue engineering, the successful modeling of scaffold for the replacement of damaged body parts depends mainly on external geometry and internal architecture in order to avoid the adverse effects such as pain and lack of ability to transfer the load to the surrounding bone. Due to flexibility in controlling the parameters, layered manufacturing processes are widely used for the fabrication of bone tissue engineering scaffold with the given computer-aided design model. This article presents a squared distance minimization approach for weight optimization of non-uniform rational B-spline curve and surface to modify the geometry that exactly fits into the defect region automatically and thus to fabricate the scaffold specific to subject and site. The study showed that though the errors associated in the B-spline curve and surface were minimized by squared distance method than point distance method and tangent distance method, the errors could be minimized further in the rational B-spline curve and surface as the optimal weight could change the shape that desired for the defect site. In order to measure the efficacy of the present approach, the results were compared with point distance method and tangent distance method in optimizing the non-rational and rational B-spline curve and surface fitting for the defect site. The optimized geometry then allowed to construct the scaffold in fused deposition modeling system as an example. The result revealed that the squared distance-based weight optimization of the rational curve and surface in making the defect specific geometry best fits into the defect region than the other methods used. © IMechE 2015.
Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan
2016-09-01
In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.
Convolution Surface Modeling for Cubic B-Spline Skeletons%三次B样条曲线骨架卷积曲面造型
Institute of Scientific and Technical Information of China (English)
张海林; 金小刚; 冯结青
2006-01-01
提出一种基于B样条曲线降阶的三次B样条曲线骨架卷积曲面造型方法.首先通过顶点扰动降阶方法把三次B样条曲线骨架(C1连续)降阶为C1连续的二次B样条,然后应用二次B样条曲线骨架的卷积曲面势函数计算方法得到三次B样条曲线骨架的势函数.
有理三次均匀B样条曲线的形状控制%Shape Control for Rational Cubic Uniform B-Spline Curves
Institute of Scientific and Technical Information of China (English)
雷开彬
2000-01-01
采用建立局部仿射坐标系的方法,研究了有理三次均匀B样条的几何结构及端点性质.给出了有理三次均匀B样条曲线的几何形状修改法,使对该样条曲线的修改更加灵活、方便.
基于三次B样条函数的话务量预测模型%Traffic Prediction Model Based on Cubic B Spline Interpolation
Institute of Scientific and Technical Information of China (English)
熊春波; 郭军峰
2009-01-01
针对某移动通信服务公司话务量预测的实际问题,利用三次B样条函数插值方法,建立了工作日和假日话务量预测模型,求解得出了移动电话的话务量随时间变化的规律性,并在某通信服务公司的话务量预测中得到了具体应用,结果是有效的.
Cubic B-spline interpolation for one-dimensional search method%一维搜索问题的三次B样条插值法
Institute of Scientific and Technical Information of China (English)
罗煦琼
2008-01-01
基于一元三次B样条函数插值, 给出了一种求解一维搜索问题的新算法和数值实验结果. 结果表明,新算法能很快地求出全局最优解, 且剖分数越大, 精度越高.
带法向约束的3次均匀B样条曲线插值%Cubic uniform B-spline curves interpolation with normal constrains
Institute of Scientific and Technical Information of China (English)
胡巧莉; 寿华好
2014-01-01
基于3次均匀B样条曲线段的端点性质,及其与控制顶点构成的三角形的几何关系,提出了一种插值给定顶点与法向约束的3次均匀B样条曲线构造算法.与以往B样条曲线的顶点法向插值算法不同的是,本算法结合由控制顶点构成的三角形的几何性质求解新添加的控制顶点,可生成严格插值型值点并且在型值点处法向与给定法向无偏移的B样条曲线.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In order to improve airfoil performance under different flight conditions and to make the performance insensitive to off-design condition at the same time,a multi-objective optimization approach considering robust design has been developed and applied to airfoil design. Non-uniform rational B-spline (NURBS) representation is adopted in airfoil design process,control points and related weights around airfoil are used as design variables. Two airfoil representation cases show that the NURBS method can get airfoil geometry with max geometry error less than 0.0019. By using six-sigma robust approach in multi-objective airfoil design,each sub-objective function of the problem has robustness property. By adopting multi-objective genetic algorithm that is based on non-dominated sorting,a set of non-dominated airfoil solutions with robustness can be obtained in the design. The optimum robust airfoil can be traded off and selected in these non-dominated solutions by design tendency. By using the above methods,a multi-objective robust optimization was conducted for NASA SC0712 airfoil. After performing robust airfoil optimization,the mean value of drag coefficient at Ma0.7-0.8 and the mean value of lift coefficient at post stall regime (Ma0.3) have been improved by 12.2% and 25.4%. By comparing the aerodynamic force coefficients of optimization result,it shows that: different from single robust airfoil design which just improves the property of drag divergence at Ma0.7-0.8,multi-objective robust design can improve both the drag divergence property at Ma0.7-0.8 and stall property at low speed. The design cases show that the multi-objective robust design method makes the airfoil performance robust under different off-design conditions.
Knot Removing and Smoothing Method of Generalized B-Spline Curves%广义B样条曲线的节点去除与光顺算法
Institute of Scientific and Technical Information of China (English)
张莉; 葛先玉; 檀结庆
2016-01-01
广义B样条曲线具备了B样条曲线的各种优良性质，又因为其独具的核函数为形状设计带来更加丰富的可能性，文中提出了广义 B 样条曲线的节点去除与光顺算法。首先给出了构造广义 B 样条对偶基的新方法，其时间计算复杂度得到了很好的控制；其次摘除需去除的节点，再利用对偶基的最佳逼近性质，采用广义 B 样条的对偶基求得新的广义B样条曲线的控制顶点；在广义B样条曲线光顺中引入跳跃值的概念，如果某个节点附近的跳跃值较大，则去除相应的节点，从而实现在此节点处的光顺。最后通过大量的数值实例，展示了算法的有效性。%Generalized B-splines are not only compatible with classical B-splines but also provide plentiful shapes for geometric modeling systems because of their flexible core functions. The paper focuses on knots removal and smooth method of generalized B-splines. Firstly, the dual bases of generalized B-splines are constructed, and the complexity can be reduced a lot. Secondly, jump value is introduced, if jump values of some knots are too big, the corresponding knots are removed. At last, by the aid of best approximation prop-erty of the generalized B-splines’ dual bases, control points of new approximating generalized B-splines are obtained. Thus, knots removal and smooth of curves are realized. Numerical examples are given to illustrate the effectiveness of the method.
Improvement of the basis for the solution of the Dirac equation in Cassini coordinates
Hahn, W.; Artemyev, A. N.; Surzhykov, A.
2017-08-01
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in our earlier article [J. Phys. B 43, 235207 (2010)]. For the calculations in the above article, we constructed the basis for approximating the energy eigenfunctions by using smooth piecewise defined polynomials, called B-splines. In the present article, we report that an analysis of the employed representation of the Dirac matrices shows that the above approximation is not efficient using B-splines only. Therefore, we include basis functions which are defined using functions with step-like behavior instead of B-splines. Thereby, we achieve a significant increase of accuracy of results.
直线网格B样条混合滤波GPU光线投射%Rectilinear Grid GPU Raycasting with B-Spline Hybrid Filtering
Institute of Scientific and Technical Information of China (English)
袁斌
2013-01-01
To render rectilinear grid quickly to produce high quality image, this paper gives B-spline hybrid filtering and implementation speed grid that are applied to GPU-raycasting for rectilinear grid. Proposition about sign property of derivative of B-spline basics is proved. Furthermore, it is shown that there are significant errors in some cases when S&H method is used to compute derivative of B-spline. According to such a conclusion, in ray integration, S&H method is used if the condition is satisfied; otherwise B-spline basic equation is used. Moreover, proposition about range of derivatives of B-spline functions is proved, so that gradient magnitude modulation and speed grid are implemented in GPU; in ray integration, interfaces between materials are shown with gradient magnitude modulation and empty space is skipped with speed grid. As a result, GPU-raycasting with the hybrid method in this paper frees artifacts caused by generalized S&H algorithm; it is faster than stationary step GPU-raycasting based on B-spline basic equation; it can represent the true feature of things measured or simulated if they are smooth.%为了快速、高质量地绘制直线网格,提出B样条混合滤波方法,实现加速网格,并将其应用到直线网格GPU光线投射.证明了三次B样条基函数导数的符号性质,进而证明用快速三次滤波方法(S& H方法)计算非均匀B样条函数的导数会出现误差.据此,在光线积分计算中,如果条件允许,采用S & H方法；否则采用基于B样条基本公式的滤波方法.另外,证明三次B样条函数导数的范围,以实现梯度量调制和加速网格；在光线积分计算中,利用梯度量调制表现物质的分界面；利用加速网格,跳过无效积分步,加快绘制速度.实验结果表明,采用混合滤波的直线网格GPU光线投射方法能消除S&H方法导致的走样现象；与基于B样条基本公式的绘制方法相比,该方法更快；如果模拟
Institute of Scientific and Technical Information of China (English)
成贤锴; 顾国刚; 陈琦; 于涌
2014-01-01
It is difficult and inefficient for an industrial robot to move along a particular complex track by teaching programming, for the control system is closed and independent. Thus, waiting process trajectory is planned in the image of workpiece surface. According to cubic B-spline interpolation algorithm, it needs some data processing to the planned trajectory path. Then, the format of data points converts to robot lan-guage by off-line programming. Complex curvilinear motion of industrial robot divides to linear motion and circular motion. During the experiment, the robot moves smoothly, and actual trajectory and planning traj-ectory are highly consistent. And the experimental results prove that the method is feasible.%工业机器人的控制系统是封闭且独立的，通过示教方式来在线编程是很难完成复杂的曲线运动，效率较低。为此在工件面型图像中对待加工轨迹进行规划，根据三次B样条曲线插值算法对规划好的加工路径轨迹进行数据处理，通过离线编程把加工轨迹数据点格式转换成机器人程序文件，把复杂的曲线运动分解成直线运动和圆弧运动，从而实现工业机器人的复杂曲线运动。实验过程中机器人运动流畅没有停顿，实际运动轨迹和规划运动轨迹吻合得很好，证明该方法有效可行。
Directory of Open Access Journals (Sweden)
Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
二次B样条曲面顶点及法向插值%Interpolation of Vertices and Their Normal Vectors with Quadratic B-Spline Surfaces
Institute of Scientific and Technical Information of China (English)
李桂清; 李现民; 李华
2001-01-01
Interpolation to vertex positions is an essential issue in surface modeling, and interpolation to normal vectors has also important applications in some CAD/CAM areas. Properties of bi-quadratic B-spline surface are investigated by the subdivision approach, and the control mesh of bi-quadratic B-spline surface is constructed by employing Doo-Sabin subdivision to derive the parametric representation of interpolation surface. For enhancing the efficiency of handling mesh with larger scale data, we first partition the mesh into a number of sub-meshes and compute their corresponding control nets satisfying interpolatory conditions, then the sub-nets are integrated to form a whole net such that its bi-quadratic B-spline surface interpolates all given vertices and normal vectors.%顶点位置插值是自由曲面造型的基本方法，法向插值在一些CAD/CAM系统中也有重要应用．文中利用子分曲面理论研究双二次B样条曲面的性质，在此基础上利用Doo-Sabin子分模式构造插值顶点位置和法向的双二次B样条曲面控制网格，得到插值曲面的参数表示．为了提高效率，对规模较大的网格数据，先把它划分成若干片子网格，分别求出满足与子网格相关的插值条件的控制网格. 最后再把它们整合在一起形成完整的控制网格，使得相应的二次B样条曲面插值所有顶点及法向.
RATIONAL QUADRATIC B-SPLINE INTERPOLATION OF FUNCTION SEGMENTS%函数的分段有理二次B样条插值
Institute of Scientific and Technical Information of China (English)
梁锡坤
2012-01-01
Based on the proper segmentation of complicated functions, the triangle convex hull of functions segment is introduced. We propose a scheme of control polygon determination by the tangent of the endpoints of the segment intervals. The algorithm of the segment rational quadratic B-spline interpolation of complicated functions is discussed in details. The interpolation keeps many important geometric features of the original function such as convexity, monotonicity and G1 continuity. The numerical experiments show that the algorithm provides an efficient approach to approximate representation of complicated functions.%0引 言 科学和工程计算中,函数的近似表示一直是一个重要课题.近似方法一般可归结为插值、逼近和拟合三种基本类型,经历长期发展,函数逼近方法[1-3]十分丰富.
外载荷的B样条曲线变形%Shape modification of B-spline curve via external loads
Institute of Scientific and Technical Information of China (English)
程仙国; 刘伟军
2011-01-01
运用能量优化的思想,提出一种B样条曲线变形的新方法,可用于B样条曲线的变形.首先将B样条曲线段类比为有限单元法中线单元,并将作用在B样条曲线段的外载荷等效成线单元的端点力,分别建立B样条曲线内部能量、外载荷能量函数方程;外载荷的改变将引起B样条曲线能量的变化,通过求解一个使曲线能量的变化量为最小的优化问题,得到变形后的B样条曲线.运用该方法实现了B样条曲线的局部、整体等变形操作.%Based on the idea of energy optimization, a new method for shape modification of the B-spine curve is proposed. First, using an analogy between the B-spline curve and the curve element of finite element method, and making the external load acting on the curve be equivalent to the end force into the element, the internal energy functional equation of the B-spline curve and the energy functional equation of the load are constructed respectively. The energy change of the Bspline curve with the change of the load, a new curve is generated by solving an optimization problem of the change of the energy. Using this approach, the local or total modification of the curve can be accomplished.
The Research of Obstacle-avoiding Problem based on Minimum Variation B-spline%基于最小变量的B-样条避障问题研究
Institute of Scientific and Technical Information of China (English)
彭辉; 曾碧
2011-01-01
为解决移动机器人在避障时的曲线优化问题，提出了基于最小变量的B-样条避障的方法．对该方法从数学模型上进行了推导，指出了该方法相对于其他弘样条方法的优点，并对该方法进行了优化，给出了相应的优化算法．研究表明：具有最小变量的B-样条函数比只用肛样条函数定义的曲线具有更优化的线性约束，其曲线具有更好的光滑性．%To solve the mobile robot in obstacle avoidance of curve optimization problems , and put for- ward based on the minimum variable B-spline obstacle-avoidance approach. The method is carried out from the derived mathematical model, that the method compared to other B-spline interpolation method has the advantage . The method was optimized, and its iterative optimization algorithm is given. Results of the em- pirical investigation indicated that the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only, Its curve has better smoothness.
Institute of Scientific and Technical Information of China (English)
张金芳; 许曼
2013-01-01
文章对动态系统的三维输出概率密度函数(PDF)进行了线性建模和控制器设计研究。首先选择合适的二维 B 样条函数，利用系统的输入输出数据通过递归最小二乘算法建立了基于二维 B 样条函数的三维输出 PDF 的线性动态模型；然后根据所建立的数学模型，选择跟踪性能指标，进行了控制器的设计；最后，选择动态输出分布系统，进行了动态系统三维输出PDF控制的仿真研究，仿真结果证实了控制算法的有效性。%Dynamic modeling and controller design for the three dimensional (3D) output probability density function (PDF) are studied in this paper. Through recursive least square algorithm, the dynamic model of 3D PDF is set up based on two dimensional (2D) B-spline basis function with output and input data of the system firstly, then a tracking performance index is chosen to design a controller based 3D PDF dynamic model, at last a dynamic output distribution system is constructed for simulation study, and the results verify the effectiveness of the presented controller.
Cubical sets and the topological topos
DEFF Research Database (Denmark)
Spitters, Bas
2016-01-01
Coquand's cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. This paper contributes to the understanding of this model. We make three contributions...... show that it can also be a target for cubical realization by showing that Coquand's cubical sets classify the geometric theory of flat distributive lattices. As a side result, we obtain a simplicial realization of a cubical set. 2. Using the internal `interval' in the topos of cubical sets, we...... construct a Moore path model of identity types. 3. We construct a premodel structure internally in the cubical type theory and hence on the fibrant objects in cubical sets....
融合SIFT的B样条红外图像非刚性配准%B-spline non-rigid registration algorithm for infrared image based on SIFT
Institute of Scientific and Technical Information of China (English)
卢朝梁; 马丽华; 陈豪; 张薇; 于敏; 崔树民
2014-01-01
手持式广角镜头红外热像仪所拍摄的不同时刻红外图像具有刚性形变和非刚性形变，传统图像配准算法很难同时矫正刚性形变与非刚性形变，针对该问题，提出一种融合SIFT的B样条配准算法。首先在待配准图像中建立控制网格，其次运用SIFT算法寻找待配准与基准图像间的匹配点对，剔除错误匹配点对并计算出待配准图像与基准图像间的刚性变换参数，接着对控制点进行刚性变换，最后以局部强度和为测度函数，运用B样条非刚性配准算法对广角镜头引起图像的非线性进行矫正。对比实验结果表明，本文算法具有很高配准精度，能够满足实际工程精度要求。%Infrared images obtained by handheld infrared camera with wide-angle lens have rigid and non-rigid deform-ations. Tradition image registration algorithm is difficult to correct the rigid and non-rigid deformations. To solve this problem,B-spline non-rigid registration algorithm based on SIFT is proposed. At first,the control mesh is created in the input image. Then,matching points between input image and template image are found by SIFT algorithm. The rigid transformation parameters are calculated after ignoring the incorrect matching points. Next,the control points are transformed by rigid transformation parameters. Finally,the sum of pattern intensity is used as measurement,and the nonlinear transformation of the image that is caused by wide-angle lens is corrected by B-spline non-rigid registration algorithm. The results of comparison show that the new method has better registration accuracy and it also can meet the requirements of practical engineering accuracy.
PET/CT成像呼吸运动B样条校正%Respiratory motion correction of PET/CT imaging based on B-spline
Institute of Scientific and Technical Information of China (English)
潘李鹏; 贺建峰; 封硕; 崔锐; 马磊; 相艳; 易三莉; 张俊
2015-01-01
The degradation of image quality of PET/CT caused by respiratory motion will affect the physician’s diagnosis. The common developed technology of respiratory motion correction is gating, but it still has some limitations. This paper proposes a new method that using CT images extract the features of respiratory motion based on B-Spline to correct respi-ration. Firstly, it obtains the sequence of CT images corresponding with PET images within same respiratory motion cycle, and extracts the features of the motion of CT sequences within respiratory cycle by B-Spline. Next it transforms the feature parameters of CT sequences into the corresponding PET image sequences for the motion correction. The geometric defor-mation phantom and voxelised phantom tests show that the proposed method can obviously improve the quality of image of PET/CT for respiratory motion, and has a value of study further.%PET/CT成像中的人体呼吸运动会造成图像运动模糊，会严重影响图像质量，对医生的诊断造成影响。目前常用的呼吸门控技术能够在一定程度上改善图像质量，但是均存在其局限性。提出了一种基于CT图像提取呼吸运动特征的B样条方法，对呼吸运动图像进行校正。在PET/CT上获取与PET图像周期匹配的CT图像序列，通过B样条配准方式对在呼吸周期内的CT图序列像提取运动信息；对CT图像所匹配的PET图像做基于运动特征信息的校正变换进行运动校正。几何位移形变和像素人体模实验结果表明，提出的方法对PET/CT呼吸运动图像质量改进明显，具有研究价值。
On Knot Modifications of B-Spline or NURBS Surface%改变B样条曲面与NURBS曲面的节点
Institute of Scientific and Technical Information of China (English)
李亚娟; 汪国昭
2005-01-01
通过改变k×h阶B样条曲面和NURBS(Non-Uniform Rational B-spline)曲面的若干节点,分别产生一个B样条曲面族和NURBS曲面族,并指出:曲面族的包络是用相同控制顶点定义的(k-α)×(h-b)阶B样条曲面和NURBS曲面,其中α,b分别是两个方向上所改变的节点的重数.对于B样条曲面来说,曲面族与其包络的任意阶相同偏微分之间只相差一个因子,文中所得结果可以作为计算机辅助设计系统中曲面造型和形状修改的理论参考.
基于三次B样条函数的SEM图像处理%SEM Image Processing Based on Third- order B- spline Function
Institute of Scientific and Technical Information of China (English)
张健
2011-01-01
SEM images, for its unique practical testing significance, need in denoising also highlight its edges and accurate edge extraction positioning, So this paper adopts a partial differential method which can maintain the edges of the denoising and a extensive application of multi - scale wavelet analysis to detect edges, all based on third - order B - spline function as the core operator, for line width test of SEM image processing, This algorithm obtained the better denoising effect and maintained edge features for SEM images.%SEM图像由于其独特的实际测试意义,需要在去噪的同时突出边缘和准确的边缘提取定位,所以提出采用能够保持边缘的偏微分方法去噪和广泛应用的多尺度小波提取边缘,基于三次B样条函数作为核心算子,对用于线宽测试的SEM图像进行处理,获得了较好的去噪并保持边缘的效果以及清晰的图像边缘检测效果.
带形状调整参数的一阶三角B样条曲线%One order trigonometric B-spline curves with shape parameters
Institute of Scientific and Technical Information of China (English)
王晶昕; 张嘉洋; 郭丽霞
2013-01-01
给出了一阶三角B样条基函数的构造，讨论这种基函数的性质以及在具有重节点情形时的变化，并利用这类三角B样条基构造了相应的三角B样条函数及三角B样条曲线。还给出了用带调节参数的控制点方法生成一阶三角B样条曲线以便对曲线形状进行调整的方法。讨论了如何利用这类B样条基以及带参数的控制点方法生成可调形状的三角样条曲线的问题。%T he construction of the one order trigonometric B-spline basic functions is presented in this paper .The properties of the basic functions and the case of multiple knots of the basic functions are discussed .T his kind basic function can be used to construct trigonometric spline functions and trigo-nometric spline curves .By the method of control points trasformation ,a kind of spline curve with shape parameters is presented and discussed .
Han, In Su; Kim, Eung Sik; Min, Suk Won; Hur, Don; Park, Jong Keun
2004-10-01
In this paper, the electric field at the spacer in a 170 kV gas-insulated switchgear (GIS) is optimized. Initially, the tangential and total electric fields around the original shape of the 170 kV GIS produced by a Korean company are calculated using a combination of the charge simulation method (CSM) and surface charge method (SCM). The contour of the spacer in the 170 kV GIS is found using a non-uniform rational B-spline (NURB) curve the effectiveness of which has been proved. By moving some control points in the NURB curve, the initial shape of the 170 kV GIS can be determined so that we may begin to optimize the electric field. Owing to the proposed algorithm, the overall process has a stable convergence. The objects that we want to design are the upper and lower parts of the spacer. Finally, we can find the shapes in which the tangential and total electric fields are optimized.
Institute of Scientific and Technical Information of China (English)
吴扬扬; 李全海
2012-01-01
介绍了建立似大地水准面模型的原理，讨论了非均匀B样条函数方法的基本原理。根据中部某地区的已知点的大地高和正常高，分别用非均匀三次B样条函数和三次曲面函数对该地区的似大地水准面进行高程拟合，结果表明了该方法具有更好的精度和稳定性。%The principles of the quasi-geoid model is introduced, and the basic principles of non-uniform B-spline method is discussed in this paper. It fits height on the quasi-geoid of this region by using non-uniform three B-spline method and three surface method separately according to the geodetic height and normal height of the known points of a certain area in central. Results show that the non-uniform B-spline method has better accuracy and stability.
Real-Time Interactive Modification of B-Spline by PIA%基于PIA的B-Spline曲面实时交互修改方法
Institute of Scientific and Technical Information of China (English)
赵宇; 蔺宏伟
2011-01-01
交互修改是几何设计中一种常用的曲线曲面编辑手段,NURBS曲线曲面是CAD系统中曲线曲面的标准表示形式.现有的B-spline曲线曲面交互修改技术往往需要求解一个带约束的能量优化问题,当曲线曲面的控制顶点较多时,这个优化问题的求解过程较慢,难以满足交互操作的实时要求.为此,基于B-spline曲线曲面的局部迭代逼近(PIA)性质提出一种实时的B-spline曲面交互编辑方法.给定一张B-spline曲面和空间待插值目标点集,首先确定距待插值目标点位置最近的曲面上的点以及最近的控制顶点,构造对应于这2个点的主差向量,并将它们扩散到其他控制顶点；然后通过平均操作获得对应于每个控制顶点的差向量；最后通过PIA迭代生成新曲面.该迭代过程的极限曲面就是插值于给定目标点集的曲面.由于PIA迭代仅需调整若干控制顶点,不需求解约束优化问题,使得其在交互修改具有大规模控制网格的B-spline曲面时,在速度方面具有较大优势；同时,文中方法生成的曲面质量与采用能量优化方法得到的曲面质量相比差别不大.%Interactive design is widely used for curve and surface editing in geometric design. Currently, the methods for B-spline curve and surface modification usually involve solving a constrained energy optimization problem, which costs lots of time when the number of control points of curves or surfaces is large. So it hardly achieves real-time response in the modification operation. In this paper, we propose a real-time surface modification method based on progressive-iteration approximation (PIA). Suppose we are given a B-spline surface and an interpolated point set as input. First, we determine the points on the given surface, which are closest to the interpolated points, and the control points closest to the interpolated points. Then, we construct the main difference vectors, diffuse them to all of the
Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates
Hahn, Walter; Surzhykov, Andrey
2016-01-01
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in [1]. For the calculations in [1], we constructed the basis for approximating the energy eigenfunctions by using smooth piecewise defined polynomials, called B-splines. In the present article, we report that an analysis of the employed representation of the Dirac matrices shows that the above approximation is not efficient using B-spines only. Therefore, we include basis functions which are defined using functions with step-like behaviour instead of B-splines. Thereby, we achieve a significant increase of accuracy of results as compared to [1].
Image Edge Detection Based on B-spline Wavelet%基于B样条小波的图像边缘检测
Institute of Scientific and Technical Information of China (English)
周何; 黄山; 盛贤
2011-01-01
研究图像边缘优化检测问题.针对图像边缘信息被噪声污染影响定位精度,经典的边缘检测方法Canny算法中的高斯平滑函数边缘定位精确度较低,导致图像缓变边缘信息丢失和假边缘的现象.为去除虚假边缘,在Canny最优边缘检测准则下,提出引入了渐进最优的B样条小波函数,采用小波变换应用于图像边缘检测中的基于模极大值的方法,并结合Kmeans聚类的自适应双阈值方法进行图像边缘检测仿真.仿真结果表明,改进的算法改善了噪声干扰情况下图像边缘提取效果,有效提高了边缘检测的准确性,得到较高的边缘检测图像质量,可为设计提供依据.%In order to improve the low positioning accuracy of image edge detection, a research on optimization of image edge detection was carried out. The Gaussian smoothing function of the classical Canny edge detection method has lower edge positioning accuracy, which causes the missing of slowly varying edges and the producing of feigned edges and the edge detection is not accurate enough. So under the Canny criteria of optimum edge detection, the asymptotically optimal B-spline wavelet function was introduced. The method of modulus maxima of wavelet transform and the method of self-adapting dual threshold of kmeans clustering was used in the edge detection experiments. The experiments proved that the new algorithm is of higher accuracy and improves the quality of the edge detection images.
Institute of Scientific and Technical Information of China (English)
王玉珠; 杨丹; 张小洪
2007-01-01
This paper presents a multi-scale curvature product corner detection technique in the framework of B-spline curvature scale space. A scale product function is derived from the curvature product of the contour at different scales. Corners are constructed as the local maxima by thresholding the curvature product results across several scales. Through scale product, the localization accuracy and detection performance can be notably improved in terms of CNN criteria. Experiments also demonstrate that proposed method shows robustness to high frequency details and provides promising detection results.
Institute of Scientific and Technical Information of China (English)
周西军
2003-01-01
Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply.%非均匀有理B样条(NURBS)曲线、曲面造型理论是当前最先进的几何造型方法之一,大量基于NURBS的实用造型系统得到发展.对NURBS而言,虽然具有参数连续性,但为了实用需要,仍需构造具有一定光滑程度的合成曲面,满足局部设计和修改的目的.在作者给出的具有公共三次曲线的NURBS曲面片G1光滑拼接算法基础上,给出了具有公共三次曲线的NURBS曲面片G2光滑拼接条件,得到了相应控制顶点、权系数的具体算法;对于一个已知NURBS曲面,构造另一个NURBS曲面,使其达到G2拼接是简单易行的.
Institute of Scientific and Technical Information of China (English)
侯朝胜; 李婧; 龙泉
2003-01-01
The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.
三次B样条参数曲线插补算法及其特性分析%Interpolation Algorithm and Characteristic Analysis for Cubic B-spline Curves
Institute of Scientific and Technical Information of China (English)
徐绍华; 田新诚; 方磊
2007-01-01
插补算法是数控系统的核心技术之一,插补算法的选择及算法特性直接影响到数控系统的控制精度、速度及加工能力等.文章介绍了两种三次B样条参数曲线插补算法,研究分析了算法的位置控制精度、插补速度稳定性等技术特性,对两种插补算法进行了对比,给出了插补算法的选取原则.
Institute of Scientific and Technical Information of China (English)
刘洪臣; 冯勇; 杨旭强
2007-01-01
亚像元动态成像技术是实现遥感器高分辨、小型化的有效方法.将双三次B样条曲面插值方法应用于亚像元动态成像,利用待插值点周围邻域范围内16个像素点做一张B样条曲面,取曲面中点的值作为待插值点的像素值.文中推导了双三次B样条曲面插值亚像元图像的插值算式,对所提方法进行了计算机仿真研究,并与其他几种常用插值方法进行了性能比较,结果表明,本文算法得到的高分辨率图像效果更佳.
Institute of Scientific and Technical Information of China (English)
胡志刚
2000-01-01
运用三次均匀B样条曲线插值法分段构造凸轮曲线,给出任意插值点的三次均匀B样条闭曲线的B特征多边形顶点的反算公式,并导出由三次均匀B样条闭曲线构成的对心直动从动件盘形凸轮轮廓曲线上任一点处的压力角计算公式.
基于周期性延伸的三次B样条闭曲线插值%Interpolation of Cubic B-spline Closed Curve Based on Periodic Extension
Institute of Scientific and Technical Information of China (English)
李学艺; 王钊; 连小珉; 曾庆良
2009-01-01
针对闭曲线具有可周期性延伸的特点,提出了一种基于求解双列带阵线性方程组的三次B样条完全闭曲线插算法.通过节点向量和控制点在曲线闭合点两端的周期性延伸,使插值曲线在闭合点实现了理论上的完全封闭.针对曲线插值线性方程组中系数矩阵具有不完全带阵的特点,提出了一种双列带阵线性方程组求解算法.应用实例表明,算法性能稳定、效率高、可插值任意形状的复杂闭曲线,适于处理大数据量闭曲线插值运算.
The Real-time Interpolation of Cubic B-spline Curves Based on TMS320F2812%基于TMS320F2812的三次B样条曲线实时插补
Institute of Scientific and Technical Information of China (English)
李广涛; 薛重德; 侯小强
2008-01-01
为提高数控系统实时插补的准确性、加工速度和加工精度,采用在每个插补周期中保持进给速度不变的三次B样条曲线参变量非均匀变化实时插补算法.利用数字信号处理器(DSP)进行三次B样条曲线实时插补,可缩短插补计算时间;通过设定DSP的定时器中断来实现各轴控制脉冲的发送,可实现最大限度地减少折线状的插补轨迹的目的.结果表明,该算法能使所有的插补点都在理论曲线上,可以保证运动控制系统的高速高精度要求.
基于三次B样条插值的形状错误隐藏算法%Spatial shape error concealment method based on cubic B-spline interpolation
Institute of Scientific and Technical Information of China (English)
符祥; 郭宝龙; 杨占龙
2008-01-01
分析了基于Bézier插值的视频对象形状错误隐藏方法的不足,即计算附加控制点的过程复杂,隐藏结果受附加控制点影响大.针对这一问题,提出了一种基于三次B样条插值的错误隐藏算法.对三次B样条插值的矩阵公式进行了改进,保证目标轮廓的平滑性;直接对已知轮廓点插值,克服了传统方法的不足.与传统方法对比实验表明,新算法简单易实现,有较好的实用意义.
Institute of Scientific and Technical Information of China (English)
郭啸; 韩旭里; 黄琳
2016-01-01
给出了形状可调的四次Hermite插值样条曲线的构造方法.四次样条曲线可提供额外的自由度用于调整曲线具有合理形状.利用导矢逼近使得四次Hermite样条曲线具有与三次B样条曲线相似的形状.通过最小化曲线间的导矢误差给出了确定自由度的方法,提出了四次Hermite插值样条曲线的构造方法.该方法增加了自由度控制曲线形状能更好满足保形要求.最后以实例对构造的四次Hermite样条曲线和标准三次Hermite插值样条曲线进行了比较.
A Local Representation of General Cubic B-Spline Interactive Interpolation%一般三次B样条交互插值的一种局部表示法
Institute of Scientific and Technical Information of China (English)
贾根莲; 包利亚; 杜新俊
2000-01-01
交互插值三次B样条曲线曲面在辅助几何设计中使用很多,但控制点和插值点之间的变化关系一直是讨论的关键.本文就一般三次B样条曲线交互性插值中控制点和插值点之间的关系进行了讨论,并提出了一个实用的局部表示法来实现曲线的交互插值.
High-speed real-time interpolation of cubic uniform B-spline curve%三次均匀B样条曲线高速实时插补研究
Institute of Scientific and Technical Information of China (English)
赵彤; 吕强; 张辉; 杨开明
2008-01-01
为满足复杂曲线高速和高精度的加工要求,研究了具有轨迹预读功能的三次均匀B样条曲线速度规划和插补算法.提出了"重叠拼接法",实现了相邻两条B样条曲线段的光滑连接;推导了插补钳制速度的计算公式,保证了加工精度,满足了系统的动态响应能力.在引入"规划单元"概念的基础上,将速度规划和插补设计成B样条曲线插值、规划单元划分、速度规划、规划单元插补四个并行计算的线程,解决了三次均匀B样条曲线高速加工的插补实时性问题.最后,在GT100数控系统中验证了算法的有效性.
Matrix Representation for Cubic B-spline Interpolation Curve and Surface%三次均匀B样条插值曲线和曲面的矩阵形式
Institute of Scientific and Technical Information of China (English)
符祥; 郭宝龙
2007-01-01
根据三次B样条曲线(CB)的矩阵形式灵活的特点、CB曲线的端点性质和插值曲线在连接点应满足的连续性条件,推导出CB插值(CBI)曲线的矩阵形式,并进一步推广,得到了双CBI曲面的矩阵形式.生成了平面和空间插值曲线、闭合插值曲线和插值面片.与传统方法进行了比较,结果表明,本文方法有较大的优越性和较好的实用价值.
Institute of Scientific and Technical Information of China (English)
罗煦琼; 刘利斌
2008-01-01
讨论了Ly(x):=y"(x)-p(x)y'(x)-q(x)y(x)=g(x)的两点边值问题的三次B样条插值解法.证明了该方法具有二阶收敛性和很好的稳定性.数值实验结果表明,该三次B样条方法比文献[8]和文献[9]的精度更高.
Institute of Scientific and Technical Information of China (English)
星蓉生; 潘日晶
2014-01-01
基于渐进迭代逼近算法生成插值数据点及其切矢的三次均匀B样条曲线.其基本思想是用偶数项控制顶点来对应拟合数据点,用奇数项控制顶点控制相应切矢逼近,根据迭代公式不断调整控制顶点,当迭代次数趋于无穷时,一系列迭代曲线的极限曲线插值于给定的数据点及其相应的切矢.用该方法构造插值曲线是一个迭代过程,不必解线性方程组.
Terrain Reconstruction Algorithm Based on Bi-cubic B-spline Interpolation%基于双三次B-样条插值的大地形重构
Institute of Scientific and Technical Information of China (English)
张立民; 邹容平; 李一平; 陈敏
2007-01-01
提出一种基于双三次B-样条的DEM地形数据重构算法.根据用户对不同地形区域关注程度的不同而采用不同的地形分辨率,可有效地降低计算机负荷.采用该算法可以有效地对关注度较高的区域进行地形重构,提高该区域的地形分辨率.实践结果表明,该算法满足大地形视景仿真系统的需要.
非均匀三次B样条曲线插值的Jacobi-PIA算法%Jacobi-PIA Algorithm for Non-uniform Cubic B-Spline Curve Interpolation
Institute of Scientific and Technical Information of China (English)
刘晓艳; 邓重阳
2015-01-01
为了求解非均匀三次B样条曲线插值问题,基于解线性方程组的Jacobi迭代方法提出一种渐进迭代插值算法——Jacobi-PIA算法.该算法以待插值点为初始控制多边形得到第0层的三次B样条曲线,递归地求得插值给定点集的三次B样条曲线;在每个迭代过程中,定义待插值点与第k层的三次B样条曲线上对应点的差向量乘以该点对应的B样条系数的倒数为偏移向量,第k层的控制顶点加上对应的偏移向量得到第k+1层的三次B样条曲线的控制顶点.由于Jacobi-PIA算法在更新控制顶点时减少了一个减法运算,因而运算量更少.理论分析表明该算法是收敛的.数值算例结果表明,Jacobi-PIA算法的收敛速度优于经典的渐进迭代插值算法,与最优权因子对应的带权渐进迭代插值算法基本相同.
Institute of Scientific and Technical Information of China (English)
宣伯凯; 杨鹏; 孙昊; 冀云
2008-01-01
由工业PC机+运动控制卡组成的数控平台具有多轴联动功能,能够完成具有复杂曲面的足底矫形器的加工.为提高足底矫形器的加工质量,将三次B样条的方法引入加工过程.B样条方法能很好的表示自由曲线曲面的形状.通过反算控制顶点的方法,使构造的轮廓曲线能精确控制到模型每个数据点,还原曲线的原形.在教据点间进行插值,计算容易曲线光滑.为提高生产效率,在加工过程中采用连续插补的方式.多点加工一次完成减少了运行过程中电机的起停频率,不仅缩短运行时间而且能减小系统震荡.
Institute of Scientific and Technical Information of China (English)
李广涛; 薛重德; 侯小强; 孟建民
2009-01-01
为充分利用PC机资源,提高数控加工精度,介绍了基于TMS320F2812数字信号处理器(DSP)的多轴运动控制卡的设计方法以及三次B样条曲线恒速进给实时插补方案在控制卡上的应用.结果表明,该方法能有效地简化插补过程中的轨迹计算,显著缩短插补计算时间,使所有的插补点都在理论曲线上;只要合理决定曲线参变量,完全可以保证运动控制系统的高速高精度要求.
The study of cubic uniform rational B-spline interpolation algorithm%三次均匀有理B样条曲线插补算法的研究
Institute of Scientific and Technical Information of China (English)
陈伟华; 张铁
2010-01-01
插补算法是机器人系统实现运动控制的核心模块,对三次均匀有理B样条曲线的插补算法进行了研究.基于三次非均匀有理B样条曲线(NURBS),得出三次均匀有理B样条曲线的表达式.反算B样务曲线的控制顶点中发现规律,采用一种简单快捷的方法求取控制顶点,这使插补算法计算简单,更易于计算机编程.并且在算法中考虑到运动控制加减速的问题,这使插补算法符合实际,实用性强.最后采用三次均匀有理B样条曲线对螺旋线进行插补,仿真结果良好.
A free-form deformation method based on B-splines surface control%一种基于B-样条曲面控制的自由变形方法
Institute of Scientific and Technical Information of China (English)
林金花; 李万龙; 王璐; 李鑫
2011-01-01
With Doo-Sabin subdivision mode,a control grid for the interpolation vertex position and the bi-quadratic B-spline surface is constructed to obtain the parametric representation of the interpolation surface.The model points are attached to the interpolation surface to get the local coordinates which keep constant during the transformation.As the subdivision can deal with random topology grid,the multi-resolution deformation of the 3D model is realized by editing the B-spline control grid.%利用Doo-Sabin细分模式构造插值顶点位置和法向双二次B样条曲面控制网格,得到插值曲面的参数表示,再将模型上的点参数化到插值曲面上,得到该点的局部坐标。由于局部坐标在变形过程中保持不变,并且细分方法具有处理任意拓扑网格的能力,从而通过编辑模型的B-样条曲面控制网格,实现了三维模型的多分辨率变形。
Cubical sets as a classifying topos
DEFF Research Database (Denmark)
Spitters, Bas
Coquand’s cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. We show that the underlying cube category is the opposite of the Lawvere theory of De...... Morgan algebras. The topos of cubical sets itself classifies the theory of ‘free De Morgan algebras’. This provides us with a topos with an internal ‘interval’. Using this interval we construct a model of type theory following van den Berg and Garner. We are currently investigating the precise relation...
Algorithms for spline and other approximations to functions and data
Phillips, G. M.; Taylor, P. J.
1992-12-01
A succinct introduction to splines, explaining how and why B-splines are used as a basis and how cubic and quadratic splines may be constructed, is followed by brief account of Hermite interpolation and Padé approximations.
Aerodynamic Shape Optimization for Wing Based on Non-uniform Rational B-spline%基于NURBS方法的机翼气动外形优化
Institute of Scientific and Technical Information of China (English)
马晓永; 范召林; 吴文华; 杨党国
2011-01-01
飞行器气动外形优化就是将设计对象的空气动力学性能分析与最优化方法相结合,通过不断改变设计对象的外形,使其气动性能在满足一定约束条件下达到最优.气动外形优化是一个涉及几何参数化、动网格、流场计算和寻优算法的综合应用平台.随着计算流体力学(CFD)的发展以及高性能计算机的使用,气动外形优化在现代飞行器设计中的作用愈加重要.为此建立了基于非均匀有理B样条(NURBS)参数化方法的机翼气动外形优化平台.优化过程中采用弹性网格变形法,由雷诺平均Navier-Stokes方程组和Baldwin-Lomax代数湍流模型求解流场,并用离散伴随方法进行目标函数梯度求解,最后结合序列二次规划( SQP)方法进行优化迭代.通过对ONERA M6机翼在跨声速条件下进行优化分析,结果表明在保持升力系数和机翼容积不变,马赫数Ma =0.84、迎角α=3.06°时,优化后机翼表面压力系数有明显变化,上翼面λ激波明显减弱,相对于原始外形优化后机翼阻力系数减小0.002 5,降幅达13.1％；优化实例验证了该方法有效可行.%Aerodynamic design optimization is to find the optimum of aircraft aerodynamic performance under certain constraints by changing the shape of the designed object. It facilitates the design process by automating both the performance a-nalysis and the optimization method. Aerodynamic design optimization is an integrated application of geometry parameterization, grid update, flow field solver and optimization method, and it has contributed to the design of aircraft with the maturity of computational fluid dynamics (CFD) and the progress of computer performance. This paper presents an aerodynamic wing shape optimization method based on non-uniform rational B-spline (NURBS), in which the mesh deformation is used with a spring-based smoothing method. The Reynolds-averaged Navier-Stokes equations with an algebraic turbulence model of
Cubic Subalgebras and Cubic Closed Ideals of B-algebras
Directory of Open Access Journals (Sweden)
Tapan Senapati
2015-06-01
Full Text Available In this paper, the concept of cubic set to subalgebras, ideals and closed ideals of B-algebras are introduced. Relations among cubic subalgebras with cubic ideals and cubic closed ideals of B-algebras investigated. The homomorphic image and inverse image of cubic subalgebras, ideals are studied and some related properties are investigated. Also, the product of cubic B-algebras are investigated.
Directory of Open Access Journals (Sweden)
Diego Mauricio Vasquez E.
2010-05-01
Full Text Available En este documento se presenta la descripción y los resultados de la estimación de la estructura a plazos de las tasas de interés en Colombia utilizando el método de funciones B-spline cúbicas. Adicionalmente, se llevan a cabo comparaciones entre los resultados obtenidos a través de esta metodología y los presentados por Arango, Melo y Vásquez (2002 respecto a los métodos de Nelson y Siegel, y de la Bolsa de Valores de Colombia. Se observa que el desempeño del método de estimación de funciones Bspline cúbicas es similar al de Nelson y Siegel, y estos dos métodos superan al de la Bolsa de Valores de Colombia.
Institute of Scientific and Technical Information of China (English)
李小霞; 汪木兰; 刘坤; 蒋荣
2012-01-01
An interpolation method based on five degrees B-spline for manipulators trajectory planning in joint space is proposed to accomplish smooth trajectory adjustment. The B-spline interpolation algorithm can ensure the continuous of velocity, acceleration and jerk in joints moving process, also can achieve start and stop velocity, acceleration and jerk be any configuration. The manipulator trajectory is simulated out and the graphs of joints position-time, velocity-time and acceleration-time are drawn out through C + + 6. 0 development platform based on MFC framework class and OpenGL graphics library. Simulation results show that, the proposed algorithm supplied manipulators with smooth adjustment of trajectory and stable movement of joints.%为实现机械手作业轨迹平滑,关节轨迹的速度、加速度、加加速度保持连续,起始和停止的速度、加速度和加加速度可以任意配置,采用5次B样条曲线插值方法构造关节轨迹.推导了B样条曲线插值轨迹算法；通过VC ++6.0开发平台,基于MFC框架类和OpenGL图形库仿真出机械手的运动过程,并绘制出各关节的位置、速度、加速度时间曲线图.仿真结果表明,该方法使机械手关节调整平滑且运动平稳,运动性能显著优于传统的三次样条轨迹规划.
Energy Technology Data Exchange (ETDEWEB)
Birchler, W.D.; Schilling, S.A.
2001-02-01
The purpose of this report is to demonstrate that modern computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems can be used in the Department of Energy (DOE) Nuclear Weapons Complex (NWC) to design new and remodel old products, fabricate old and new parts, and reproduce legacy data within the inspection uncertainty limits. In this study, two two-dimensional splines are compared with several modern CAD curve-fitting modeling algorithms. The first curve-fitting algorithm is called the Wilson-Fowler Spline (WFS), and the second is called a parametric cubic spline (PCS). Modern CAD systems usually utilize either parametric cubic and/or B-splines.
Kaiser-Bessel Basis for the Particle-Mesh Interpolation
Gao, Xingyu; Wang, Han
2016-01-01
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B-spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, saying a relatively small real space cutoff, a relatively small reciprocal space mesh and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate. Therefore, it is worth trying the Kaiser-Bessel basis in the simulations where the computational accuracy of the electrostatic interaction is critical.
Bueno, Pablo; Cano, Pablo A.
2016-11-01
We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D -dimensional cubic theory of gravity which satisfies the following properties: (1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; (2) it is defined in the same way in general dimensions; (3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones. We show that, up to cubic order, there exists only one additional theory satisfying requirements (1) and (2). Interestingly, this theory is, along with Einstein gravity, the only one which also satisfies (3).
Kaiser-Bessel basis for particle-mesh interpolation
Gao, Xingyu; Fang, Jun; Wang, Han
2017-06-01
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B -spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, say, a relatively small real-space cutoff, a relatively small reciprocal space mesh, and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate.
Institute of Scientific and Technical Information of China (English)
胡良臣; 寿华好
2016-01-01
若是 B 样条拟合曲线的节点向量与控制顶点均为变量，则该问题变为一个带约束的多维多变量高度非线性的优化问题，反求方程系统的方法已经难以求得最优解。针对该类问题，提出一种带有法向约束的粒子群优化算法(PSO)求解曲线逼近问题的方法，首先将带有法向约束的非线性最优化问题以罚函数的方法转化为无约束的最优化问题，建立一个与数据点和法向同时相关且比较合适的适应度函数(误差函数)，然后以PSO调节节点向量，并使用最小二乘法求解在该节点向量下的最优拟合曲线，通过判断适应度函数值的优劣循环迭代，直到达到终止条件或者产生令人满意(误差容忍值)的拟合曲线为止。将文中算法产生的拟合曲线通过实验数据的对比与说明，突出了该方法的优越性，表明其用于解决带法向约束的逼近问题切实可行。%If the knot vector and control points of a B-spline curve are variable, the B-spline curve approxi-mation with normal constraint problem becomes a multidimensional, multivariate and highly nonlinear op-timization problem with normal constraints, the conventional method of inverse equation system is difficult to obtain the optimal solution. Aiming at this kind of problem, a particle swarm optimization (PSO) method is introduced to solve the curve approximation problem with normal constraints. Firstly, the penalty function method is used to transform the constrained optimization problem into an unconstrained optimization prob-lem. Secondly, a suitable fitness function which is closely related to both data points and normal constraints is constructed. Finally, PSO is applied to adjust the knot vector, and at the same time, the least square method is used to solve the optimal control points, do loop iteration until the best B-spline curve approxima-tion is produced. By a comparison with existing methods, the superiority of
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with co...
Dai, Xiaoyan; Guo, Zhongyang; Zhang, Liquan; Xu, Wencheng
2009-12-01
Soft classification methods can be used for mixed-pixel classification on remote sensing imagery by estimating different land cover class fractions of every pixel. However, the spatial distribution and location of these class components within the pixel remain unknown. To map land cover at subpixel scale and increase the spatial resolution of land cover classification maps, in this paper, a prediction model combining wavelet transform and Radial Basis Functions (RBF) neural network, abbreviated as Wavelet-RBFNN, is constructed by predicting high-frequency wavelet coefficients from low-frequency coefficients at the same resolution with RBF network and taking wavelet coefficients at coarser resolution as training samples. According to different land cover class fraction images obtained from mixed-pixel classification, based on the assumption of neighborhood dependence of wavelet coefficients, subpixel mapping on remote sensing imagery can be accomplished through two steps, i.e., prediction of land cover class compositions within subpixels and hard classification. The experimental results obtained with artificial images, QuickBird image and Landsat 7 ETM+ image indicate that the subpixel mapping method proposed in this paper can successfully produce super-resolution land cover classification maps from remote sensing imagery, outperforming cubic B-spline and Kriging interpolation method in visual effect and prediction accuracy. The Wavelet-RBFNN model can also be applied to simulate higher spatial resolution image, and automatically identify and locate land cover targets at the subpixel scales, when the cost and availability of high resolution imagery prohibit its use in many areas of work.
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive...
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality...
Fernández-Menchero, L; Bartschat, K
2016-01-01
There are major discrepancies between recent ICFT (Intermediate Coupling Frame Transformation) and DARC (Dirac Atomic R-matrix Code) calculations (Fern\\'andez-Menchero et al. 2014, Astron. Astroph. 566 A104, Aggarwal et al. 2016 Mon. Not. R Astr. Soc. 461 3997) regarding electron impact excitation rates for transitions in several Be-like ions, as well as claims that DARC calculations are much more accurate and the ICFT results might even be wrong. To resolve possible reasons for these discrepancies and to estimate the accuracy of the various results, we carried out independent B-Spline R-Matrix (BSR) calculations for electron-impact excitation of the Be-like ion N$^{3+}$. Our close-coupling expansions contain the same target states (238 levels overall) as the previous ICFT and DARC calculations, but the representation of the target wave functions is completely different. We find close agreement among all calculations for the strong transitions between low-lying states, whereas there remain serious discrepanci...
Interactive Manipulation and Reuse of Geodesic B-spline Curves on Meshes%网格曲面上测地B样条曲线交互操作与重用
Institute of Scientific and Technical Information of China (English)
刘斌; 韩林; 林俊义; 黄常标; 江开勇
2012-01-01
针对现有曲面上自由曲线设计重用方法的不足,提出一种流形网格曲面上曲线几何变换方法,达到曲线重用与再设计的目的.网格曲面上的曲线用测地B样条表示,具有与欧氏空间中传统B样条相一致的明确数学模型；引入对数映射理论将给定的源曲线控制顶点映射到切空间,获得它们的法坐标,按照曲线迁移前后控制顶点法坐标保持不变的原则,建立曲线迁移前后控制顶点的对应关系,实现类似于欧氏空间中的平移、旋转和缩放等几何变换.以网格曲面上离散对数映射理论为基础,将欧氏空间中的对称定义拓展到曲面空间,提出曲面上曲线的广义镜像概念并给出具体的算法实现.法坐标很好地保持了控制顶点之间的测地距离和相对位置关系,因而也保证了曲线迁移重用过程中的形状保持性.试验结果表明,所介绍方法健壮、有效,能满足曲面上曲线的交互设计要求.%In allusion to the deficiencies of the existing methods of reuse designing free curve on the surface, a geometric transformation method of curves on Manifold triangulation surface is proposed to achieve the aim of curves reuse and redesign. The curve on the mesh surface is represented as Geodesic B- spline curve, which has the clear uniform mathematical model with the classical B-spline curves in Euclidean space; by introduction of the logarithmic mapping theory, the control points of source curves can be mapped into tangent space and its Normal Coordinates can be obtained. According to the principle of those Normal Coordinates of remained unchanged, establishing the corresponding relation between pre and post transfer of curves, and curve's translation, rotation and scaling could be realized similaring to its geometric transformation in Euclidean space. The symmetry definition in Euclidean space is expand to curved space based on discrete logarithmic mapping theory, the generalized mirror
Fernández-Menchero, L.; Zatsarinny, O.; Bartschat, K.
2017-03-01
There are major discrepancies between recent intermediate coupling frame transformation (ICFT) and Dirac atomic R-matrix code (DARC) calculations (Fernández-Menchero et al 2014 Astron. Astrophys. 566 A104; Aggarwal et al 2016 Mon. Not. R. Astron. Soc. 461 3997) regarding electron-impact excitation rates for transitions in several Be-like ions, as well as claims that the DARC calculations are much more accurate and the ICFT results might even be wrong. To identify possible reasons for these discrepancies and to estimate the accuracy of the various results, we carried out independent B-spline R-matrix calculations for electron-impact excitation of the Be-like ion {{{N}}}3+. Our close-coupling (CC) expansions contain the same target states (238 levels overall) as the previous ICFT and DARC calculations, but the representation of the target wave functions is completely different. We find close agreement among all calculations for the strong transitions between low-lying states, whereas there remain serious discrepancies for the weak transitions as well as for transitions to highly excited states. The differences in the final results for the collision strengths are mainly due to differences in the structure description, specifically the inclusion of correlation effects, rather than the treatment of relativistic effects or problems with the validity of the three methods to describe the collision. Hence there is no indication that one approach is superior to another, until the convergence of both the target configuration and the CC expansions have been fully established.
Anisotropic cubic curvature couplings
Bailey, Quentin G
2016-01-01
To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied do not result in any linearized gravity modifications and instead are revealed in the first nonlinear terms in an expansion of spacetime around a flat background. We consider effects on gravitational radiation through the energy loss of a binary system and we study two-body orbital perturbations using the post-Newtonian metric. Some effects depend on the internal structure of the source and test bodies, thereby breaking the Weak Equivalence Principle for self-gravitating bodies. These coefficients can be measured in solar-system tests, while binary-pulsar systems and short-range gravity tests are particularly sensitive.
Testing for additivity with B-splines
Institute of Scientific and Technical Information of China (English)
Heng-jian CUI; Xu-ming HE; Li LIU
2007-01-01
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernelbased tests. The score test is found to have a good overall performance.
Testing for additivity with B-splines
Institute of Scientific and Technical Information of China (English)
2007-01-01
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.
Ideal Compliant Joints and Integration of Computer Aided Design and Analysis
2013-11-17
in B - spline geometry, one must have 1, 1r n p s m q (7) Using Eq. 7, one can show that if a cubic interpolation is used for both...geometry does not impose restrictions on the number of basis functions used in the interpolating polynomials. In contrast, B - spline rigid recurrence...loss of the flexibility offered by the FE method. As the degree of the polynomial interpolation increases, this drawback of B - spline becomes more
National Research Council Canada - National Science Library
Goodwin, Adrian N
2009-01-01
A flexible tree taper model based on a cubic polynomial is described. It is algebraically invertible and integrable, and can be constrained by one or two diameters, neither of which need be diameter at breast height (DBH...
Phase diagrams and synthesis of cubic boron nitride
Turkevich, V Z
2002-01-01
On the basis of phase equilibria, the lowest temperatures, T sub m sub i sub n , above which at high pressures cubic boron nitride crystallization from melt solution is allowable in terms of thermodynamics have been found for a number of systems that include boron nitride.
Universal Reconfiguration of (Hyper-)cubic Robots
Abel, Zachary; Kominers, Scott D.
2008-01-01
We study a simple reconfigurable robot model which has not been previously examined: cubic robots comprised of three-dimensional cubic modules which can slide across each other and rotate about each others' edges. We demonstrate that the cubic robot model is universal, i.e., that an n-module cubic robot can reconfigure itself into any specified n-module configuration. Additionally, we provide an algorithm that efficiently plans and executes cubic robot motion. Our results directly extend to a...
Li, Wen-long; Wang, Gang; Zhang, Gang; Pang, Chang-tao; Yin, Zhou-pin
2016-09-01
Onsite surface inspection with a touch probe or a laser scanner is a promising technique for efficiently evaluating surface profile error. The existing work of 5-axis inspection path generation bears a serious drawback, however, as there is a drastic orientation change of the inspection axis. Such a sudden change may exceed the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. In this paper, we propose a novel path generation method for onsite 5-axis surface inspection. The accessibility cones are defined and used to generate alternative interference-free inspection directions. Then, the control points are optimally calculated to obtain the dual-cubic non-Uniform rational B-splines (NURBS) curves, which respectively determine the path points and the axis vectors in an inspection path. The generated inspection path is smooth and non-interference, which deals with the ‘mutation and shake’ problems and guarantees a stable speed and acceleration of machine tool rotary motions. Its feasibility and validity is verified by the onsite inspection experiments of impeller blade.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Cryptographic Analysis in Cubic Time
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Seidl, H.
2004-01-01
The spi-calculus is a variant of the polyadic pi-calculus that admits symmetric cryptography and that admits expressing communication protocols in a precise though still abstract way. This paper shows that context-independent control flow analysis can be calculated in cubic time despite the fact ...
The diagonalization of cubic matrices
Cocolicchio, D.; Viggiano, M.
2000-08-01
This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.
平行分度凸轮轮廓曲线的三次NURBS表示%Cubic NURBS expression for contour curves of parallel indexing cam
Institute of Scientific and Technical Information of China (English)
何晶昌; 滕华驹
2009-01-01
For the sake of obtaining the designing data to be used for CAD/CAM plotting and machining of numerical controlled machine tools that possessing the non-uniform rational B-spline (NURBS) function, the NURBS technology and the cubic NURBS expression method for the contour curves of parallel indexing cam were discussed in this paper. The estimation method of designing error produced in the contour curves of the parallel indexing cam to be expressed after using the cubic NURBS was put forward.%为了获得供具有非均匀有理B样条(Non-Uniform Rational B-Sphne,NURBS)插值功能的CAD/CAM绘图和数控机床加工使用的设计数据,文中讨论了NURBS技术和平行分度凸轮轮廓曲线的三次NURBS表示方法,提出了用三次NURBS表示平行分度凸轮轮廓曲线后产生的设计误差的估计方法.
Song, Dong; Wang, Haonan; Tu, Catherine Y.; Marmarelis, Vasilis Z.; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.
2013-01-01
One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions. PMID:23674048
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Cubic Matrix, Nambu Mechanics and Beyond
Kawamura, Y
2002-01-01
We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a “quantum” generalization of Nambu mechanics.
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
Solving Cubic Equations by Polynomial Decomposition
Kulkarni, Raghavendra G.
2011-01-01
Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…
Cubic Icosahedra? A Problem in Assigning Symmetry
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
Cubic metaplectic forms and theta functions
Proskurin, Nikolai
1998-01-01
The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Weighted cubic and biharmonic splines
Kvasov, Boris; Kim, Tae-Wan
2017-01-01
In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.
Transparent polycrystalline cubic silicon nitride
Nishiyama, Norimasa; Ishikawa, Ryo; Ohfuji, Hiroaki; Marquardt, Hauke; Kurnosov, Alexander; Taniguchi, Takashi; Kim, Byung-Nam; Yoshida, Hidehiro; Masuno, Atsunobu; Bednarcik, Jozef; Kulik, Eleonora; Ikuhara, Yuichi; Wakai, Fumihiro; Irifune, Tetsuo
2017-01-01
Glasses and single crystals have traditionally been used as optical windows. Recently, there has been a high demand for harder and tougher optical windows that are able to endure severe conditions. Transparent polycrystalline ceramics can fulfill this demand because of their superior mechanical properties. It is known that polycrystalline ceramics with a spinel structure in compositions of MgAl2O4 and aluminum oxynitride (γ-AlON) show high optical transparency. Here we report the synthesis of the hardest transparent spinel ceramic, i.e. polycrystalline cubic silicon nitride (c-Si3N4). This material shows an intrinsic optical transparency over a wide range of wavelengths below its band-gap energy (258 nm) and is categorized as one of the third hardest materials next to diamond and cubic boron nitride (cBN). Since the high temperature metastability of c-Si3N4 in air is superior to those of diamond and cBN, the transparent c-Si3N4 ceramic can potentially be used as a window under extremely severe conditions. PMID:28303948
Analysis and application of B-spline wavelet on interval hybrid stress element%区间B样条小波杂交应力元分析及其应用
Institute of Scientific and Technical Information of China (English)
刘艳红; 商中新
2013-01-01
Wavelet function is introduced into hybrid stress element. The scaling functions of BSWI are used to construct the rectangular and cubic wavelet element as interpolation function. The results obtained in this paper are compared with those by Abaqus. The numerical examples illustrate that the wavelet-based element method has higher accuracy and higher accuracy, while it's less sensitive to the density of elements.%将小波函数引入到杂交应力元中,以其尺度函数作为插值函数,构造了二维四节点和三维八节点的B样条小波杂交应力元.将数值算例结果与理论解和Abaqus软件计算结果相对比,本文所构造的新型单元具有计算精度高、对单元划分密度不敏感、收敛速度快的优点.
Institute of Scientific and Technical Information of China (English)
邱绵浩; 刘箐; 丛华
2007-01-01
经典的经验模式分解(EMD)方法通过求解信号的上下2条三次样条包络曲线的均值曲线,实现对原始信号的分解.但是对于非平稳、非线性信号,包络平均无法代替真正的局部平均.另外,基于包络平均的分解方法还会引入极值过冲和欠冲问题.利用B样条的良好局部性质直接计算信号的局部均值插值曲线,克服了三次样条包络方法在EMD分解中的不足.通过对旋转机械故障振动信号的分解处理,表明基于B样条局部均值插值曲线的经验模式分解方法得到的固有模式函数更符合信号的真实物理意义,分解结果更好.
Institute of Scientific and Technical Information of China (English)
王秀峰; 陈心昭
2001-01-01
基于三次B样条插值的统计边界元法，对随机振动结构声辐射的计算进行了研究。以随机振动球作为算例，计算了其在表面振速功率谱密度函数分布已知情况下的随机声场，计算结果与理论解比较表明：即使在边界剖分比较粗的情况下，利用该方法计算随机振动结构声辐射问题在相当宽的振动频率范围内，也能给出良好的计算精度。
Institute of Scientific and Technical Information of China (English)
冯仁忠; 查理
2005-01-01
为了避免一般的局部插值算法生成的B样条曲线和曲面在段点处达不到理想的连续性以及出现多重内节点的问题,一种局部构造C2连续的三次B样条插值曲线和双三次插值曲面的方法被介绍.该方法借助节点插入算法逐步地迭代出样条控制顶点,其思想简单、几何直观、算法速度快,在曲线中夹直线段、尖点以及在曲面中夹棱边和平面都能比较容易实现.生成的曲线光滑度高、无重节点.文章最后还利用这种构造方法给出了一种在指定范围内按规定变形曲线的方法.
Tame Kernels of Pure Cubic Fields
Institute of Scientific and Technical Information of China (English)
Xiao Yun CHENG
2012-01-01
In this paper,we study the p-rank of the tame kernels of pure cubic fields.In particular,we prove that for a fixed positive integer m,there exist infinitely many pure cubic fields whose 3-rank of the tame kernel equal to m.As an application,we determine the 3-rank of their tame kernels for some special pure cubic fields.
Two-dimensional cubic convolution.
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
The Body Center Cubic Quark Lattice Model
Lin Xu, Jiao
2004-01-01
The Standard Model while successful in many ways is incomplete; many questions remain. The origin of quark masses and hadronization of quarks are awaiting an answer. From the Dirac sea concept, we infer that two kinds of elementary quarks (u(0) and d(0)) constitute a body center cubic (BCC) quark lattice with a lattice constant a < $10^{-18}$m in the vacuum. Using energy band theory and the BCC quark lattice, we can deduce the rest masses and the intrinsic quantum numbers (I, S, C, b and Q) of quarks. With the quark spectrum, we deduce a baryon spectrum. The theoretical spectrum is in agreement well with the experimental results. Not only will this paper provide a physical basis for the Quark Model, but also it will open a door to study the more fundamental nature at distance scales <$10^{-18}$m. This paper predicts some new quarks $u_{c}$(6490) and d$_{b}$(9950), and new baryons $\\Lambda_{c}^{+}$(6500), $\\Lambda_{b}^{0}$(9960).
Cubical local partial orders on cubically subdivided spaces - Existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2006-01-01
The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...
Cubical local partial orders on cubically subdivided spaces - existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
Karnal H.Yasir; TANG Yun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented. This classification is an extension of the result given by Takens to the cubic homogeneous parameterized vector fields with six parameters.
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
KamalH.Yasir; TNAGYun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented.This classification is an extension of the result given by takens to the cubic homogeneous parameterized vector fields with six parameters.
Ultrahard nanotwinned cubic boron nitride.
Tian, Yongjun; Xu, Bo; Yu, Dongli; Ma, Yanming; Wang, Yanbin; Jiang, Yingbing; Hu, Wentao; Tang, Chengchun; Gao, Yufei; Luo, Kun; Zhao, Zhisheng; Wang, Li-Min; Wen, Bin; He, Julong; Liu, Zhongyuan
2013-01-17
Cubic boron nitride (cBN) is a well known superhard material that has a wide range of industrial applications. Nanostructuring of cBN is an effective way to improve its hardness by virtue of the Hall-Petch effect--the tendency for hardness to increase with decreasing grain size. Polycrystalline cBN materials are often synthesized by using the martensitic transformation of a graphite-like BN precursor, in which high pressures and temperatures lead to puckering of the BN layers. Such approaches have led to synthetic polycrystalline cBN having grain sizes as small as ∼14 nm (refs 1, 2, 4, 5). Here we report the formation of cBN with a nanostructure dominated by fine twin domains of average thickness ∼3.8 nm. This nanotwinned cBN was synthesized from specially prepared BN precursor nanoparticles possessing onion-like nested structures with intrinsically puckered BN layers and numerous stacking faults. The resulting nanotwinned cBN bulk samples are optically transparent with a striking combination of physical properties: an extremely high Vickers hardness (exceeding 100 GPa, the optimal hardness of synthetic diamond), a high oxidization temperature (∼1,294 °C) and a large fracture toughness (>12 MPa m(1/2), well beyond the toughness of commercial cemented tungsten carbide, ∼10 MPa m(1/2)). We show that hardening of cBN is continuous with decreasing twin thickness down to the smallest sizes investigated, contrasting with the expected reverse Hall-Petch effect below a critical grain size or the twin thickness of ∼10-15 nm found in metals and alloys.
Cubic III-nitrides: potential photonic materials
Onabe, K.; Sanorpim, S.; Kato, H.; Kakuda, M.; Nakamura, T.; Nakamura, K.; Kuboya, S.; Katayama, R.
2011-01-01
The growth and characterization of some cubic III-nitride films on suitable cubic substrates have been done, namely, c- GaN on GaAs by MOVPE, c-GaN and c-AlGaN on MgO by RF-MBE, and c-InN and c-InGaN (In-rich) on YSZ by RFMBE. This series of study has been much focused on the cubic-phase purity as dependent on the respective growth conditions and resulting electrical and optical properties. For c-GaN and c-InN films, a cubic-phase purity higher than 95% is attained in spite of the metastable nature of the cubic III-nitrides. However, for c-AlGaN and c-InGaN films, the cubic-phase purity is rapidly degraded with significant incorporation of the hexagonal phase through stacking faults on cubic {111} faces which may be exposed on the roughened growing or substrate surface. It has been shown that the electron mobilities in c-GaN and c-AlGaN films are much related to phase purity.
Cubic Curves, Finite Geometry and Cryptography
Bruen, A A; Wehlau, D L
2011-01-01
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.
Generalized Vaidya spacetime for cubic gravity
Ruan, Shan-Ming
2015-01-01
We present a kind of generalized Vaidya solutions of a new cubic gravity in five dimensions whose field equations in spherically spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally we present the first law and second law hold in this gravity. Although all the results are analogue to those in Lovelock gravity, we in fact introduce the contribution of new cubic term in five dimensions where cubic Lovelock term is just zero.
CLOSED SMOOTH SURFACE DEFINED FROM CUBIC TRIANGULAR SPLINES
Institute of Scientific and Technical Information of China (English)
Ren-zhong Feng; Ren-hong Wang
2005-01-01
In order to construct closed surfaces with continuous unit normal, we introduce a new spline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'Geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.
MOVING SCREW DISLOCATION IN CUBIC QUASICRYSTAL
Institute of Scientific and Technical Information of China (English)
ZHOU Wang-min; SONG Yu-hai
2005-01-01
The elasticity theory of the dislocation of cubic quasicrystals is developed.The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions,and the analytical expressions of displacements, stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained. These provide important information for studying the plastic deformation of the new solid material.
2-rational Cubic Spline Involving Tension Parameters
Indian Academy of Sciences (India)
M Shrivastava; J Joseph
2000-08-01
In the present paper, 1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given monotonic data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a 2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
Semisymmetric Cubic Graphs of Order 162
Indian Academy of Sciences (India)
Mehdi Alaeiyan; Hamid A Tavallaee; B N Onagh
2010-02-01
An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order 162. It is shown that for every odd prime , there exists a semisymmetric cubic graph of order 162 and its structure is explicitly specified by giving the corresponding voltage rules generating the covering projections.
Cubical version of combinatorial differential forms
DEFF Research Database (Denmark)
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
Institute of Scientific and Technical Information of China (English)
刘运峰; 宋寿鹏; 马晓鲲; 王成
2012-01-01
在超声检测中,液位、压力、应力等参数的测量实际上转化为超声信号度越时间的测量,如何有效地提取超声回波信号的波至时刻成为能否准确测量的关键.在分析了连续复小波变换的模极大值包络提取和小波的奇异点检测理论的基础上,提出了一种新的超声信号波至检测函数,并选用复频域B样条和高斯函数为小波基,在MATLAB上对仿真信号及原始超声信号分析处理.实验结果表明,此检测函数在较低的信噪比条件下也可有效地提取到超声回波信号的波至时刻.%In ultrasonic testing,the measurement of the liquid level,the pressure, the stress and so on is in fact the measurement of the time-of-flight of the ultrasonic signal. Then how to implement the extraction of ultrasonic signal arrival time precisely becomes so important. Based on envelop extraction of continuous complex wavelet transform and the singularity point detection theory , a new arrival time detection function is shown. Emulation and the real acquired ultrasonic data were processed with MATLAB u-sing complex frequency B-spline and Gaussian function as wavelet. It is proved that the function has good detection effect even under low SNR condition.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
Sparse B-spline polynomial descriptors for human activity recognition
Oikonomopoulos, Antonios; Pantic, Maja; Patras, Ioannis
2009-01-01
The extraction and quantization of local image and video descriptors for the subsequent creation of visual codebooks is a technique that has proved very effective for image and video retrieval applications. In this paper we build on this concept and propose a new set of visual descriptors that
Superhard BC(3) in cubic diamond structure.
Zhang, Miao; Liu, Hanyu; Li, Quan; Gao, Bo; Wang, Yanchao; Li, Hongdong; Chen, Changfeng; Ma, Yanming
2015-01-01
We solve the crystal structure of recently synthesized cubic BC(3) using an unbiased swarm structure search, which identifies a highly symmetric BC(3) phase in the cubic diamond structure (d-BC(3)) that contains a distinct B-B bonding network along the body diagonals of a large 64-atom unit cell. Simulated x-ray diffraction and Raman peaks of d-BC(3) are in excellent agreement with experimental data. Calculated stress-strain relations of d-BC(3) demonstrate its intrinsic superhard nature and reveal intriguing sequential bond-breaking modes that produce superior ductility and extended elasticity, which are unique among superhard solids. The present results establish the first boron carbide in the cubic diamond structure with remarkable properties, and these new findings also provide insights for exploring other covalent solids with complex bonding configurations.
Cubical Cohomology Ring of 3D Photographs
Gonzalez-Diaz, Rocio; Medrano, Belen; 10.1002/ima.20271
2011-01-01
Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary, facilitating efficient algorithms for the computation of topological invariants in the image context. In this paper, we present formulas to directly compute the cohomology ring of 3D cubical complexes without making use of any additional triangulation. Starting from a cubical complex $Q$ that represents a 3D binary-valued digital picture whose foreground has one connected component, we compute first the cohomological information on the boundary of the object, $\\partial Q$ by an incremental technique; then, using a face reduction algorithm, we compute it on the whole object; finally, applying the mentioned formulas, the cohomology ring is computed from such information.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
DEFICIENT CUBIC SPLINES WITH AVERAGE SLOPE MATCHING
Institute of Scientific and Technical Information of China (English)
V. B. Das; A. Kumar
2005-01-01
We obtain a deficient cubic spline function which matches the functions with certain area matching over a greater mesh intervals, and also provides a greater flexibility in replacing area matching as interpolation. We also study their convergence properties to the interpolating functions.
Counting rational points on cubic curves
Institute of Scientific and Technical Information of China (English)
HEATH-BROWN; Roger; TESTA; Damiano
2010-01-01
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals.The bounds are uniform in the curve and involve the rank of the corresponding Jacobian.The method used in the proof is a combination of the "determinant method" with an m-descent on the curve.
CONSTRAINED RATIONAL CUBIC SPLINE AND ITS APPLICATION
Institute of Scientific and Technical Information of China (English)
Qi Duan; Huan-ling Zhang; Xiang Lai; Nan Xie; Fu-hua (Frank) Cheng
2001-01-01
In this paper, a kind of rational cubic interpolation functionwith linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivative of the interpolating function is studied by using this interpolation, and as the consequent result, the convex interpolation conditions have been derived.
Anisotropy of a cubic ferromagnet at criticality
Kudlis, A.; Sokolov, A. I.
2016-10-01
Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear susceptibility acquires at Tc the universal value δ4*=2/v* 3 (u*+v*) where u* and v* are coordinates of the cubic fixed point on the flow diagram of renormalization group equations. In the paper, the critical value of the reduced anisotropy is estimated within the pseudo-ɛ expansion approach. The six-loop pseudo-ɛ expansions for u*, v*, and δ4* are derived for the arbitrary spin dimensionality n . For cubic crystals (n =3 ) higher-order coefficients of the pseudo-ɛ expansions obtained turn out to be so small that use of simple Padé approximants yields reliable numerical results. Padé resummation of the pseudo-ɛ series for u*, v*, and δ4* leads to the estimate δ4*=0.079 ±0.006 , indicating that detection of the anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is certainly possible.
Binomial Squares in Pure Cubic Number Fields
Lemmermeyer, Franz
2011-01-01
Let K = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m.
The cactus rank of cubic forms
Bernardi, Alessandra
2011-01-01
We prove that the smallest degree of an apolar 0-dimensional scheme to a general cubic form in $n+1$ variables is at most $2n+2$, when $n\\geq 8$, and therefore smaller than the rank of the form. When n=8 we show that the bound is sharp, i.e. the smallest degree of an apolar subscheme is 18.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
Ytterbium: Transition at High Pressure from Face-Centered Cubic to Body-Centered Cubic Structure.
Hall, H T; Barnett, J D; Merrill, L
1963-01-11
Pressure of 40,000 atmospheres at 25 degrees C induces a phase transformation in ytterbium metal; the face-centered cubic structure changes to body-centered cubic. The radius of the atom changes from 1.82 to 1.75 A. At the same time the atom's volume decreases by 11 percent and the volume, observed macroscopically, decreases 3.2 percent.
THERMODYNAMIC PARAMETERS OF LEAD SULFIDE CRYSTALS IN THE CUBIC PHASE
Directory of Open Access Journals (Sweden)
T. O. Parashchuk
2016-07-01
Full Text Available Geometric and thermodynamic parameters of cubic PbS crystals were obtained using the computer calculations of the thermodynamic parameters within density functional theory method DFT. Cluster models for the calculation based on the analysis of the crystal and electronic structure. Temperature dependence of energy ΔE and enthalpy ΔH, Gibbs free energy ΔG, heat capacity at constant pressure CP and constant volume CV, entropy ΔS were determined on the basis of ab initio calculations of the crystal structure of molecular clusters. Analytical expressions of temperature dependences of thermodynamic parameters which were approximated with quantum-chemical calculation points have been presented. Experimental results compared with theoretically calculated data.
Spinor bose gases in cubic optical lattice
Energy Technology Data Exchange (ETDEWEB)
Mobarak, Mohamed Saidan Sayed Mohamed
2014-01-27
In recent years the quantum simulation of condensed-matter physics problems has resulted from exciting experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry-breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand-canonical free energy allows to recover the mean-field theory. Applying a Legendre transformation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. Without external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the
Face-Centered-Cubic Nanostructured Polymer Foams
Cui, C.; Baughman, R. H.; Liu, L. M.; Zakhidov, A. A.; Khayrullin, I. I.
1998-03-01
Beautifully iridescent polymer foams having Fm-3m cubic symmetry and periodicities on the scale of the wavelength of light have been synthesized by the templating of porous synthetic opals. These fabrication processes involve the filling of porous SiO2 opals (with typical cubic lattice parameters of 250 nm) with either polymers or polymer precursors, polymerization of the precursors if necessary, and removal of the fcc array of SiO2 balls to provide an all-polymer structure. The structures of these foams are similar to periodic minimal surfaces, although the Gaussian curvature can have both positive and negative values. Depending upon whether the internal surfaces of the opal are polymer filled or polymer coated, the polymer replica has either one or two sets of independent channels. We fill these channels with semiconductors, metals, or superconductors to provide electronic and optical materials with novel properties dependent on the nanoscale periodicity.
Cubic Polynomials with Rational Roots and Critical Points
Gupta, Shiv K.; Szymanski, Waclaw
2010-01-01
If you want your students to graph a cubic polynomial, it is best to give them one with rational roots and critical points. In this paper, we describe completely all such cubics and explain how to generate them.
Use of Pom Pons to Illustrate Cubic Crystal Structures.
Cady, Susan G.
1997-01-01
Describes a method that uses olefin pom pons to illustrate cubic crystal structure. Facilitates hands-on examination of different packing arrangements such as hexagonal close-packed and cubic close-packed structures. (JRH)
Shape preserving rational bi-cubic function
Directory of Open Access Journals (Sweden)
Malik Zawwar Hussain
2012-11-01
Full Text Available The study is dedicated to the development of shape preserving interpolation scheme for monotone and convex data. A rational bi-cubic function with parameters is used for interpolation. To preserve the shape of monotone and convex data, the simple data dependent constraints are developed on these parameters in each rectangular patch. The developed scheme of this paper is confined, cheap to run and produce smooth surfaces.
Cubic Lienard Equations with Quadratic Damping (Ⅱ)
Institute of Scientific and Technical Information of China (English)
Yu-quan Wang; Zhu-jun Jing
2002-01-01
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
Local atomic structure in cubic stabilized zirconia
Energy Technology Data Exchange (ETDEWEB)
Villella, P.; Conradson, S. D.; Espinosa-Faller, F. J.; Foltyn, S. R.; Sickafus, K. E.; Valdez, J. A.; Degueldre, C. A.
2001-09-01
X-ray-absorption fine structure measurements have been used to elucidate the local atomic structure of quaternary Zr, Y, Er, Ce/U cubic stabilized zirconia. These compounds display more complicated local environments than those reported for simpler binary systems. While the shortest cation-O distances are similar to those found in the binary cubic stabilized compounds, responding to the different sizes of the cations, we have identified large distortions in the first-shell oxygen distribution involving long, 2.8--3.2 {angstrom} cation-O distances that are similar to those found in the amorphous phase of zirconium. The cation-cation distributions are also found to be quite complicated (non-Gaussian) and element specific. The U-near neighbor distances are expanded relative to the Ce ions for which it substitutes, consistent with the larger size of the actinide, and the U-cation distribution is also more complicated. In terms of the effects of this substitution on the other cation sites, the local environment around Y is altered while the Zr and Er local environments remain unchanged. These results point out the importance of collective and correlated interactions between the different pairs of cations and the host lattice that are mediated by the local strain fields generated by the different cations. The presence of pair-specific couplings has not been commonly included in previous analyses and may have implications for the stabilization mechanisms of cubic zirconia.
The special symplectic structure of binary cubics
Slupinski, Marcus
2009-01-01
Let $k$ be a field of characteristic not 2 or 3. Let $V$ be the $k$-space of binary cubic polynomials. The natural symplectic structure on $k^2$ promotes to a symplectic structure $\\omega$ on $V$ and from the natural symplectic action of $\\textrm{Sl}(2,k)$ one obtains the symplectic module $(V,\\omega)$. We give a complete analysis of this symplectic module from the point of view of the associated moment map, its norm square $Q$ (essentially the classical discriminant) and the symplectic gradient of $Q$. Among the results are a symplectic derivation of the Cardano-Tartaglia formulas for the roots of a cubic, detailed parameters for all $\\textrm{Sl}(2,k)$ and $\\textrm{Gl}(2,k)$-orbits, in particular identifying a group structure on the set of $\\textrm{Sl}(2,k)$-orbits of fixed nonzero discriminant, and a purely symplectic generalization of the classical Eisenstein syzygy for the covariants of a binary cubic. Such fine symplectic analysis is due to the special symplectic nature inherited from the ambient excepti...
Method of synthesizing cubic system boron nitride
Energy Technology Data Exchange (ETDEWEB)
Yuzu, S.; Sumiya, H.; Degawa, J.
1987-10-13
A method is described for synthetically growing cubic system boron nitride crystals by using boron nitride sources, solvents for dissolving the boron nitride sources, and seed crystals under conditions of ultra-high pressure and high temperature for maintaining the cubic system boron nitride stable. The method comprises the following steps: preparing a synthesizing vessel having at least two chambers, arrayed in order in the synthesizing vessel so as to be heated according to a temperature gradient; placing the solvents having different eutectic temperatures in each chamber with respect to the boron nitride sources according to the temperature gradient; placing the boron nitride source in contact with a portion of each of the solvents heated at a relatively higher temperature and placing at least a seed crystal in a portion of each of the solvents heated at a relatively lower temperature; and growing at least one cubic system boron nitride crystal in each of the solvents in the chambers by heating the synthesizing vessel for establishing the temperature gradient while maintaining conditions of ultra-high pressure and high temperature.
Cherenkov and Scintillation Properties of Cubic Zirconium
Christl, M.J.; Adams, J.H.; Parnell, T.A.; Kuznetsov, E.N.
2008-01-01
Cubic zirconium (CZ) is a high index of refraction (n =2.17) material that we have investigated for Cherenkov counter applications. Laboratory and proton accelerator tests of an 18cc sample of CZ show that the expected fast Cherenkov response is accompanied by a longer scintillation component that can be separated by pulse shaping. This presents the possibility of novel particle spectrometers which exploits both properties of CZ. Other high index materials being examined for Cherenkov applications will be discussed. Results from laboratory tests and an accelerator exposure will be presented and a potential application in solar energetic particle instruments will be discussed
Tachyon Vacuum in Cubic Superstring Field Theory
Erler, Theodore
2008-01-01
In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansion. Second, the solution {\\it vanishes} in the GSO$(-)$ sector, implying a ``tachyon vacuum'' solution exists even for a {\\it BPS} D-brane.
Generalized fairing algorithm of parametric cubic splines
Institute of Scientific and Technical Information of China (English)
WANG Yuan-jun; CAO Yuan
2006-01-01
Kjellander has reported an algorithm for fairing uniform parametric cubic splines. Poliakoff extended Kjellander's algorithm to non-uniform case. However, they merely changed the bad point's position, and neglected the smoothing of tangent at bad point. In this paper, we present a fairing algorithm that both changed point's position and its corresponding tangent vector. The new algorithm possesses the minimum property of energy. We also proved Poliakoff's fairing algorithm is a deduction of our fairing algorithm. Several fairing examples are given in this paper.
Fractal Symmetries: Ungauging the Cubic Code
Williamson, Dominic J
2016-01-01
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post- gauging models and use this to construct short range entangled phases with fractal like symmetries, one of which is mapped to the cubic code by the gauging.
The Exact Limit of Some Cubic Towers
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2016-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as good...... as Zink’s bound; i.e. λ(BBGS/Fq3 ) ≥ 2(q2 - 1)/(q + 2). In this paper, the exact value of λ(BBGS/Fq3 ) is computed. We also settle a question stated by Ihara....
Competing structural instabilities in cubic perovskites
Vanderbilt, D
1994-01-01
We study the antiferrodistortive instability and its interaction with ferroelectricity in cubic perovskite compounds. Our first-principles calculations show that coexistence of both instabilities is very common. We develop a first-principles scheme to study the thermodynamics of these compounds when both instabilities are present, and apply it to SrTiO$_3$. We find that increased pressure enhances the antiferrodistortive instability while suppressing the ferroelectric one. Moreover, the presence of one instability tends to suppress the other. A very rich $P$--$T$ phase diagram results.
Strong phonon anomalies and Fermi surface nesting of simple cubic Polonium
Belabbes, A.; Zaoui, A.; Ferhat, M.
2010-12-01
The unknown lattice dynamics of simple cubic Polonium is calculated using first-principles density-functional perturbation theory with pseudopotentials and a plane-wave basis set. We notice several phonon anomalies, in particular along major symmetry directions namely M-R, R-Γ, Γ-M, M-X, and X-Γ. The analysis of the Fermi surface strongly suggests that the observed phonon anomalies are Kohn anomalies arising from strong Fermi surface nesting.
Rheological properties of Cubic colloidal suspensions
Boromand, Arman; Maia, Joao
2016-11-01
Colloidal and non-colloidal suspensions are ubiquitous in many industrial application. There are numerous studies on these systems to understand and relate their complex rheological properties to their microstructural evolution under deformation. Although most of the experimental and simulation studies are centered on spherical particles, in most of the industrial applications the geometry of the colloidal particles deviate from the simple hard sphere and more complex geometries exist. Recent advances in microfabrication paved the way to fabricate colloidal particles with complex geometries for applications in different areas such as drug delivery where the fundamental understanding of their dynamics has remained unexplored. In this study, using dissipative particle dynamics, we investigate the rheological properties of cubic (superball) particles which are modeled as the cluster of core-modified DPD particles. Explicit representation of solvent particles in the DPD scheme will conserve the full hydrodynamic interactions between colloidal particles. Rheological properties of these cubic suspensions are investigated in the dilute and semi-dilute regimes. The Einstein and Huggins coefficients for these particles with different superball exponent will be calculate which represent the effect of single particle's geometry and multibody interactions on viscosity, respectively. The response of these suspensions is investigated under simple shear and oscillatory shear where it is shown that under oscillation these particles tend to form crystalline structure giving rise to stronger shear-thinning behavior recently measured experimentally.
All unitary cubic curvature gravities in D dimensions
Energy Technology Data Exchange (ETDEWEB)
Sisman, Tahsin Cagri; Guellue, Ibrahim; Tekin, Bayram, E-mail: sisman@metu.edu.tr, E-mail: e075555@metu.edu.tr, E-mail: btekin@metu.edu.tr [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey)
2011-10-07
We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D-dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.
Cubic meter volume optical coherence tomography
WANG, ZHAO; POTSAID, BENJAMIN; CHEN, LONG; DOERR, CHRIS; LEE, HSIANG-CHIEH; NIELSON, TORBEN; JAYARAMAN, VIJAYSEKHAR; CABLE, ALEX E.; SWANSON, ERIC; FUJIMOTO, JAMES G.
2017-01-01
Optical coherence tomography (OCT) is a powerful three-dimensional (3D) imaging modality with micrometer-scale axial resolution and up to multi-GigaVoxel/s imaging speed. However, the imaging range of high-speed OCT has been limited. Here, we report 3D OCT over cubic meter volumes using a long coherence length, 1310 nm vertical-cavity surface-emitting laser and silicon photonic integrated circuit dual-quadrature receiver technology combined with enhanced signal processing. We achieved 15 µm depth resolution for tomographic imaging at a 100 kHz axial scan rate over a 1.5 m range. We show 3D macroscopic imaging examples of a human mannequin, bicycle, machine shop gauge blocks, and a human skull/brain model. High-bandwidth, meter-range OCT demonstrates new capabilities that promise to enable a wide range of biomedical, scientific, industrial, and research applications. PMID:28239628
Black holes in Einsteinian cubic gravity
Hennigar, Robie A
2016-01-01
Using numerical and perturbative methods, we construct the first examples of black hole solutions in Einsteinian cubic gravity and study their thermodynamics. Focusing first on four dimensional solutions, we show that these black holes have a novel equation of state in which the pressure is a quadratic function of the temperature. Despite this, they undergo a first order phase transition with associated van der Waals behaviour. We then construct perturbative solutions for general $D \\ge 5$ and study the properties of these solutions for $D=5$ and $D=6$ in particular. We find novel examples of zeroth order phase transitions and find super-entropic behaviour over a large portion of the parameter space. We analyse the specific heat, determining that the black holes are thermodynamically stable over large regions of parameter space.
Triangulation of cubic panorama for view synthesis.
Zhang, Chunxiao; Zhao, Yan; Wu, Falin
2011-08-01
An unstructured triangulation approach, new to our knowledge, is proposed to apply triangular meshes for representing and rendering a scene on a cubic panorama (CP). It sophisticatedly converts a complicated three-dimensional triangulation into a simple three-step triangulation. First, a two-dimensional Delaunay triangulation is individually carried out on each face. Second, an improved polygonal triangulation is implemented in the intermediate regions of each of two faces. Third, a cobweblike triangulation is designed for the remaining intermediate regions after unfolding four faces to the top/bottom face. Since the last two steps well solve the boundary problem arising from cube edges, the triangulation with irregular-distribution feature points is implemented in a CP as a whole. The triangular meshes can be warped from multiple reference CPs onto an arbitrary viewpoint by face-to-face homography transformations. The experiments indicate that the proposed triangulation approach provides a good modeling for the scene with photorealistic rendered CPs.
Black holes in a cubic Galileon universe
Babichev, Eugeny; Lehébel, Antoine; Moskalets, Tetiana
2016-01-01
We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.
Finite element differential forms on cubical meshes
Arnold, Douglas N
2012-01-01
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.
Capturing dynamic cation hopping in cubic pyrochlores
Brooks Hinojosa, Beverly; Asthagiri, Aravind; Nino, Juan C.
2011-08-01
In direct contrast to recent reports, density functional theory predicts that the most stable structure of Bi2Ti2O7 pyrochlore is a cubic Fd3¯m space group by accounting for atomic displacements. The displaced Bi occupies the 96g(x,x,z) Wyckoff position with six equivalent sites, which create multiple local minima. Using nudged elastic band method, the transition states of Bi cation hopping between equivalent minima were investigated and an energy barrier between 0.11 and 0.21 eV was determined. Energy barriers associated with the motion of Bi between equivalent sites within the 96g Wyckoff position suggest the presence of dielectric relaxation in Bi2Ti2O7.
On the plane-wave cubic vertex
Lucietti, J; Sinha, A K; Lucietti, James; Schäfer-Nameki, Sakura; Sinha, Aninda
2004-01-01
The exact bosonic Neumann matrices of the cubic vertex in plane-wave light-cone string field theory are derived using the contour integration techniques developed in our earlier paper. This simplifies the original derivation of the vertex. In particular, the Neumann matrices are written in terms of \\mu-deformed Gamma-functions, thus casting them into a form that elegantly generalizes the well-known flat-space solution. The asymptotics of the \\mu-deformed Gamma-functions allow one to determine the large-\\mu behaviour of the Neumann matrices including exponential corrections. We provide an explicit expression for the first exponential correction and make a conjecture for the subsequent exponential correction terms.
Polarization conversion in cubic Raman crystals
McKay, Aaron; Sabella, Alexander; Mildren, Richard P.
2017-01-01
Nonlinear conversion of unpolarized beams to lower frequencies is generally inefficient in c(2) materials, as it is challenging to achieve phase-matching for input ordinary and extraordinary beams simultaneously in the normal dispersion regime. Here, we show that cubic Raman crystals having doubly and triply degenerate (E and F type) modes provide a method for efficient nonlinear frequency downconversion of an unpolarized beam and yield a linearly polarized output state. Using Mueller calculus, optimal crystal directions for such polarization conversion are determined. Using diamond, an example of an F-class Raman crystal, we have verified that such conversion is possible with near quantum-defect-limited slope efficiency and a linear polarization contrast of more than 23.9 dB. PMID:28169327
On the Stability of Cubic Galileon Accretion
Bergliaffa, Santiago P E
2016-01-01
We examine the stability of steady-state galileon accretion for the case of a Schwarzshild black hole. Considering the galileon action up to the cubic term in a static and spherically symmetric background we obtain the general solution for the equation of motion which is divided in two branches. By perturbing this solution we define an effective metric which determines the propagation of fluctuations. In this general picture we establish the position of the sonic horizon together with the matching condition of the two branches on it. Restricting to the case of a Schwarzschild background, we show, via the analysis of the energy of the perturbations and its time derivative, that the accreting field is linearly stable.
Low pressure growth of cubic boron nitride films
Ong, Tiong P. (Inventor); Shing, Yuh-Han (Inventor)
1997-01-01
A method for forming thin films of cubic boron nitride on substrates at low pressures and temperatures. A substrate is first coated with polycrystalline diamond to provide a uniform surface upon which cubic boron nitride can be deposited by chemical vapor deposition. The cubic boron nitride film is useful as a substitute for diamond coatings for a variety of applications in which diamond is not suitable. any tetragonal or hexagonal boron nitride. The cubic boron nitride produced in accordance with the preceding example is particularly well-suited for use as a coating for ultra hard tool bits and abrasives, especially those intended to use in cutting or otherwise fabricating iron.
Shape preserving rational cubic spline for positive and convex data
Directory of Open Access Journals (Sweden)
Malik Zawwar Hussain
2011-11-01
Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.
Diamine Functionalized Cubic Mesoporous Silica for Ibuprofen Controlled Delivery.
Sivaguru, J; Selvaraj, M; Ravi, S; Park, H; Song, C W; Chun, H H; Ha, C-S
2015-07-01
A diamine functionalized cubic mesostructured KIT-6 (N-KIT-6) has been prepared by post-synthetic method using calcined mesoporous KIT-6 with a diamine source, i.e., N-'[3-(tri methoxysilyl)- propyl]'ethylenediamine. The KIT-6 mesoporous silica used for N-KIT-6 was synthesized under weak acidic hydrothermal method using bitemplates, viz., Pluronic P123 and 1-butanol. The synthesized mesoporous materials, KIT-6 and N-KIT-6, have been characterized by the relevant instrumental techniques such as SAXS, N2 sorption isotherm, FT-IR, SEM, TEM and TGA to prove the standard mesoporous materials with the identification of diamine groups. The characterized mesoporous materials, KIT-6 and N-KIT-6, have been extensively used in the potential application of controlled drug delivery, where ibuprofen (IBU) employed as a model drug. The rate of IBU adsorption and release was monitored by UV vis-spectrometer. On the basis of the experimental results of controlled drug delivery system, the results of IBU adsorption and releasing rate in N-KIT-6 are higher than those of KIT-6 because of the higher hydrophobic nature as well as rich basic sites on the surface of inner pore wall silica.
Statistics of the single mode light in the transparent medium with cubic nonlinearity
Gorbachev, V N
1999-01-01
The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated, namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Planck equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics.
Analytic cubic and quartic force fields using density-functional theory
Energy Technology Data Exchange (ETDEWEB)
Ringholm, Magnus; Gao, Bin; Thorvaldsen, Andreas J.; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); Jonsson, Dan [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); High Performance Computing Group, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm, Sweden and PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Ekström, Ulf; Helgaker, Trygve [Center for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo (Norway)
2014-01-21
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn–Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange–correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree–Fock results. The Hartree–Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.
Interplay between lattice dynamics and the low-pressure phase of simple cubic polonium
Zaoui, A.; Belabbes, A.; Ahuja, R.; Ferhat, M.
2011-04-01
Low-pressure structural properties of simple cubic polonium are explored through first-principles density-functional theory based relativistic total energy calculations using pseudopotentials and plane-wave basis set, as well as linear-response theory. We have found that Po undergoes structural phase transition at low pressure near 2 GPa, where the element transforms from simple cubic to a mixture of two trigonal phases namely, hR1 (α=86°) and hR2 (α=97.9°) structures. The lattice dynamics calculations provide strong support for the observed phase transition, and show the dynamical stability (instability) of the hR2 (hR1) phase.
CRACK PROBLEM UNDER SHEAR LOADING IN CUBIC QUASICRYSTAL
Institute of Scientific and Technical Information of China (English)
周旺民; 范天佑; 尹姝媛
2003-01-01
The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. Based on the work, the analytic solutions of elastic field of cubic quasicrystal with a penny-shaped crack under the shear loading are found, and the stress intensity factor and strain energy release rate are determined.
Cubic Polynomials with Real or Complex Coefficients: The Full Picture
Bardell, Nicholas S.
2016-01-01
The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance…
An application of Cubical Cohomology to Adinkras and Supersymmetry Representations
Doran, Charles; Landweber, Greg
2012-01-01
An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincar\\'e algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds.
Institute of Scientific and Technical Information of China (English)
吴泽福
2012-01-01
Based on the comparision of basic static estimate methods of term structure of interest rate (TSIR), we improved B-spline function estimate method, which involved optimization on estimation programmes, node numbers choice, and node placement design. To overcome the subjective effect of B-spline node distribution and C2 smoothness condition of discount function, we introduced negative exponential smoothness cubic Li-spline optimization technology with minimum constraint function of estimation error from quadratic sum to absolute value and minimum volatility of discount function, to increase the estimation reliability and prediction ability of short-term interest rate's volatility structure mutation, improve the advantage on depicting the long-term interest rate volatility trend, and reduce the excessive volatility of discount function.%通过对比国内外利率期限结构静态估计模型的优劣,分析节点数目变化和定位改进B样条函数对利率期限结构静态估计的误差,构建最小化定价误差的节点组合布局搜索程序,并引入负指数平滑立方L1样条优化模型,将误差函数最小化结构从平方和最小化转化为误差距离最小化,权衡拟合误差绝对距离最小化与贴现函数波动性约束,克服B样条函数对节点数目与定位的人工干预和放宽对贴现函数的二阶平滑要求,保留B样条函数刻画中长期利率波动趋势的优势,增强对短期利率波动结构突变的估计和预测能力,提高定价精确度和缓解利率期限结构曲线的过度波动问题.
Rational Cubics and Conics Representation: A Practical Approach
Directory of Open Access Journals (Sweden)
M. Sarfraz
2012-08-01
Full Text Available A rational cubic spline, with one family of shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights, in the description of the spline curve can be used to modify the shape of the curve, locally and globally, at the knot intervals. The rational cubic spline attains parametric smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline.Key Words: Computer Graphics, Interpolation, Spline, Conic, Rational Cubic
On cubic equations over $P-$adic field
Mukhamedov, Farrukh; Saburov, Mansoor
2012-01-01
We provide a solvability criteria for a depressed cubic equation in domains $\\bz_p^{*},\\bz_p,\\bq_p$. We show that, in principal, the Cardano method is not always applicable for such equations. Moreover, the numbers of solutions of the depressed cubic equation in domains $\\bz_p^{*},\\bz_p,\\bq_p$ are provided. Since $\\bbf_p\\subset\\bq_p,$ we generalize J.-P. Serre's \\cite{JPSJ} and Z.H.Sun's \\cite{ZHS1,ZHS3} results concerning with depressed cubic equations over the finite field $\\bbf_p$. Finally, all depressed cubic equations, for which the Cardano method could be applied, are described and the $p-$adic Cardano formula is provided for those cubic equations.
Directory of Open Access Journals (Sweden)
Jie Lai
2009-12-01
Full Text Available Jie Lai1,2, Yi Lu1, Zongning Yin2, Fuqiang Hu3, Wei Wu11School of Pharmacy, Fudan University, Shanghai, China, 2West China School of Pharmacy, Sichuan University, Chengdu, China, 3School of Pharmacy, Zhejiang University, Hangzhou, ChinaAbstract: Efforts to improve the oral bioavailability of cyclosporine A (CyA remains a challenge in the field of drug delivery. In this study, glyceryl monooleate (GMO/poloxamer 407 cubic nanoparticles were evaluated as potential vehicles to improve the oral bioavailability of CyA. Cubic nanoparticles were prepared via the fragmentation of a bulk GMO/poloxamer 407 cubic phase gel by sonication and homogenization. The cubic inner structure formed was verified using Cryo-TEM. The mean diameters of the nanoparticles were about 180 nm, and the entrapment efficiency of these particles for CyA was over 85%. The in vitro release of CyA from these nanoparticles was less than 5% at 12 h. The results of a pharmacokinetic study in beagle dogs showed improved absorption of CyA from cubic nanoparticles as compared to microemulsion-based Neoral®; higher Cmax (1371.18 ± 37.34 vs 969.68 ± 176.3 ng mL-1, higher AUC0–t (7757.21 ± 1093.64 vs 4739.52 ± 806.30 ng h mL-1 and AUC0–∞ (9004.77 ± 1090.38 vs 5462.31 ± 930.76 ng h mL-1. The relative oral bioavailability of CyA cubic nanoparticles calculated on the basis of AUC0–∞ was about 178% as compared to Neoral®. The enhanced bioavailability of CyA is likely due to facilitated absorption by cubic nanoparticles rather than improved release.Keywords: nanoparticles, cubosomes, cyclosporine A, glyceryl monooleate, oral drug delivery, bioavailability, beagle dogs
On q-power cycles in cubic graphs
DEFF Research Database (Denmark)
Bensmail, Julien
2017-01-01
In the context of a conjecture of Erdos and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning...... the remaining case q = 2 (which corresponds to the conjecture of Erdos and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only....
On q-power cycles in cubic graphs
DEFF Research Database (Denmark)
Bensmail, Julien
2016-01-01
In the context of a conjecture of Erdos and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning...... the remaining case q = 2 (which corresponds to the conjecture of Erdos and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only....
The compressibility of cubic white and orthorhombic, rhombohedral, and simple cubic black phosphorus
Energy Technology Data Exchange (ETDEWEB)
Clark, Simon M; Zaug, Joseph
2010-03-10
The effect of pressure on the crystal structure of white phosphorus has been studied up to 22.4 GPa. The ?alpha phase was found to transform into the alpha' phase at 0.87 +- 0.04 GPa with a volume change of 0.1 +- 0.3 cc/mol. A fit of a second order Birch- Murnaghan equation to the data gave Vo = 16.94 ? 0.08 cc/mol and Ko = 6.7 +- 0.5 GPa for the alpha phase and Vo = 16.4 +- 0.1 cc/mol and Ko = 9.1 +- 0.3 GPa for the alpha' phase. The alpha' phase was found to transform to the A17 phase of black phosphorus at 2.68 +- 0.34 GPa and then with increasing pressure to the A7 and then simple cubic phase of black phosphorus. A fit of a second order Birch-Murnaghan equation to our data combined with previous measurements gave Vo = 11.43 +- 0.05 cc/mol and Ko = 34.7 +- 0.5 GPa for the A17 phase, Vo = 9.62 +- 0.01 cc/mol and Ko = 65.0 +- 0.6 GPa for the A7 phase and , Vo = 9.23 +- 0.01 cc/mol and Ko = 72.5 +- 0.3 GPa for the simple cubic phase.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
On the basis of integrated intensity of rocking curves, the multiplicity factor and the diffraction geometry factor for single crystal X-ray diffraction (XRD) analysis were proposed and a general formula for calculating the content of mixed phases was obtained. With a multifunction four-circle X-ray double-crystal diffractometer, pole figures of cubic (002), {111} and hexagonal {1010} and reciprocal space mapping were measured to investigate the distributive character of mixed phases and to obtain their multiplicity factors and diffraction geometry factors. The contents of cubic twins and hexagonal inclusions were calculated by the integrated intensities of rocking curves of cubic (002), cubic twin {111}, hexagonal {1010} and {1011}.
Global infinite energy solutions for the cubic wave equation
Burq, N.; L. Thomann; Tzvetkov, N.
2012-01-01
International audience; We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
The Coulombic Lattice Potential of Ionic Compounds: The Cubic Perovskites.
Francisco, E.; And Others
1988-01-01
Presents coulombic models representing the particles of a system by point charges interacting through Coulomb's law to explain coulombic lattice potential. Uses rubidium manganese trifluoride as an example of cubic perovskite structure. Discusses the effects on cluster properties. (CW)
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Lucian-Cornel Crasovan; Boris A Malomed; Dumitru Mihalache
2001-11-01
We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.
Stress Intensity of Antiplane Conjugate Cracks in Cubic Quasicrystal
Institute of Scientific and Technical Information of China (English)
ZHANG Lei
2008-01-01
Based on the theory of Muskhelishvili, the general solutions for stress and strain of conjugate cracks in cubic quasicrystal are obtained, with which the stress intensity factors of cubic quasicrystal at crack tips and the stress distribution functions of phonon and phason fields are given. The results show that though phason field is coupled with phonon field by constitutive equations, the stress intensity factors are not coupled with any other factors.
Optical studies of cubic III-nitride structures
Powell, Ross E L
2014-01-01
The properties of cubic nitrides grown by molecular beam epitaxy (MBE) on GaAs (001) have been studied using optical and electrical techniques. The aim of these studies was the improvement of the growth techniques in order to improve the quality of grown nitrides intended for bulk substrate and optoelectronic device applications. We have also characterised hexagonal nanocolumn structures incorporating indium. Firstly, bulk films of cubic AlxGa1-xN with aluminium fractions (x) spanning the ...
Bobrovskij, N. M.; Levashkin, D. G.; Bobrovskij, I. N.; Melnikov, P. A.; Lukyanov, A. A.
2017-01-01
Article is devoted the decision of basing holes machining accuracy problems of automatically replaceable cubical units (carriers) for reconfigurable manufacturing systems with low-waste production (RMS). Results of automatically replaceable units basing holes machining modeling on the basis of the dimensional chains analysis are presented. Influence of machining parameters processing on accuracy spacings on centers between basing apertures is shown. The mathematical model of carriers basing holes machining accuracy is offered.
Institute of Scientific and Technical Information of China (English)
魏永伟; 汪国昭
2012-01-01
In order to develop the theory of orthogonal basis for algebraic-trigonometric spline space, a novel approach is presented to construct an orthogonal basis for the uniform four-order algebraic trigonometric spline space.Based on the C-B spline functions of order six, a set of auxiliary functions is constructed.And the proposed orthogonal splines are given as the second-order derivatives of these auxiliary functions.This orthogonal basis is also called Legendre-like basis.The result of the practical examples shows that using this basis can simplify inner product computation and facilitate solving least-squares approximation.%为解决代数三角样条空间上正交基的理论问题,提出了4阶均匀代数三角样条空间上构造正交基的方法.该方法利用6阶C-B样条基函数构造一组辅助函数,并以这组辅助函数的二阶导数形式定义样条空间上的一组正交基,称为拟Legendre基.实例结果表明,使用这组正交基可以简化内积计算,便于最佳平方逼近问题求解.
A new hypercube variant: Fractal Cubic Network Graph
Directory of Open Access Journals (Sweden)
Ali Karci
2015-03-01
Full Text Available Hypercube is a popular and more attractive interconnection networks. The attractive properties of hypercube caused the derivation of more variants of hypercube. In this paper, we have proposed two variants of hypercube which was called as “Fractal Cubic Network Graphs”, and we have investigated the Hamiltonian-like properties of Fractal Cubic Network Graphs FCNGr(n. Firstly, Fractal Cubic Network Graphs FCNGr(n are defined by a fractal structure. Further, we show the construction and characteristics analyses of FCNGr(n where r=1 or r=2. Therefore, FCNGr(n is a Hamiltonian graph which is obtained by using Gray Code for r=2 and FCNG1(n is not a Hamiltonian Graph. Furthermore, we have obtained a recursive algorithm which is used to label the nodes of FCNG2(n. Finally, we get routing algorithms on FCNG2(n by utilizing routing algorithms on the hypercubes.
Ferromagnetic Ground States in Face-Centered Cubic Hubbard Clusters
Souza, T. X. R.; Macedo, C. A.
2016-01-01
In this study, the ground state energies of face-centered cubic Hubbard clusters are analyzed using the Lanczos method. Examination of the ground state energy as a function of the number of particle per site n showed an energy minimum for face-centered cubic structures. This energy minimum decreased in n with increasing coulombic interaction parameter U. We found that the ground state energy had a minimum at n = 0.6, when U = 3W, where W denotes the non-interacting energy bandwidth and the face-centered cubic structure was ferromagnetic. These results, when compared with the properties of nickel, shows strong similarity with other finite temperature analyses in the literature and supports the Hirsh’s conjecture that the interatomic direct exchange interaction dominates in driving the system into a ferromagnetic phase. PMID:27583653
Superconductivity in cubic noncentrosymmetric PdBiSe Crystal
Joshi, B.; Thamizhavel, A.; Ramakrishnan, S.
2015-03-01
Mixing of spin singlet and spin triplet superconducting pairing state is expected in noncentrosymmetric superconductors (NCS) due to the inherent presence of Rashba-type antisymmetric spin-orbit coupling. Unlike low symmetry (tetragonal or monoclinic) NCS, parity is isotropicaly broken in space for cubic NCS and can additionally lead to the coexistence of magnetic and superconducting state under certain conditions. Motivated with such enriched possibility of unconventional superconducting phases in cubic NCS we are reporting successful formation of single crystalline cubic noncentrosymmetric PdBiSe with lattice parameter a = 6.4316 Å and space group P21 3 (space group no. 198) which undergoes to superconducting transition state below 1.8 K as measured by electrical transport and AC susceptibility measurements. Significant strength of Rashba-type antisymmetric spin-orbit coupling can be expected for PdBiSe due to the presence of high Z (atomic number) elements consequently making it potential candidate for unconventional superconductivity.
Cubic interactions of Maxwell-like higher spins
Francia, Dario; Mkrtchyan, Karapet
2016-01-01
We study the cubic vertices for Maxwell-like higher-spins in flat space. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.
Extended temperature dependence of elastic constants in cubic crystals.
Telichko, A V; Sorokin, B P
2015-08-01
To extend the theory of the temperature dependence of the elastic constants in cubic crystals beyond the second- and third-order elastic constants, the fourth-order elastic constants, as well as the non-linearity in the thermal expansion temperature dependence, have been taken into account. Theoretical results were represented as temperature functions of the effective elastic constants and compared with experimental data for a number of cubic crystals, such as alkali metal halides, and elements gold and silver. The relations obtained give a more accurate description of the experimental temperature dependences of second-order elastic constants for a number of cubic crystals, including deviations from linear behavior. A good agreement between theoretical estimates and experimental data has been observed.
Tetragonal and cubic zirconia multilayered ceramic constructs created by EPD.
Mochales, Carolina; Frank, Stefan; Zehbe, Rolf; Traykova, Tania; Fleckenstein, Christine; Maerten, Anke; Fleck, Claudia; Mueller, Wolf-Dieter
2013-02-14
The interest in electrophoretic deposition (EPD) for nanomaterials and ceramics production has widely increased due to the versatility of this technique to effectively combine different materials in unique shapes and structures. We successfully established an EPD layering process with submicrometer sized powders of Y-TZP with different mol percentages of yttrium oxide (3 and 8%) and produced multilayers of alternating tetragonal and cubic phases with a clearly defined interface. The rationale behind the design of these multilayer constructs was to optimize the properties of the final ceramic by combining the high mechanical toughness of the tetragonal phase of zirconia together with the high ionic conductivity of its cubic phase. In this work, a preliminary study of the mechanical properties of these constructs proved the good mechanical integrity of the multilayered constructs obtained as well as crack deflection in the interface between tetragonal and cubic zirconia layers.
Body-centered-cubic Ni and its magnetic properties.
Tian, C S; Qian, D; Wu, D; He, R H; Wu, Y Z; Tang, W X; Yin, L F; Shi, Y S; Dong, G S; Jin, X F; Jiang, X M; Liu, F Q; Qian, H J; Sun, K; Wang, L M; Rossi, G; Qiu, Z Q; Shi, J
2005-04-08
The body-centered-cubic (bcc) phase of Ni, which does not exist in nature, has been achieved as a thin film on GaAs(001) at 170 K via molecular beam epitaxy. The bcc Ni is ferromagnetic with a Curie temperature of 456 K and possesses a magnetic moment of 0.52+/-0.08 micro(B)/atom. The cubic magnetocrystalline anisotropy of bcc Ni is determined to be +4.0x10(5) ergs x cm(-3), as opposed to -5.7x10(4) ergs x cm(-3) for the naturally occurring face-centered-cubic (fcc) Ni. This sharp contrast in the magnetic anisotropy is attributed to the different electronic band structures between bcc Ni and fcc Ni, which are determined using angle-resolved photoemission with synchrotron radiation.
Hardness and thermal stability of cubic silicon nitride
DEFF Research Database (Denmark)
Jiang, Jianzhong; Kragh, Flemming; Frost, D. J.
2001-01-01
The hardness and thermal stability of cubic spinel silicon nitride (c-Si3N4), synthesized under high-pressure and high-temperature conditions, have been studied by microindentation measurements, and x-ray powder diffraction and scanning electron microscopy, respectively The phase at ambient...... temperature has an average hardness of 35.31 GPa, slightly larger than SiO2 stishovite, which is often referred to as the third hardest material after diamond and cubic boron nitride. The cubic phase is stable up to 1673 K in air. At 1873 K, alpha -and beta -Si3N4 phases are observed, indicating a phase...... transformation sequence of c-to-alpha -to-beta -Si3N4 phases....
Image interpolation by two-dimensional parametric cubic convolution.
Shi, Jiazheng; Reichenbach, Stephen E
2006-07-01
Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.
Higher-spin Interactions from CFT: The Complete Cubic Couplings
Sleight, Charlotte
2016-01-01
In this letter we provide a complete holographic reconstruction of the cubic couplings in the minimal bosonic higher-spin theory in AdS$_{d+1}$. For this purpose we also determine the OPE coefficients of all single-trace conserved currents in the $d$-dimensional free scalar $O\\left(N\\right)$ vector model, and compute the tree-level three-point Witten diagram amplitudes for a generic cubic interaction of higher-spin gauge fields in the metric-like formulation.
Classifying Cubic Edge-Transitive Graphs of Order 8
Indian Academy of Sciences (India)
Mehdi Alaeiyan; M K Hosseinipoor
2009-11-01
A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let be a prime. It was shown by Folkman (J. Combin. Theory 3(1967) 215--232) that a regular edge-transitive graph of order 2 or 22 is necessarily vertex-transitive. In this paper, an extension of his result in the case of cubic graphs is given. It is proved that, every cubic edge-transitive graph of order 8 is symmetric, and then all such graphs are classified.
Possible form of multi-polar interaction in cubic lattice
Energy Technology Data Exchange (ETDEWEB)
Sakai, Osamu; Shiina, Ryousuke; Shiba, Hiroyuki
2003-05-01
The invariant form of interaction between multi-poles, including the octupole, is studied for the simple cubic (SC), body centered and face centered cubic lattices. The coupling terms can be arranged in a way similar to that of the hopping matrix between the LCAO's. A table for SC by Shiina et al. (J. Phys. Soc. Japan 66 (1997) 1741) is generalized for the general wave number case of the three types of lattice. Recent experimental result of TmTe is thereby analyzed. The development of the ferromagnetic moment below the anti-ferromagnetic transition under the anti-ferro quadrupolar order phase is discussed in this connection.
Possible form of multi-polar interaction in cubic lattice
Sakai, Osamu; Shiina, Ryousuke; Shiba, Hiroyuki
2003-05-01
The invariant form of interaction between multi-poles, including the octupole, is studied for the simple cubic (SC), body centered and face centered cubic lattices. The coupling terms can be arranged in a way similar to that of the hopping matrix between the LCAO's. A table for SC by Shiina et al. (J. Phys. Soc. Japan 66 (1997) 1741) is generalized for the general wave number case of the three types of lattice. Recent experimental result of TmTe is thereby analyzed. The development of the ferromagnetic moment below the anti-ferromagnetic transition under the anti-ferro quadrupolar order phase is discussed in this connection.
Counting perfect matchings of cubic graphs in the geometric dual
Jiménez, Andrea
2010-01-01
Lov\\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph G with no cutedge has an exponential in |V(G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3 times the golden ratio to |V(G)|/72 distinct perfect matchings. Our work builds on a novel approach relating Lov\\'asz and Plummer's conjecture and the number of so called groundstates of the widely studied Ising model from statistical physics.
Elastic interaction of point defects in crystals with cubic symmetry
Kuz'michev, S. V.; Kukushkin, S. A.; Osipov, A. V.
2013-07-01
The energy of elastic mechanical interaction between point defects in cubic crystals is analyzed numerically. The finite-element complex ANSYS is used to investigate the character of interaction between point defects depending on their location along the crystallographic directions , , and on the distance from the free boundary of the crystal. The numerical results are compared with the results of analytic computations of the energy of interaction between two point defects in an infinite anisotropic medium with cubic symmetry. The interaction between compressible and incompressible defects of general type is studied. Conditions for onset of elastic attraction between the defects, which leads to general relaxation of the crystal elastic energy, are obtained.
Cubic surfaces and their invariants: Some memories of Raymond Stora
Directory of Open Access Journals (Sweden)
Michel Bauer
2016-11-01
I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4(C splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
Evaluation method of multiaxial low cycle fatigue life for cubic single crystal material
Institute of Scientific and Technical Information of China (English)
CHEN Jiping; DING Zhiping
2007-01-01
The coupling effect of normal stress and shear stress on orthotropic materials happens when applied loading deflects from the directions of the principal axes of the material coordinate system.By taking account of the coupling effects,formulas of equivalent stress and strain for cubic single crystal materials are cited.Using the equivalent strain and equivalent stress for such material and a variable k,which is introduced to express the effect of asymmetrical cyclic loading on fatigue life,a low cycle fatigue (LCF) life prediction model for such material in multiaxial stress starts is proposed.On the basis of the yield criterion and constitutive model of cubic single crystal materials,a subroutine to calculate the thermo elastic-plastic stress-strain of the material on an ANSYS platform was developed.The cyclic stress-strain of DD3 notched specimens under asymmetrical loading at 680℃ was analyzed.Low cycle fatigue test data of the single crystal nickel-based superalloy are used to fit the different parameters of the power law with multiple linear regression analysis.The equivalent stress and strain for a cubic single crystal material as failure parameters have the largest correlation coefficient.A power law exists between k and the failure cycle.The model was validated with LCF test data of CMSX-2 and DD3 single crystal nickel-based superalloys.All the test data fall into the factor of 2.5 for CMSX-2 hollow cylinder specimens and 2.0 scatter band for DD3 notched specimens,respectively.
Interaction of dispersed cubic phases with blood components
DEFF Research Database (Denmark)
Bode, J C; Kuntsche, Judith; Funari, S S;
2013-01-01
The interaction of aqueous nanoparticle dispersions, e.g. based on monoolein/poloxamer 407, with blood components is an important topic concerning especially the parenteral way of administration. Therefore, the influence of human and porcine plasma on dispersed cubic phases was investigated...
Cubic surfaces and their invariants: Some memories of Raymond Stora
Bauer, Michel
2016-11-01
Cubic surfaces embedded in complex projective 3-space are a classical illustration of the use of old and new methods in algebraic geometry. Recently, they made their appearance in physics, and in particular aroused the interest of Raymond Stora, to the memory of whom these notes are dedicated, and to whom I'm very much indebted. Each smooth cubic surface has a rich geometric structure, which I review briefly, with emphasis on the 27 lines and the combinatorics of their intersections. Only elementary methods are used, relying on first order perturbation/deformation theory. I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4 (C) splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric) invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
Exact solutions for the cubic-quintic nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiamin [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)]. E-mail: zjm64@163.com; Ma Zhengyi [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China); Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 (China)
2007-08-15
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Combinatorics on Words in Symbolic Dynamics: the Antisymmetric Cubic Map
Institute of Scientific and Technical Information of China (English)
Wan Ji DAI; Kebo L(U); Jun WANG
2008-01-01
This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval.The least words of given lengths,the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established.
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Orientational phase transition in cubic liquid crystals with positional order
Pokrovsky, V.L.; Saidachmetov, P.A.
1988-01-01
An electric field can give rise to a shear deformation of a cubic liquid crystal with long-range positional order fixed by two plates. The critical value of the field does not depend on the size of the system and depends crucially on the orientation.
An effective packing density of binary cubic crystals
Eremin, I. E.; Eremina, V. V.; Sychev, M. S.; Moiseenko, V. G.
2015-04-01
The methodology of effective macroscopic calculation of numerical values of internuclear distances in binary crystals of a cubic crystal system is based on the use of coefficients of the structural packing density of the crystal lattice. The possibility of combining the reference data on the main physicochemical parameters of the substance is implemented by synthesis of the corresponding mathematical models.
Trapping of cubic ZnO nanocrystallites at ambient conditions
DEFF Research Database (Denmark)
Decremps, F.; Pellicer-Porres, J.; Datchi, F.
2002-01-01
Dense powder of nanocrystalline ZnO has been recovered at ambient conditions in the metastable cubic structure after a heat treatment at high pressure (15 GPa and 550 K). Combined x-ray diffraction (XRD) and x-ray absorption spectroscopy (XAS) experiments have been performed to probe both long-ra...
Specific heat of the simple-cubic Ising model
Feng, X.; Blöte, H.W.J.
2010-01-01
We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions
Connecting the Dots Parametrically: An Alternative to Cubic Splines.
Hildebrand, Wilbur J.
1990-01-01
Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)
Cubic spline approximation techniques for parameter estimation in distributed systems
Banks, H. T.; Crowley, J. M.; Kunisch, K.
1983-01-01
Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.
Rheology of cubic particles suspended in a Newtonian fluid.
Cwalina, Colin D; Harrison, Kelsey J; Wagner, Norman J
2016-05-18
Many real-world industrial processes involve non-spherical particles suspended in a fluid medium. Knowledge of the flow behavior of these suspensions is essential for optimizing their transport properties and designing processing equipment. In the present work, we explore and report on the rheology of concentrated suspensions of cubic-shaped colloidal particles under steady and dynamic shear flow. These suspensions exhibit a rich non-Newtonian rheology that includes shear thickening and normal stress differences at high shear stresses. Scalings are proposed to connect the material properties of these suspensions of cubic particle to those measured for suspensions of spherical particles. Negative first normal stress differences indicate that lubrication hydrodynamic forces dominate the stress in the shear-thickened state. Accounting for the increased lubrication hydrodynamic interactions between the flat surfaces of the cubic particles allows for a quantitative comparison of the deviatoric stress in the shear-thickened state to that of spherical particles. New semi-empirical models for the viscosity and normal stress difference coefficients are presented for the shear-thickened state. The results of this study indicate that cubic particles offer new and unique opportunities to formulate colloidal dispersions for field-responsive materials.
Infinite Face Centered Cubic Network of Identical Resistors
Asad, J H
2012-01-01
The equivalent resistance between the origin and any other lattice site, in an infinite Face Centered Cubic network consisting from identical resistors, has been expressed rationally in terms of the known value and . The asymptotic behavior is investigated, and some calculated values for the equivalent resistance are presented.
Trace spaces in a pre-cubical complex
DEFF Research Database (Denmark)
Raussen, Martin
In directed algebraic topology, (spaces of) directed irreversible (d)-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths are equipped with a natural...
Morphosynthesis of cubic silver cages on monolithic activated carbon.
Wang, Fei; Zhao, Hong; Lai, Yijian; Liu, Siyu; Zhao, Binyuan; Ning, Yuesheng; Hu, Xiaobin
2013-11-14
Cubic silver cages were prepared on monolithic activated carbon (MAC) pre-absorbed with Cl(-), SO4(2-), or PO4(3-) anions. Silver insoluble salts served as templates for the morphosynthesis of silver cages. The silver ions were reduced by reductive functional groups on MAC micropores through a galvanic cell reaction mechanism.
SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULAR ELEMENT OF THE FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
Qi-ding Zhu
2000-01-01
In this paper, we construct a projection interpolation for cubic triangular ele- ment by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1 -e order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.
Integrability of Lotka-Volterra Planar Complex Cubic Systems
Dukarić, Maša; Giné, Jaume
In this paper, we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods.
Global Well-Posedness for Cubic NLS with Nonlinear Damping
Antonelli, Paolo
2010-11-04
We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.
Facão, M; Carvalho, M I
2015-08-01
We found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity.
Directory of Open Access Journals (Sweden)
S.Sasikala
2013-04-01
Full Text Available Information processing and decision support system using image mining techniques is in advance drive with huge availability of remote sensing image (RSI. RSI describes inherent properties of objects by recording their natural reflectance in the electro-magnetic spectral (ems region. Information on such objects could be gathered by their color properties or their spectral values in various ems range in the form of pixels. Present paper explains a method of such information extraction using cubical distance method and subsequent results. Thismethod is one among the simpler in its approach and considers grouping of pixels on the basis of equal distance from a specified point in the image or selected pixel having definite attribute values (DN in different spectral layers of the RSI. The color distance and the occurrence pixel distance play a vital role in determining similarobjects as clusters aid in extracting features in the RSI domain.
Cubic ideal ferromagnets at low temperature and weak magnetic field
Hofmann, Christoph P.
2017-04-01
The low-temperature series for the free energy density, pressure, magnetization and susceptibility of cubic ideal ferromagnets in weak external magnetic fields are discussed within the effective Lagrangian framework up to three loops. The structure of the simple, body-centered, and face-centered cubic lattice is taken into account explicitly. The expansion involves integer and half-integer powers of the temperature. The corresponding coefficients depend on the magnetic field and on low-energy effective constants that can be expressed in terms of microscopic quantities. Our formulas may also serve as efficiency or consistency check for other techniques like Green's function methods, where spurious terms in the low-temperature expansion have appeared. We explore the sign and magnitude of the spin-wave interaction in the pressure, magnetization and susceptibility, and emphasize that our effective field theory approach is fully systematic and rigorous.
Counting real cubics with passage/tangency conditions
Lanzat, Sergei
2010-01-01
We study the following question: given a set of seven points and an immersed curve in the real plane R^2, all in general position, how many real rational nodal plane cubics pass through these points and are tangent to this curve. We count each such cubic with a certain sign, and present an explicit formula for their algebraic number. This number is preserved under small regular homotopies of the curve, but jumps (in a well-controlled way) when in the process of homotopy we pass a certain singular discriminant. We discuss the relation of such enumerative problems with finite type invariants. Our approach is based on maps of configuration spaces and the intersection theory in the spirit of classical algebraic topology.
Reversible Nanoparticle Cubic Lattices in Blue Phase Liquid Crystals.
Gharbi, Mohamed Amine; Manet, Sabine; Lhermitte, Julien; Brown, Sarah; Milette, Jonathan; Toader, Violeta; Sutton, Mark; Reven, Linda
2016-03-22
Blue phases (BPs), a distinct class of liquid crystals (LCs) with 3D periodic ordering of double twist cylinders involving orthogonal helical director twists, have been theoretically studied as potential templates for tunable colloidal crystals. Here, we report the spontaneous formation of thermally reversible, cubic crystal nanoparticle (NP) assemblies in BPs. Gold NPs, functionalized to be highly miscible in cyanobiphenyl-based LCs, were dispersed in BP mixtures and characterized by polarized optical microscopy and synchrotron small-angle X-ray scattering (SAXS). The NPs assemble by selectively migrating to periodic strong trapping sites in the BP disclination lines. The NP lattice, remarkably robust given the small particle size (4.5 nm diameter), is commensurate with that of the BP matrix. At the BP I to BP II phase transition, the NP lattice reversibly switches between two different cubic structures. The simultaneous presence of two different symmetries in a single material presents an interesting opportunity to develop novel dynamic optical materials.
Highly Aminated Mesoporous Silica Nanoparticles with Cubic Pore Structure
Suteewong, Teeraporn
2011-01-19
Mesoporous silica with cubic symmetry has attracted interest from researchers for some time. Here, we present the room temperature synthesis of mesoporous silica nanoparticles possessing cubic Pm3n symmetry with very high molar ratios (>50%) of 3-aminopropyl triethoxysilane. The synthesis is robust allowing, for example, co-condensation of organic dyes without loss of structure. By means of pore expander molecules, the pore size can be enlarged from 2.7 to 5 nm, while particle size decreases. Adding pore expander and co-condensing fluorescent dyes in the same synthesis reduces average particle size further down to 100 nm. After PEGylation, such fluorescent aminated mesoporous silica nanoparticles are spontaneously taken up by cells as demonstrated by fluorescence microscopy.
The Piecewise Cubic Method (PCM) for computational fluid dynamics
Lee, Dongwook; Faller, Hugues; Reyes, Adam
2017-07-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges at fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme on a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
The Piecewise Cubic Method (PCM) for Computational Fluid Dynamics
Lee, Dongwook; Reyes, Adam
2016-01-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges in fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme in a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
Cubic Composite Sensor with Photodiodes for Tracking Solar Orientation
Directory of Open Access Journals (Sweden)
Yong-Nong Chang
2013-01-01
Full Text Available A cubic composite solar sensor with photo diode is proposed for tracking the relative solar orientation. The proposed solar sensor composes of five photodiode detectors which are placed on the front, rear, left, right, and horizontal facets in a cubic body, respectively. The solar detectors placed on five facets can detect solar power of different facets. Based on the geometric coordinate transformation principle, the relationship equations of solar light orientation between measured powers with respect to various facets can be conducted. As a result, the solar orientation can be precisely achieved without needing any assistance of electronic compass and extra orientation angle corrector. Eventually, the relative solar light orientation, the elevation angle, and azimuth angle of the solar light can be measured precisely.
Nonlinear optical imaging of defects in cubic silicon carbide epilayers.
Hristu, Radu; Stanciu, Stefan G; Tranca, Denis E; Matei, Alecs; Stanciu, George A
2014-06-11
Silicon carbide is one of the most promising materials for power electronic devices capable of operating at extreme conditions. The widespread application of silicon carbide power devices is however limited by the presence of structural defects in silicon carbide epilayers. Our experiment demonstrates that optical second harmonic generation imaging represents a viable solution for characterizing structural defects such as stacking faults, dislocations and double positioning boundaries in cubic silicon carbide layers. X-ray diffraction and optical second harmonic rotational anisotropy were used to confirm the growth of the cubic polytype, atomic force microscopy was used to support the identification of silicon carbide defects based on their distinct shape, while second harmonic generation microscopy revealed the detailed structure of the defects. Our results show that this fast and noninvasive investigation method can identify defects which appear during the crystal growth and can be used to certify areas within the silicon carbide epilayer that have optimal quality.
Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem
Directory of Open Access Journals (Sweden)
Xiaomei Zhang
2012-01-01
Full Text Available We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006. The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006 and Y. Wang et al. (2010. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
Quantum spectra and classical periodic orbit in the cubic billiard
Institute of Scientific and Technical Information of China (English)
Dehua Wang; Yongjiang Yu; Shenglu Lin
2006-01-01
Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.
Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices
Wellard, C J; Wellard, Cameron; Orus, Roman
2004-01-01
Motivated by its relation to an NP-hard problem we analyze the ground state properties of anti-ferromagnetic Ising-spin networks in planar cubic lattices under the action of homogeneous transverse and longitudinal magnetic fields. We consider different instances of the cubic geometry and find a set of quantum phase transitions for each one of the systems, which we characterize by means of entanglement behavior and majorization theory. Entanglement scaling at the critical region is in agreement with results arising from conformal symmetry, therefore even the simplest planar systems can display very large amounts of quantum correlation. No conclusion can be made as to the scaling behavior of the minimum energy gap, with the data allowing equally good fits to exponential and power law decays. Analysis of entanglement and especially of majorization instead of the energy spectrum proves to be a good way of detecting quantum phase transitions in highly frustrated configurations.
Higher-Order Approximation of Cubic-Quintic Duffing Model
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Babazadeh, H.
2011-01-01
We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...... without analytical solution which makes it a unique solution. It is demonstrated that this method works very well for the whole range of parameters in the case of the cubic-quintic oscillator, and excellent agreement of the approximate frequencies with the exact one has been observed and discussed....... Moreover, it is not limited to the small parameter such as in the classical perturbation method. Interestingly, this study revealed that the relative error percentage in the second-order approximate analytical period is less than 0.042% for the whole parameter values. In addition, we compared...
3D Medical Image Interpolation Based on Parametric Cubic Convolution
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
Experimental core electron density of cubic boron nitride
DEFF Research Database (Denmark)
Wahlberg, Nanna; Bindzus, Niels; Bjerg, Lasse
candidate because of its many similarities with diamond: bonding pattern in the extended network structure, hardness, and the quality of the crystallites.3 However, some degree ionic interaction is a part of the bonding in boron nitride, which is not present in diamond. By investigating the core density...... beyond multipolar modeling of the valence density. As was recently shown in a benchmark study of diamond by Bindzus et al.1 The next step is to investigate more complicated chemical bonding motives, to determine the effect of bonding on the core density. Cubic boron nitride2 lends itself as a perfect...... in boron nitride we may obtain a deeper understanding of the effect of bonding on the total density. We report here a thorough investigation of the charge density of cubic boron nitride with a detailed modelling of the inner atom charge density. By combining high resolution powder X-ray diffraction data...
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
The Number of Real Roots of a Cubic Equation
Kavinoky, Richard; Thoo, John B.
2008-01-01
To find the number of distinct real roots of the cubic equation (1) x[caret]3 + bx[caret]2 + cx + d = 0, we could attempt to solve the equation. Fortunately, it is easy to tell the number of distinct real roots of (1) without having to solve the equation. The key is the discriminant. The discriminant of (1) appears in Cardan's (or Cardano's) cubic…
A highly ordered cubic mesoporous silica/graphene nanocomposite
Lee, Chang-Wook; Roh, Kwang Chul; Kim, Kwang-Bum
2013-09-01
A highly ordered cubic mesoporous silica (KIT-6)/graphene nanocomposite and 2D KIT-6 nanoflakes were synthesized using a novel synthesis methodology. The non-ionic triblock copolymer, P123, played a dual role as a structure-directing agent in the formation of the cubic mesoporous structure and as a cross-linking agent between mesoporous silica and graphene. The prepared (KIT-6)/graphene nanocomposite could act as a template for the preparation of mesoporous material/graphene nanocomposites.A highly ordered cubic mesoporous silica (KIT-6)/graphene nanocomposite and 2D KIT-6 nanoflakes were synthesized using a novel synthesis methodology. The non-ionic triblock copolymer, P123, played a dual role as a structure-directing agent in the formation of the cubic mesoporous structure and as a cross-linking agent between mesoporous silica and graphene. The prepared (KIT-6)/graphene nanocomposite could act as a template for the preparation of mesoporous material/graphene nanocomposites. Electronic supplementary information (ESI) available: S1: TEM images of disordered mesoporous silica/graphene nanocomposite; S2: TEM images of KIT-6/GO nanocomposite; S3: Thermogravimetric analysis of KIT-6/GO and KG-400-700; S4: SEM and TEM images of KIT-6; S5: Low angle XRD, Raman spectra, N2 adsorption isotherms, pore size distribution and photographic images of the prepared samples; S6: TEM image and N2 adsorption isotherms of mesoporous carbon/graphene nanocomposite; S7: XPS C1s spectra of the prepared samples. See DOI: 10.1039/c3nr03108j
Multiscale Modeling of Point and Line Defects in Cubic Lattices
2007-01-01
and discli- nations with finite micropolar elastoplasticity . Int. J. Plasticity. 22:210–256, 2006. 56. Menzel, A., and Steinmann, P., On the contin...Voyiadjis, G. Z., A finite strain plastic- damage model for high velocity impact using combined viscosity and gradient localization limiters: Part I...Theoretical for- mulation. Int. J. Damage Mech. 15:293–334, 2006. 58. Milstein, F., and Chantasiriwan, S,. Theoretical study of the response of 12 cubic
INTEGRABILITY AND LINEARIZABILITY FOR A CLASS OF CUBIC KOLMOGOROV SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using c...
Photonic Crystal Cavities in Cubic Polytype Silicon Carbide Films
Radulaski, Marina; Buckley, Sonia; Rundquist, Armand; Provine, J; Alassaad, Kassem; Ferro, Gabriel; Vučković, Jelena
2013-01-01
We present the design, fabrication, and characterization of high quality factor and small mode volume planar photonic crystal cavities from cubic (3C) thin films (thickness ~ 200 nm) of silicon carbide (SiC) grown epitaxially on a silicon substrate. We demonstrate cavity resonances across the telecommunications band, with wavelengths from 1250 - 1600 nm. Finally, we discuss possible applications in nonlinear optics, optical interconnects, and quantum information science.
Infinite Body Centered Cubic Network of Identical Resistors
Asad, J H
2013-01-01
We express the equivalent resistance between the origin and any other lattice site in an infinite Body Centered Cubic (BCC) network consisting of identical resistors each of resistance R rationally in terms of known values and . The equivalent resistance is then calculated. Finally, for large separation between the origin and the lattice site two asymptotic formulas for the resistance are presented and some numerical results with analysis are given.
Lipidic cubic phase injector facilitates membrane protein serial femtosecond crystallography.
Weierstall, Uwe; James, Daniel; Wang, Chong; White, Thomas A; Wang, Dingjie; Liu, Wei; Spence, John C H; Bruce Doak, R; Nelson, Garrett; Fromme, Petra; Fromme, Raimund; Grotjohann, Ingo; Kupitz, Christopher; Zatsepin, Nadia A; Liu, Haiguang; Basu, Shibom; Wacker, Daniel; Han, Gye Won; Katritch, Vsevolod; Boutet, Sébastien; Messerschmidt, Marc; Williams, Garth J; Koglin, Jason E; Marvin Seibert, M; Klinker, Markus; Gati, Cornelius; Shoeman, Robert L; Barty, Anton; Chapman, Henry N; Kirian, Richard A; Beyerlein, Kenneth R; Stevens, Raymond C; Li, Dianfan; Shah, Syed T A; Howe, Nicole; Caffrey, Martin; Cherezov, Vadim
2014-01-01
Lipidic cubic phase (LCP) crystallization has proven successful for high-resolution structure determination of challenging membrane proteins. Here we present a technique for extruding gel-like LCP with embedded membrane protein microcrystals, providing a continuously renewed source of material for serial femtosecond crystallography. Data collected from sub-10-μm-sized crystals produced with less than 0.5 mg of purified protein yield structural insights regarding cyclopamine binding to the Smoothened receptor.
Rotary Ultrasonic Machining of Poly-Crystalline Cubic Boron Nitride
2014-01-01
Poly-crystalline cubic boron nitride (PCBN) is one of the hardest material. Generally, so hard materials could not be machined by conventional machining methods. Therefore, for this purpose, advanced machining methods have been designed. Rotary ultrasonic machining (RUM) is included among them. RUM is based on abrasive removing mechanism of ultrasonic vibrating diamond particles, which are bonded on active part of rotating tool. It is suitable especially for machining hard and brittle materia...
Bicontinuous cubic liquid crystalline nanoparticles for oral delivery of Doxorubicin
DEFF Research Database (Denmark)
Swarnakar, Nitin K; Thanki, Kaushik; Jain, Sanyog
2014-01-01
PURPOSE: The present study explores the potential of bicontinous cubic liquid crystalline nanoparticles (LCNPs) for improving therapeutic potential of doxorubicin. METHODS: Phytantriol based Dox-LCNPs were prepared using hydrotrope method, optimized for various formulation components, process...... variables and lyophilized. Structural elucidation of the reconstituted formulation was performed using HR-TEM and SAXS analysis. The developed formulation was subjected to exhaustive cell culture experiments for delivery potential (Caco-2 cells) and efficacy (MCF-7 cells). Finally, in vivo pharmacokinetics...
The traveling salesman problem on cubic and subcubic graphs
Boyd, Sylvia; van der Ster, Suzanne; Stougie, Leen
2011-01-01
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation (the subtour elimination relaxation), is 4/3. We present the first algorithm for cubic graphs with approximation ratio 4/3. The proof uses polyhedral techniques in a surprising way, which is of independent interest. In fact we prove constructively that for any cubic graph on $n$ vertices a tour of length 4n/3-2 exists, which also implies the 4/3 conjecture, as an upper bound, for this class of graph-TSP. Recently, M\\"omke and Svensson presented a randomized algorithm that gives a 1.461-approximation for graph-TSP on general graphs and as a side result a 4/3-approximation algorithm for this problem on subcubic graphs, also settling the 4/3 conjectur...
Field-effect transistors based on cubic indium nitride.
Oseki, Masaaki; Okubo, Kana; Kobayashi, Atsushi; Ohta, Jitsuo; Fujioka, Hiroshi
2014-02-04
Although the demand for high-speed telecommunications has increased in recent years, the performance of transistors fabricated with traditional semiconductors such as silicon, gallium arsenide, and gallium nitride have reached their physical performance limits. Therefore, new materials with high carrier velocities should be sought for the fabrication of next-generation, ultra-high-speed transistors. Indium nitride (InN) has attracted much attention for this purpose because of its high electron drift velocity under a high electric field. Thick InN films have been applied to the fabrication of field-effect transistors (FETs), but the performance of the thick InN transistors was discouraging, with no clear linear-saturation output characteristics and poor on/off current ratios. Here, we report the epitaxial deposition of ultrathin cubic InN on insulating oxide yttria-stabilized zirconia substrates and the first demonstration of ultrathin-InN-based FETs. The devices exhibit high on/off ratios and low off-current densities because of the high quality top and bottom interfaces between the ultrathin cubic InN and oxide insulators. This first demonstration of FETs using a ultrathin cubic indium nitride semiconductor will thus pave the way for the development of next-generation high-speed electronics.
Malmir, Hessam; Sahimi, Muhammad; Tabar, M Reza Rahimi
2016-12-01
Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO_{2} sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016)2045-232210.1038/srep35024]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.
Dry Powder Precursors of Cubic Liquid Crystalline Nanoparticles (cubosomes)
Spicer, Patrick T.; Small, William B.; Small, William B.; Lynch, Matthew L.; Burns, Janet L.
2002-08-01
Cubosomes are dispersed nanostructured particles of cubic phase liquid crystal that have stimulated significant research interest because of their potential for application in controlled-release and drug delivery. Despite the interest, cubosomes can be difficult to fabricate and stabilize with current methods. Most of the current work is limited to liquid phase processes involving high shear dispersion of bulk cubic liquid crystalline material into sub-micron particles, limiting application flexibility. In this work, two types of dry powder cubosome precursors are produced by spray-drying: (1) starch-encapsulated monoolein is produced by spray-drying a dispersion of cubic liquid crystalline particles in an aqueous starch solution and (2) dextran-encapsulated monoolein is produced by spray-drying an emulsion formed by the ethanol-dextran-monoolein-water system. The encapsulants are used to decrease powder cohesion during drying and to act as a soluble colloidal stabilizer upon hydration of the powders. Both powders are shown to form (on average) 0.6 μm colloidally-stable cubosomes upon addition to water. However, the starch powders have a broader particle size distribution than the dextran powders because of the relative ease of spraying emulsions versus dispersions. The developed processes enable the production of nanostructured cubosomes by end-users rather than just specialized researchers and allow tailoring of the surface state of the cubosomes for broader application.
Malmir, Hessam; Sahimi, Muhammad; Tabar, M. Reza Rahimi
2016-12-01
Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO2 sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016), 10.1038/srep35024]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.
Integer roots of quadratic and cubic polynomials with integer coefficients
Zelator, Konstantine
2011-01-01
The subject matter of this work is quadratic and cubic polynomial functions with integer coefficients;and all of whose roots are integers. The material of this work is directed primarily at educators,students,and teachers of mathematics,grades K12 to K20.The results of this work are expressed in Theorems3,4,and5. Of these theorems, Theorem3, is the one that most likely, the general reader of this article will have some familiarity with.In Theorem3, precise coefficient conditions are given;in order that a quadratic trinomial(with integer) have two integer roots or zeros.On the other hand, Theorems4 and5 are largely unfamiliar territory. In Theorem4, precise coefficient conditions are stated; for a monic cubic polynomial to have a double(i.e.of multiplicity 2) integer root, and a single integer root(i.e.of multiplicity 1).The entire family of such cubics can be described in terms of four groups or subfamilies; each such group being a two-integer parameter subfamily. In Theorem5, a one-integer parameter family o...
Arithmetic Problems in Cubic and Quartic Function Fields
Bembom, Tobias
2010-01-01
One of the main themes in this thesis is the description of the signature of both the infinite place and the finite places in cubic function fields of any characteristic and quartic function fields of characteristic at least 5. For these purposes, we provide a new theory which can be applied to cubic and quartic function fields and to even higher dimensional function fields. One of the striking advantages of this theory to other existing methods is that is does not use the concept of p-adic completions and we can dispense of Cardano's formulae. Another key result comprises the construction of cubic function fields of unit rank 1 and 2, with an obvious fundamental system. One of the main ingredients for such constructions is the definition of the maximum value. This definition is new and very prolific in the context of finding fundamental systems. We conclude the thesis with miscellaneous results on the divisor class number h, including a new approach for finding divisors of h.
Dynamic properties of the cubic nonlinear Schr(o)dinger equation by symplectic method
Institute of Scientific and Technical Information of China (English)
Liu Xue-Shen; Wei Jia-Yu; Ding Pei-Zhu
2005-01-01
The dynamic properties of a cubic nonlinear Schrodinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schrodinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.
Sanz-Vicario, José Luis; Pérez-Torres, Jhon Fredy; Moreno-Polo, Germán
2017-08-01
We compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.
Evarestov, Robert A.; Blokhin, Evgeny; Gryaznov, Denis; Kotomin, Eugene A.; Maier, Joachim
2010-01-01
The atomic, electronic structure and phonon frequencies have been calculated in a cubic and low-temperature tetragonal SrTiO3 phases at the ab initio level. We demonstrate that the use of hybrid exchange-correlation PBE0 functional gives the best agreement with experimental data. The results for the standard PBE and hybrid PBE0 are compared for the two types of basis sets: a linear combination of atomic orbitals (LCAO, CRYSTAL09 computer code) and plane waves (PW, VASP 5.2 code). Relation bet...
Xu, Song; Li, Yang; Guo, Qi; Yang, Xiao-Feng; Chan, Rosa H M
2017-02-15
Tracking the changes of neural dynamics based on neuronal spiking activities is a critical step to understand the neurobiological basis of learning from behaving animals. These dynamical neurobiological processes associated with learning are also time-varying, which makes the modeling problem challenging. We developed a novel multiwavelet-based time-varying generalized Laguerre-Volterra (TVGLV) modeling framework to study the time-varying neural dynamical systems using natural spike train data. By projecting the time-varying parameters in the TVGLV model onto a finite sequence of multiwavelet basis functions, the time-varying identification problem is converted into a time invariant linear-in-the-parameters one. An effective forward orthogonal regression (FOR) algorithm aided by mutual information (MI) criterion is then applied for the selection of significant model regressors or terms and the refinement of model structure. A generalized linear model fit approach is finally employed for parameter estimation from spike train data. The proposed multiwavelet-based TVGLV approach is used to identify both synthetic input-output spike trains and spontaneous retinal spike train recordings. The proposed method gives excellent the performance of tracking either sharply or slowly changing parameters with high sensitivity and accuracy regardless of the a priori knowledge of spike trains, which these results indicate that the proposed method is shown to deal well with spike train data. The proposed multiwavelet-based TVGLV approach was compared with several state-of-art parametric estimation methods like the steepest descent point process filter (SDPPF) or Chebyshev polynomial expansion method. The conventional SDPPF algorithm, or SDPPF with B-splines wavelet expansion method was shown to have the poor performance of tracking the time-varying system changes with the synthetic spike train data due to the slow convergence of the adaptive filter methods. Although the Chebyshev
Energy Technology Data Exchange (ETDEWEB)
R.J. Garrett
2002-01-14
As part of the internal Integrated Safety Management Assessment verification process, it was determined that there was a lack of documentation that summarizes the safety basis of the current Yucca Mountain Project (YMP) site characterization activities. It was noted that a safety basis would make it possible to establish a technically justifiable graded approach to the implementation of the requirements identified in the Standards/Requirements Identification Document. The Standards/Requirements Identification Documents commit a facility to compliance with specific requirements and, together with the hazard baseline documentation, provide a technical basis for ensuring that the public and workers are protected. This Safety Basis Report has been developed to establish and document the safety basis of the current site characterization activities, establish and document the hazard baseline, and provide the technical basis for identifying structures, systems, and components (SSCs) that perform functions necessary to protect the public, the worker, and the environment from hazards unique to the YMP site characterization activities. This technical basis for identifying SSCs serves as a grading process for the implementation of programs such as Conduct of Operations (DOE Order 5480.19) and the Suspect/Counterfeit Items Program. In addition, this report provides a consolidated summary of the hazards analyses processes developed to support the design, construction, and operation of the YMP site characterization facilities and, therefore, provides a tool for evaluating the safety impacts of changes to the design and operation of the YMP site characterization activities.
Vacancy-induced mechanical stabilization of cubic tungsten nitride
Balasubramanian, Karthik; Khare, Sanjay; Gall, Daniel
2016-11-01
First-principles methods are employed to determine the structural, mechanical, and thermodynamic reasons for the experimentally reported cubic WN phase. The defect-free rocksalt phase is both mechanically and thermodynamically unstable, with a negative single crystal shear modulus C44=-86 GPa and a positive enthalpy of formation per formula unit Hf=0.623 eV with respect to molecular nitrogen and metallic W. In contrast, WN in the NbO phase is stable, with C44=175 GPa and Hf=-0.839 eV . A charge distribution analysis reveals that the application of shear strain along [100] in rocksalt WN results in an increased overlap of the t2 g orbitals which causes electron migration from the expanded to the shortened W-W bond axes, yielding a negative shear modulus due to an energy reduction associated with new bonding states 8.1-8.7 eV below the Fermi level. A corresponding shear strain in WN in the NbO phase results in an energy increase and a positive shear modulus. The mechanical stability transition from the NaCl to the NbO phase is explored using supercell calculations of the NaCl structure containing Cv=0 %-25 % cation and anion vacancies, while keeping the N-to-W ratio constant at unity. The structure is mechanically unstable for Cvconcentration, the isotropic elastic modulus E of cubic WN is zero, but increases steeply to E =445 GPa for Cv=10 % , and then less steeply to E =561 GPa for Cv=25 % . Correspondingly, the hardness estimated using Tian's model increases from 0 to 15 to 26 GPa as Cv increases from 5% to 10% to 25%, indicating that a relatively small vacancy concentration stabilizes the cubic WN phase and that the large variations in reported mechanical properties of WN can be attributed to relatively small changes in Cv.
Cubic Phases, Cubosomes and Ethosomes for Cutaneous Application.
Esposito, Elisabetta; Drechsler, Markus; Nastruzzi, Claudio; Cortesi, Rita
2016-01-01
Cutaneous administration represents a good strategy to treat skin diseases, avoiding side effects related to systemic administration. Apart from conventional therapy, based on the use of semi-solid formulation such as gel, ointments and creams, recently the use of specialized delivery systems based on lipid has been taken hold. This review provides an overview about the use of cubic phases, cubosomes and ethosomes, as lipid systems recently proposed to treat skin pathologies. In addition in the final part of the review cubic phases, cubosomes and ethosomes are compared to solid lipid nanoparticles and lecithin organogel with respect to their potential as delivery systems for cutaneous application. It has been reported that lipid nanosystems are able to dissolve and deliver active molecules in a controlled fashion, thereby improving their bioavailability and reducing side-effects. Particularly lipid matrixes are characterized by skin affinity and biocompatibility allowing their application on skin. Indeed, after cutaneous administration, the lipid matrix of cubic phases and cubosomes coalesces with the lipids of the stratum comeum and leads to the formation of a lipid depot from which the drug associated to the nanosystem can be released in the deeper skin strata in a controlled manner. Ethosomes are characterized by a malleable structure that promotes their interaction with skin, improving their potential as skin delivery systems with respect to liposomes. Also in the case of solid lipid nanoparticles it has been suggested a deep interaction between lipid matrix and skin strata that endorses sustained and prolonged drug release. Concerning lecithin organogel, the peculiar structure of this system, where lecithin exerts a penetration enhancer role, allows a deep interaction with skin strata, promoting the transdermal absorption of the encapsulated drugs.
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Cubature Formula and Interpolation on the Cubic Domain
Institute of Scientific and Technical Information of China (English)
Huiyuan Li; Jiachang Sun; Yuan Xu
2009-01-01
Several cubature formulas on the cubic domains are derived using the dis-crete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Cheby-shev weight functions and associated interpolation polynomials on [-1,1]2, as well as new results on [-1,1]3. In particular, compact formulas for the fundamental interpo-lation polynomials are derived, based on n3/4 + (n2) nodes of a cubature formula on [-1,1]3.
Exotic Universal Solutions in Cubic Superstring Field Theory
Erler, Theodore
2010-01-01
We present a class of analytic solutions of cubic superstring field theory in the universal sector on a non-BPS D-brane. Computation of the action and gauge invariant overlap reveal that the solutions carry half the tension of a non-BPS D-brane. However, the solutions do not satisfy the reality condition. In fact, they display an intriguing topological structure: We find evidence that conjugation of the solutions is equivalent to a gauge transformation that cannot be continuously deformed to the identity.
Research on the Cutting Performance of Cubic Boron Nitride Tools
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
There were only two kinds of superhard tool material at the past, i.e. diamond and cubic boron nitride (CBN). Manmade diamond and CBN are manufactured by the middle of 20th century. Various manufacturing methods and manmade superhard materials were developed later. They were widely used in different industry and science areas. Recently, a new kind of superhard tool material, C 3N 4 coating film, had been developed. American physical scientists, A. M. Liu and M. L. Cohen, designed a new kind of inorganic c...
Self-trapping transition in nonlinear cubic lattices
Naether, Uta; Guzmán-Silva, Diego; Molina, Mario I; Vicencio, Rodrigo A
2013-01-01
We explore the fundamental question about the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization, performing several numerical simulations in one-, two-, and three-dimensional lattices. A simple criterium is developed - for the case of an initially localized excitation - defining the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. A general analytical estimate of the critical nonlinearity value for which this transition occurs is obtained.
Cubic versus spherical magnetic nanoparticles: the role of surface anisotropy.
Salazar-Alvarez, G; Qin, J; Sepelák, V; Bergmann, I; Vasilakaki, M; Trohidou, K N; Ardisson, J D; Macedo, W A A; Mikhaylova, M; Muhammed, M; Baró, M D; Nogués, J
2008-10-08
The magnetic properties of maghemite (gamma-Fe2O3) cubic and spherical nanoparticles of similar sizes have been experimentally and theoretically studied. The blocking temperature, T(B), of the nanoparticles depends on their shape, with the spherical ones exhibiting larger T(B). Other low temperature properties such as saturation magnetization, coercivity, loop shift or spin canting are rather similar. The experimental effective anisotropy and the Monte Carlo simulations indicate that the different random surface anisotropy of the two morphologies combined with the low magnetocrystalline anisotropy of gamma-Fe2O3 is the origin of these effects.
Configuration spaces of an embedding torus and cubical spaces
Jourdan, Jean-Philippe
2006-01-01
For a smooth manifold M obtained as an embedding torus, A U Cx[-1,1], we consider the ordered configuration space F_k(M) of k distinct points in M. We show that there is a homotopical cubical resolution of F_k(M) defined from the configuration spaces of A and C. From it, we deduce a universal method for the computation of the pure braid groups of a manifold. We illustrate the method in the case of the Mobius band.
Ionic Conduction in Cubic Zirconias at Low Temperatures
Institute of Scientific and Technical Information of China (English)
Ying LI; Yunfa CHEN; Jianghong GONG
2004-01-01
The ac conductivities of Y2O3 or CaO-stabilized cubic zirconias were obtained from complex impedance measurements in the temperature range from 373 to 473 K. By analyzing the temperature-dependence of the resultant dc conductivities, it was shown that the activation energies for conduction are lower than those reported previously for the same materials at high temperatures. Comparing the activation energy data with the theoretically estimated values revealed that there may exist a certain, although very small, amount of free oxygen vacancies in the test samples at low temperatures and the conduction in the test samples is a result of the migration of these free oxygen vacancies.
Cubic to tetragonal crystal lattice reconstruction during ordering or decomposition
Energy Technology Data Exchange (ETDEWEB)
Cheong, Byung-kl [Carnegie-Mellon Univ., Pittsburgh, PA (United States). Dept. of Materials Science and Engineering
1992-09-01
This thesis studied thermodynamic stability and morphology of product phases in diffusional phase transformations involving cubic-to-tetragonal crystal lattice reconstructions. Two different kinds of diffusional transformations were examined: L1{sub 0} ordering (fcc to fct lattice change) and decomposition of off-stoichiometric B2 ordering alloys accompanying bcc to fcc Bain transformation. In the first case, Fe-45 at.% Pd alloys were studied by TEM; in the second, the Bain strain relaxation during decomposition of hyper-eutectoid Cu-9.04 wt% Be alloy was studied. CuAu and InMg were also studied.
On the {P2, P3}-Factor of Cubic Graphs
Institute of Scientific and Technical Information of China (English)
GOU Kui-xiang; SUN Liang
2005-01-01
Let G = ( V, E) be a finite simple graph and Pn denote the path of order n. A spanning subgraph F is called a {P2, P3}-factor of G if each component of F is isomorphic to P2 or P3. With the path-covering method, it is proved that any connected cubic graph with at least 5 vertices has a { P2, P3 }-factor F such that | P3 (F) |≥|P2 (F) |, where P2 (F) and P3 (F) denote the set of components of P2 and P3 in F,respectively.
Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices.
Cramer, M; Eisert, J; Illuminati, F
2004-11-05
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.
Compressibility and thermal expansion of cubic silicon nitride
DEFF Research Database (Denmark)
Jiang, Jianzhong; Lindelov, H.; Gerward, Leif
2002-01-01
The compressibility and thermal expansion of the cubic silicon nitride (c-Si3N4) phase have been investigated by performing in situ x-ray powder-diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first-principles calculations. The bulk...... compressibility of the c-Si3N4 phase originates from the average of both Si-N tetrahedral and octahedral compressibilities where the octahedral polyhedra are less compressible than the tetrahedral ones. The origin of the unit cell expansion is revealed to be due to the increase of the octahedral Si-N and N-N bond...
Theoretical and Experimental Study of Time Reversal in Cubic Crystals
Institute of Scientific and Technical Information of China (English)
陆铭慧; 张碧星; 汪承灏
2004-01-01
The self-adaptive focusing of the time reversal in anisotropic media is studied theoretically and experimentally. It is conducted for the compressional wave field in the cubic crystal silicon. The experimental result is in agreement with our theoretical analysis. The focusing gain and the displacement distributions of the time reversal field are analysed in detail. It is shown that the waves from different elements of the transducer array arrive at the original place of the source simultaneously after the time reversal operation. The waveform distortions caused by the velocity anisotropy can automatically be compensated for after the time reversal processing.
Rotary Ultrasonic Machining of Poly-Crystalline Cubic Boron Nitride
Directory of Open Access Journals (Sweden)
Kuruc Marcel
2014-12-01
Full Text Available Poly-crystalline cubic boron nitride (PCBN is one of the hardest material. Generally, so hard materials could not be machined by conventional machining methods. Therefore, for this purpose, advanced machining methods have been designed. Rotary ultrasonic machining (RUM is included among them. RUM is based on abrasive removing mechanism of ultrasonic vibrating diamond particles, which are bonded on active part of rotating tool. It is suitable especially for machining hard and brittle materials (such as glass and ceramics. This contribution investigates this advanced machining method during machining of PCBN.
Cubic Plus Association Equation of State for Flow Assurance Projects
DEFF Research Database (Denmark)
dos Santos, Leticia Cotia; Abunahman, Samir Silva; Tavares, Frederico Wanderley
2015-01-01
Thermodynamic hydrate inhibitors such as methanol, ethanol, (mono) ethylene glycol (MEG), and triethylene glycol (TEG) are widely used in the oil and gas industry. On modeling these compounds, we show here how the CPA equation of state was implemented in an in-house process simulator as an in......-built model: To validate the implementation, we show calulations for binary systems containing hydrate inhibitors and water or hydrocarbons using the Cubic Plus Association (CPA) and Soave-Redlich-Kwong (SRK) equation of states, also comparing against experimental data. For streams containing natural gas...
Elasticity tensor and ultrasonic velocities for anisotropic cubic polycrystal
Institute of Scientific and Technical Information of China (English)
2008-01-01
The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.
Tensor tomography of stresses in cubic single crystals
Directory of Open Access Journals (Sweden)
Dmitry D. Karov
2015-03-01
Full Text Available The possibility of optical tomography applying to investigation of a two-dimensional and a three-dimensional stressed state in single cubic crystals has been studied. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses and weak optical anisotropy. It is shown that a complete reconstruction of stresses in a sample is impossible both by translucence it in the parallel planes system and by using of the elasticity theory equations. For overcoming these difficulties, it is offered to use a method of magnetophotoelasticity.
Cubic optical elements for an accommodative intraocular lens.
Simonov, Aleksey N; Vdovin, Gleb; Rombach, Michiel C
2006-08-21
We present a new accommodative intraocular lens based on a two-element varifocal Alvarez lens. The intraocular lens consists of (1) an anterior element combining a spherical lens for refractive power with a cubic surface for the varifocal effect, and (2) a posterior element with a cubic surface only. The focal length of the IOL lens changes when the superimposed refractive elements shift in opposite directions in a plane perpendicular to the optical axis. The ciliary muscle will drive the accommodation by a natural process of contraction and relaxation. Results of ray-tracing simulations of the model eye with the two-element intraocular lens are presented for on-axis and off-axis vision. The configuration of the lens is optimized to reduce refractive errors as well as effects of misalignment. A prototype with a clear aperture of ~5.7 mm is manufactured and evaluated in air with a Shack-Hartmann wave-front sensor. It provides an accommodation range of ~4 dioptres in the eye at a ~0.75-mm lateral displacement of the optical elements. The experimentally measured on-axis optical performance of the IOL lens agrees with the theoretically predicted performance.
Nonlinear structure formation in the Cubic Galileon gravity model
Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia
2013-01-01
We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the {\\tt ECOSMOG} code. Our simulations include the Vainshtein screening effect, which reconciles the Cubic Galileon model with local tests of gravity. In the linear regime, the amplitude of the matter power spectrum increases by $\\sim 25%$ with respect to the standard $\\Lambda$CDM model today. The modified expansion rate accounts for $\\sim 20%$ of this enhancement, while the fifth force is responsible for only $\\sim 5%$. This is because the effective unscreened gravitational strength deviates from standard gravity only at late times, even though it can be twice as large today. In the nonlinear regime ($k \\gtrsim 0.1 h\\rm{Mpc}^{-1}$), the fifth force leads to only a modest increase ($\\lesssim 8%$) in the clustering power on all scales due to the very efficient operation of the Vainshtein mechanism. Such a strong effect is typically not seen in other...
Partially Blended Constrained Rational Cubic Trigonometric Fractal Interpolation Surfaces
Chand, A. K. B.; Tyada, K. R.
2016-08-01
Fractal interpolation is an advance technique for visualization of scientific shaped data. In this paper, we present a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonometric fractal interpolation functions (FIFs) along the grid lines of the interpolation domain. The developed FIFs use rational trigonometric functions pi,j(θ) qi,j(θ), where pi,j(θ) and qi,j(θ) are cubic trigonometric polynomials with four shape parameters. The convergence analysis of partially blended RCTFIS with the original surface data generating function is discussed. We derive sufficient data-dependent conditions on the scaling factors and shape parameters such that the fractal grid line functions lie above the grid lines of a plane Π, and consequently the proposed partially blended RCTFIS lies above the plane Π. Positivity preserving partially blended RCTFIS is a special case of the constrained partially blended RCTFIS. Numerical examples are provided to support the proposed theoretical results.
Observation of Body-Centered Cubic Gold Nanocluster.
Liu, Chao; Li, Tao; Li, Gao; Nobusada, Katsuyuki; Zeng, Chenjie; Pang, Guangsheng; Rosi, Nathaniel L; Jin, Rongchao
2015-08-17
The structure of nanoparticles plays a critical role in dictating their material properties. Gold is well known to adopt face-centered cubic (fcc) structure. Herein we report the first observation of a body-centered cubic (bcc) gold nanocluster composed of 38 gold atoms protected by 20 adamantanethiolate ligands and two sulfido atoms ([Au38S2(SR)20], where R=C10H15) as revealed by single-crystal X-ray crystallography. This bcc structure is in striking contrast with the fcc structure of bulk gold and conventional Au nanoparticles, as well as the bi-icosahedral structure of [Au38(SCH2CH2Ph)24]. The bcc nanocluster has a distinct HOMO-LUMO gap of ca. 1.5 eV, much larger than the gap (0.9 eV) of the bi-icosahedral [Au38(SCH2CH2Ph)24]. The unique structure of the bcc gold nanocluster may be promising in catalytic applications.
Four-dimensional black holes in Einsteinian cubic gravity
Bueno, Pablo; Cano, Pablo A.
2016-12-01
We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(anti-)de Sitter [RN-(A)dS] black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are characterized by a single function which satisfies a nonlinear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature T , the Wald entropy S and the Abbott-Deser mass M of the solutions analytically as functions of the horizon radius and the ECG coupling constant λ . Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.
Novel Cubic Magnetite Nanoparticle Synthesis Using Room Temperature Ionic Liquid
Directory of Open Access Journals (Sweden)
M. Sundrarajan
2012-01-01
Full Text Available Room Temperature Ionic liquids are relatively more useful in the synthesis of inorganic nanostructured materials because of their unique properties. To synthesize the iron oxide nanoparticle in simple precipitation method, a novel ionic liquid was used as the greener medium and stabilizing agent namely “1-n-butyl-3-methylimidazolium trifluoromethane sulfonate [BMIM][TfO]”. The crystallinity, chemical structure, morphology and magnetic properties of the synthesized magnetite nanoparticles have been characterized by using X-ray diffraction (XRD, Fourier Transform Infrared (FT-IR, Scanning electron microscopy (SEM, Atomic force microscopy(AFM, Transmission electron microscopy (TEM and Vibrating sample magnetometer (VSM studies. The XRD study is divulge that the synthesized magnetite nanoparticles have inverse spinel face centered cubic structure. The FT-IR vibration peaks show the formation of Fe3O4 nanoparticles, where the vibration peak for Fe-O is deliberately presence at 584 cm-1. The average particle size of the synthesized nanoparticles is found to be 35 nm. Homogeneously dispersed cubic shape with superstructure is found through SEM, AFM and TEM examination studies. The synthesized iron oxide nanoparticles have a high saturation magnetization value of 25 emu/g, which is very much useful for biomedical applications.
Projection of curves on B-spline surfaces using quadratic reparameterization
Yang, Yijun
2010-09-01
Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.
Adaptive Hierarchical B-spline Surface Representation of Large-Scale Scattered Data
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The representation of large scale scattered data is a difficult problem, especially when various features of the representation, such as C2-continuity, are required. This paper describes a fast algorithm for large scale scattered data approximation and interpolation. The interpolation algorithm uses a coarse-to-fine hierarchical control lattice to fit the scattered data. The refinement process is only used in the regions where the error between the scattered data and the result in a surface is greater than a specified tolerance. A method to ensure C2-continuity is introduced to calculate the control lattice under constrained conditions. Experimental results show that this method can quickly represent large scale scattered data set.
Isogeometric Divergence-conforming B-splines for the Darcy-Stokes-Brinkman Equations
2012-01-01
equations for the driven cavity problem. Journal of Computational Physics, 43:260–267, 1981. [33] A Hannukainen, M Juntunen, and R Stenberg . Computations...Fluid Mechanics: Transport in Microfluidic Devices. Cambridge University Press, 2010. [42] J Könnö and R Stenberg . Non-conforming finite element
P wave onset time picking with the B-spline biorthogonal wavelet
Institute of Scientific and Technical Information of China (English)
TENG Yun-tian; WANG Xi-zhen; WANG Xiao-mei; MA Jie-mei; XU Jian-hua
2006-01-01
@@ The seismic wave consists of many seismic phases, which contain rich geophysical information from the hypocenter, medium of seismic wave passing through and so on. It is very important to detect and pick these seismic phases for understanding the mechanism of earthquake, the Earth structure and property of seismic waves. In order to reduce or avoid the loss resulted from the earthquake, one of the important goals of seismic event detecting is to obtain its related information before and after it occurs. Because of the particularity of P wave and S wave,the seismic event detecting focuses on distinguishing P and S waves and picking their onset time, it has been becoming one of the research hotspots for many geophysicists to pick the P and S wave arrival accurately and effectively.