Non-coaxial superposition of vector vortex beams.

PubMed

Aadhi, A; Vaity, Pravin; Chithrabhanu, P; Reddy, Salla Gangi; Prabakar, Shashi; Singh, R P

2016-02-10

Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams. It is observed that the superposition of two vector vortex beams with same polarization singularity leads to a beam with another kind of polarization singularity in their interaction region. The results may be of importance in ultrahigh security of the polarization-encrypted data that utilizes vector vortex beams and multiple optical trapping with non-coaxial superposition of vector vortex beams. We verified our experimental results with theory.

A Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

2016-02-25

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

A Cartesian parametrization for the numerical analysis of material instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

Singular Vectors' Subtle Secrets

ERIC Educational Resources Information Center

James, David; Lachance, Michael; Remski, Joan

2011-01-01

Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra

NASA Astrophysics Data System (ADS)

Ohkubo, Yusuke

2018-05-01

In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level N representation of the Ding-Iohara-Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).

Singular reduction of resonant Hamiltonians

NASA Astrophysics Data System (ADS)

Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2018-06-01

We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.

Intelligent Diagnosis Method for Rotating Machinery Using Dictionary Learning and Singular Value Decomposition.

PubMed

Han, Te; Jiang, Dongxiang; Zhang, Xiaochen; Sun, Yankui

2017-03-27

Rotating machinery is widely used in industrial applications. With the trend towards more precise and more critical operating conditions, mechanical failures may easily occur. Condition monitoring and fault diagnosis (CMFD) technology is an effective tool to enhance the reliability and security of rotating machinery. In this paper, an intelligent fault diagnosis method based on dictionary learning and singular value decomposition (SVD) is proposed. First, the dictionary learning scheme is capable of generating an adaptive dictionary whose atoms reveal the underlying structure of raw signals. Essentially, dictionary learning is employed as an adaptive feature extraction method regardless of any prior knowledge. Second, the singular value sequence of learned dictionary matrix is served to extract feature vector. Generally, since the vector is of high dimensionality, a simple and practical principal component analysis (PCA) is applied to reduce dimensionality. Finally, the K -nearest neighbor (KNN) algorithm is adopted for identification and classification of fault patterns automatically. Two experimental case studies are investigated to corroborate the effectiveness of the proposed method in intelligent diagnosis of rotating machinery faults. The comparison analysis validates that the dictionary learning-based matrix construction approach outperforms the mode decomposition-based methods in terms of capacity and adaptability for feature extraction.

Argand-plane vorticity singularities in complex scalar optical fields: an experimental study using optical speckle.

PubMed

Rothschild, Freda; Bishop, Alexis I; Kitchen, Marcus J; Paganin, David M

2014-03-24

The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as "vorticity singularities" that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

USGS Publications Warehouse

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

2011-01-01

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

Fast higher-order MR image reconstruction using singular-vector separation.

PubMed

Wilm, Bertram J; Barmet, Christoph; Pruessmann, Klaas P

2012-07-01

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Conformal Galilei algebras, symmetric polynomials and singular vectors

NASA Astrophysics Data System (ADS)

Křižka, Libor; Somberg, Petr

2018-01-01

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga_ℓ (d,C) with d=1 for any integer value ℓ \\in N. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.

Intelligent Diagnosis Method for Rotating Machinery Using Dictionary Learning and Singular Value Decomposition

PubMed Central

Han, Te; Jiang, Dongxiang; Zhang, Xiaochen; Sun, Yankui

2017-01-01

Rotating machinery is widely used in industrial applications. With the trend towards more precise and more critical operating conditions, mechanical failures may easily occur. Condition monitoring and fault diagnosis (CMFD) technology is an effective tool to enhance the reliability and security of rotating machinery. In this paper, an intelligent fault diagnosis method based on dictionary learning and singular value decomposition (SVD) is proposed. First, the dictionary learning scheme is capable of generating an adaptive dictionary whose atoms reveal the underlying structure of raw signals. Essentially, dictionary learning is employed as an adaptive feature extraction method regardless of any prior knowledge. Second, the singular value sequence of learned dictionary matrix is served to extract feature vector. Generally, since the vector is of high dimensionality, a simple and practical principal component analysis (PCA) is applied to reduce dimensionality. Finally, the K-nearest neighbor (KNN) algorithm is adopted for identification and classification of fault patterns automatically. Two experimental case studies are investigated to corroborate the effectiveness of the proposed method in intelligent diagnosis of rotating machinery faults. The comparison analysis validates that the dictionary learning-based matrix construction approach outperforms the mode decomposition-based methods in terms of capacity and adaptability for feature extraction. PMID:28346385

River flow prediction using hybrid models of support vector regression with the wavelet transform, singular spectrum analysis and chaotic approach

NASA Astrophysics Data System (ADS)

Baydaroğlu, Özlem; Koçak, Kasım; Duran, Kemal

2018-06-01

Prediction of water amount that will enter the reservoirs in the following month is of vital importance especially for semi-arid countries like Turkey. Climate projections emphasize that water scarcity will be one of the serious problems in the future. This study presents a methodology for predicting river flow for the subsequent month based on the time series of observed monthly river flow with hybrid models of support vector regression (SVR). Monthly river flow over the period 1940-2012 observed for the Kızılırmak River in Turkey has been used for training the method, which then has been applied for predictions over a period of 3 years. SVR is a specific implementation of support vector machines (SVMs), which transforms the observed input data time series into a high-dimensional feature space (input matrix) by way of a kernel function and performs a linear regression in this space. SVR requires a special input matrix. The input matrix was produced by wavelet transforms (WT), singular spectrum analysis (SSA), and a chaotic approach (CA) applied to the input time series. WT convolutes the original time series into a series of wavelets, and SSA decomposes the time series into a trend, an oscillatory and a noise component by singular value decomposition. CA uses a phase space formed by trajectories, which represent the dynamics producing the time series. These three methods for producing the input matrix for the SVR proved successful, while the SVR-WT combination resulted in the highest coefficient of determination and the lowest mean absolute error.

High-order optical vortex position detection using a Shack-Hartmann wavefront sensor.

PubMed

Luo, Jia; Huang, Hongxin; Matsui, Yoshinori; Toyoda, Haruyoshi; Inoue, Takashi; Bai, Jian

2015-04-06

Optical vortex (OV) beams have null-intensity singular points, and the intensities in the region surrounding the singular point are quite low. This low intensity region influences the position detection accuracy of phase singular point, especially for high-order OV beam. In this paper, we propose a new method for solving this problem, called the phase-slope-combining correlation matching method. A Shack-Hartmann wavefront sensor (SH-WFS) is used to measure phase slope vectors at lenslet positions of the SH-WFS. Several phase slope vectors are combined into one to reduce the influence of low-intensity regions around the singular point, and the combined phase slope vectors are used to determine the OV position with the aid of correlation matching with a pre-calculated database. Experimental results showed that the proposed method works with high accuracy, even when detecting an OV beam with a topological charge larger than six. The estimated precision was about 0.15 in units of lenslet size when detecting an OV beam with a topological charge of up to 20.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

Reduced Order Model Basis Vector Generation: Generates Basis Vectors fro ROMs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arrighi, Bill

2016-03-03

libROM is a library that implements order reduction via singular value decomposition (SVD) of sampled state vectors. It implements 2 parallel, incremental SVD algorithms and one serial, non-incremental algorithm. It also provides a mechanism for adaptive sampling of basis vectors.

Observer-dependent sign inversions of polarization singularities.

PubMed

Freund, Isaac

2014-10-15

We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

NASA Astrophysics Data System (ADS)

Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

2018-05-01

A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

Correlation singularities in a partially coherent electromagnetic beam with initially radial polarization.

PubMed

Zhang, Yongtao; Cui, Yan; Wang, Fei; Cai, Yangjian

2015-05-04

We have investigated the correlation singularities, coherence vortices of two-point correlation function in a partially coherent vector beam with initially radial polarization, i.e., partially coherent radially polarized (PCRP) beam. It is found that these singularities generally occur during free space propagation. Analytical formulae for characterizing the dynamics of the correlation singularities on propagation are derived. The influence of the spatial coherence length of the beam on the evolution properties of the correlation singularities and the conditions for creation and annihilation of the correlation singularities during propagation have been studied in detail based on the derived formulae. Some interesting results are illustrated. These correlation singularities have implication for interference experiments with a PCRP beam.

An accelerated training method for back propagation networks

NASA Technical Reports Server (NTRS)

Shelton, Robert O. (Inventor)

1993-01-01

The principal objective is to provide a training procedure for a feed forward, back propagation neural network which greatly accelerates the training process. A set of orthogonal singular vectors are determined from the input matrix such that the standard deviations of the projections of the input vectors along these singular vectors, as a set, are substantially maximized, thus providing an optimal means of presenting the input data. Novelty exists in the method of extracting from the set of input data, a set of features which can serve to represent the input data in a simplified manner, thus greatly reducing the time/expense to training the system.

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n-2α.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-05-01

We study the evolution of finite perturbations in the Lorenz ‘96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-01-01

We study the evolution of finite perturbations in the Lorenz `96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Singular value description of a digital radiographic detector: Theory and measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kyprianou, Iacovos S.; Badano, Aldo; Gallas, Brandon D.

The H operator represents the deterministic performance of any imaging system. For a linear, digital imaging system, this system operator can be written in terms of a matrix, H, that describes the deterministic response of the system to a set of point objects. A singular value decomposition of this matrix results in a set of orthogonal functions (singular vectors) that form the system basis. A linear combination of these vectors completely describes the transfer of objects through the linear system, where the respective singular values associated with each singular vector describe the magnitude with which that contribution to the objectmore » is transferred through the system. This paper is focused on the measurement, analysis, and interpretation of the H matrix for digital x-ray detectors. A key ingredient in the measurement of the H matrix is the detector response to a single x ray (or infinitestimal x-ray beam). The authors have developed a method to estimate the 2D detector shift-variant, asymmetric ray response function (RRF) from multiple measured line response functions (LRFs) using a modified edge technique. The RRF measurements cover a range of x-ray incident angles from 0 deg. (equivalent location at the detector center) to 30 deg. (equivalent location at the detector edge) for a standard radiographic or cone-beam CT geometric setup. To demonstrate the method, three beam qualities were tested using the inherent, Lu/Er, and Yb beam filtration. The authors show that measures using the LRF, derived from an edge measurement, underestimate the system's performance when compared with the H matrix derived using the RRF. Furthermore, the authors show that edge measurements must be performed at multiple directions in order to capture rotational asymmetries of the RRF. The authors interpret the results of the H matrix SVD and provide correlations with the familiar MTF methodology. Discussion is made about the benefits of the H matrix technique with regards to signal detection theory, and the characterization of shift-variant imaging systems.« less

The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

NASA Astrophysics Data System (ADS)

Novaes, Douglas D.; Teixeira, Marco A.; Zeli, Iris O.

2018-05-01

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of 2-parameter families, , of planar Filippov systems assuming that Z 0,0 presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.

Moving singularity creep crack growth analysis with the /Delta T/c and C/asterisk/ integrals. [path-independent vector and energy rate line integrals

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1982-01-01

The physical meaning of (Delta T)c and its applicability to creep crack growth are reviewed. Numerical evaluation of (Delta T)c and C(asterisk) is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.

Rapid surface defect detection based on singular value decomposition using steel strips as an example

NASA Astrophysics Data System (ADS)

Sun, Qianlai; Wang, Yin; Sun, Zhiyi

2018-05-01

For most surface defect detection methods based on image processing, image segmentation is a prerequisite for determining and locating the defect. In our previous work, a method based on singular value decomposition (SVD) was used to determine and approximately locate surface defects on steel strips without image segmentation. For the SVD-based method, the image to be inspected was projected onto its first left and right singular vectors respectively. If there were defects in the image, there would be sharp changes in the projections. Then the defects may be determined and located according sharp changes in the projections of each image to be inspected. This method was simple and practical but the SVD should be performed for each image to be inspected. Owing to the high time complexity of SVD itself, it did not have a significant advantage in terms of time consumption over image segmentation-based methods. Here, we present an improved SVD-based method. In the improved method, a defect-free image is considered as the reference image which is acquired under the same environment as the image to be inspected. The singular vectors of each image to be inspected are replaced by the singular vectors of the reference image, and SVD is performed only once for the reference image off-line before detecting of the defects, thus greatly reducing the time required. The improved method is more conducive to real-time defect detection. Experimental results confirm its validity.

Polarization singularity indices in Gaussian laser beams

NASA Astrophysics Data System (ADS)

Freund, Isaac

2002-01-01

Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincaré-Hopf index η, with generic value η=±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC=±1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations. Algorithms are also given for generating continuous lines of these singularities in the plane, V-lines and C-lines. V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles.

Magnetic charge and photon mass: Physical string singularities, Dirac condition, and magnetic confinement

NASA Astrophysics Data System (ADS)

Evans, Timothy J.; Singleton, Douglas

2018-04-01

We find exact, simple solutions to the Proca version of Maxwell’s equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on r and 𝜃 and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum even when the electric and magnetic charges are located at the same place (i.e. for dyons); (v) for these dyons, one recovers the standard Dirac condition despite the photon being massive. We discuss the reason for this. We conclude by proposing that the string singularity in the magnetic field of an isolated magnetic charge suggests a confinement mechanism for magnetic charge, similar to the flux tube confinement of quarks in QCD.

Primer Vector Optimization: Survey of Theory, new Analysis and Applications

NASA Astrophysics Data System (ADS)

Guzman

This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and rotation of the line of apsides, are utilized as test cases. Recommendations, future work, and the possible addition of other optimization techniques are also discussed. References: [1] Lawden D.F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963. [2] Wilson, R.S., Howell, K.C., and, Lo, M, "Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits", AIAA/AAS Astrodynamics Specialist Conference, AAS 99-041, Girdwood, Alaska, August 16-19, 1999. [3] Goodson, T, "Monte-Carlo Maneuver Analysis for the Microwave Anisotropy Probe", AAS/AIAA Astrodynamics Specialist Conference, AAS 01-331, Quebec City, Canada, July 30 - August 2, 2001. [4] Stern, R.G., "Singularities in the Analytic Solution of the Linearized Variational Equations of Elliptical Motion", Report RE-8, May 1964, Experimental Astronomy Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts.

Dual Vector Spaces and Physical Singularities

NASA Astrophysics Data System (ADS)

Rowlands, Peter

Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

Numerical Methods for Partial Differential Equations.

DTIC Science & Technology

1984-01-09

Y2] L(i) . ) M Q)(i) - where R is k x k upper triangular. Rill Y1 2, is lower triangular, Y ,2 and the parameters of the rotations that make F i up Q...then x is a left singular vector of B and y is a right singular vector of B (5]. Thus we may attempt (1) x c*x + oy to find the eigendecomposition of C...After a sym- y ’ - -ox + cy metric interchange of rows and columns corresponding to the permutation (n+l, 2, n+2, 2, ..., 2n, n), where x, y , and c

A Systolic Architecture for Singular Value Decomposition,

DTIC Science & Technology

1983-01-01

Presented at the 1 st International Colloquium on Vector and Parallel Computing in Scientific Applications, Paris, March 191J Contract N00014-82-K.0703...Gene Golub. Private comunication . given inputs x and n 2 , compute 2 2 2 2 /6/ G. H. Golub and F. T. Luk : "Singular Value I + X1 Decomposition

Incoherent averaging of phase singularities in speckle-shearing interferometry.

PubMed

Mantel, Klaus; Nercissian, Vanusch; Lindlein, Norbert

2014-08-01

Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected √N behavior. Using speckle-shearing interferometry as an example, we investigate the mechanism behind the reduction of phase singularities, both by calculations and by computer simulations. Key to an understanding of the reduction mechanism during incoherent averaging is the representation of the physical averaging process in terms of certain vector fields associated with each speckle field.

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

NASA Astrophysics Data System (ADS)

Tjong, Tiffany; Yihaa’ Roodhiyah, Lisa; Nurhasan; Sutarno, Doddy

2018-04-01

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-12-15

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), andmore » (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.« less

Computing singularities of perturbation series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

2011-03-15

Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be usefulmore » for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.« less

The incorrect usage of singular spectral analysis and discrete wavelet transform in hybrid models to predict hydrological time series

NASA Astrophysics Data System (ADS)

Du, Kongchang; Zhao, Ying; Lei, Jiaqiang

2017-09-01

In hydrological time series prediction, singular spectrum analysis (SSA) and discrete wavelet transform (DWT) are widely used as preprocessing techniques for artificial neural network (ANN) and support vector machine (SVM) predictors. These hybrid or ensemble models seem to largely reduce the prediction error. In current literature researchers apply these techniques to the whole observed time series and then obtain a set of reconstructed or decomposed time series as inputs to ANN or SVM. However, through two comparative experiments and mathematical deduction we found the usage of SSA and DWT in building hybrid models is incorrect. Since SSA and DWT adopt 'future' values to perform the calculation, the series generated by SSA reconstruction or DWT decomposition contain information of 'future' values. These hybrid models caused incorrect 'high' prediction performance and may cause large errors in practice.

Influence of vorticity distribution on singularities in linearized supersonic flow

NASA Astrophysics Data System (ADS)

Gopal, Vijay; Maddalena, Luca

2018-05-01

The linearized steady three-dimensional supersonic flow can be analyzed using a vector potential approach which transforms the governing equation to a standard form of two-dimensional wave equation. Of particular interest are the canonical horseshoe line-vortex distribution and the resulting induced velocity field in supersonic flow. In this case, the singularities are present at the vortex line itself and also at the surface of the cone of influence originating from the vertices of the horseshoe structure. This is a characteristic of the hyperbolic nature of the flow which renders the study of supersonic vortex dynamics a challenging task. It is conjectured in this work that the presence of the singularity at the cone of influence is associated with the step-function nature of the vorticity distribution specified in the canonical case. At the phenomenological level, if one considers the three-dimensional steady supersonic flow, then a sudden appearance of a line-vortex will generate a ripple of singularities in the induced velocity field which convect downstream and laterally spread, at the most, to the surface of the cone of influence. Based on these findings, this work includes an exploration of potential candidates for vorticity distributions that eliminate the singularities at the cone of influence. The analysis of the resulting induced velocity field is then compared with the canonical case, and it is observed that the singularities were successfully eliminated. The manuscript includes an application of the proposed method to study the induced velocity field in a confined supersonic flow.

Theoretical aspects of fracture mechanics

NASA Astrophysics Data System (ADS)

Atkinson, C.; Craster, R. V.

1995-03-01

In this review we try to cover various topics in fracture mechanics in which mathematical analysis can be used both to aid numerical methods and cast light on key features of the stress field. The dominant singular near crack tip stress field can often be parametrized in terms of three parameters K(sub I), K(sub II) and K(sub III) designating three fracture modes each having an angular variation entirely specified for the stress tensor and displacement vector. These results and contact zone models for removing the interpenetration anomaly are described. Generalizations of the above results to viscoelastic media are described. For homogeneous media with constant Poisson's ratio the angular variation of singular crack tip stresses and displacements are shown to be the same for all time and the same inverse square root singularity as occurs in the elastic medium case is found (this being true for a time varying Poisson ratio too). Only the stress intensity factor varies through time dependence of loads and relaxation properties of the medium. For cracks against bimaterial interfaces both the stress singularity and angular form evolve with time as a function of the time dependent properties of the bimaterial. Similar behavior is identified for sharp notches in viscoelastic plates. The near crack tip behavior in material with non-linear stress strain laws is also identified and stress singularities classified in terms of the hardening exponent for power law hardening materials. Again for interface cracks the near crack tip behavior requires careful analysis and it is shown that more than one singular term may be present in the near crack tip stress field. A variety of theory and applications is presented for inhomogeneous elastic media, coupled thermoelasticity etc. Methods based on reciprocal theorems and dual functions which can also aid in getting awkward singular stress behavior from numerical solutions are also reviewed. Finally theoretical calculations of fiber reinforced and particulate composite toughening mechanisms are briefly reviewed.

Geostrophic balance with a full Coriolis Force: implications for low latitutde studies

NASA Technical Reports Server (NTRS)

Juarez, M. de la Torre

2002-01-01

In its standard form, geostrophic balance uses a partial representation of the Coriolis force. The resulting formation has a singularity at the equator, and violates mass and momentum conservation. When the horizontal projection of the planetary rotation vector is considered, the singularity at the equator disappears, continuity can be preserved, and quasigeostrophy can be formulated at planetary scale.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

The presence of a phantom field in a Randall–Sundrum scenario

NASA Astrophysics Data System (ADS)

Acuña-Cárdenas, Rubén O.; Astorga-Moreno, J. A.; García-Aspeitia, Miguel A.; López-Domínguez, J. C.

2018-02-01

The presence of phantom dark energy in brane world cosmology generates important new effects, causing a premature big rip singularity when we increase the presence of extra dimensions and considerably competing with the other components of our Universe. This article first considers only a field with the characteristic equation ω<-1 and then the explicit form of the scalar field with a potential with a maximum (with the aim of avoiding a big rip singularity). In both cases we study the dynamics robustly through dynamical analysis theory, considering in detail parameters such as the deceleration q and the vector field associated to the dynamical system. Results are discussed with the purpose of treating the cosmology with a phantom field as dark energy in a Randall–Sundrum scenario.

Singular vector-based targeted observations of chemical constituents: description and first application of the EURAD-IM-SVA v1.0

NASA Astrophysics Data System (ADS)

Goris, N.; Elbern, H.

2015-12-01

Measurements of the large-dimensional chemical state of the atmosphere provide only sparse snapshots of the state of the system due to their typically insufficient temporal and spatial density. In order to optimize the measurement configurations despite those limitations, the present work describes the identification of sensitive states of the chemical system as optimal target areas for adaptive observations. For this purpose, the technique of singular vector analysis (SVA), which has proven effective for targeted observations in numerical weather prediction, is implemented in the EURAD-IM (EURopean Air pollution and Dispersion - Inverse Model) chemical transport model, yielding the EURAD-IM-SVA v1.0. Besides initial values, emissions are investigated as critical simulation controlling targeting variables. For both variants, singular vectors are applied to determine the optimal placement for observations and moreover to quantify which chemical compounds have to be observed with preference. Based on measurements of the airship based ZEPTER-2 campaign, the EURAD-IM-SVA v1.0 has been evaluated by conducting a comprehensive set of model runs involving different initial states and simulation lengths. For the sake of brevity, we concentrate our attention on the following chemical compounds, O3, NO, NO2, HCHO, CO, HONO, and OH, and focus on their influence on selected O3 profiles. Our analysis shows that the optimal placement for observations of chemical species is not entirely determined by mere transport and mixing processes. Rather, a combination of initial chemical concentrations, chemical conversions, and meteorological processes determines the influence of chemical compounds and regions. We furthermore demonstrate that the optimal placement of observations of emission strengths is highly dependent on the location of emission sources and that the benefit of including emissions as target variables outperforms the value of initial value optimization with growing simulation length. The obtained results confirm the benefit of considering both initial values and emission strengths as target variables and of applying the EURAD-IM-SVA v1.0 for measurement decision guidance with respect to chemical compounds.

A Random Algorithm for Low-Rank Decomposition of Large-Scale Matrices With Missing Entries.

PubMed

Liu, Yiguang; Lei, Yinjie; Li, Chunguang; Xu, Wenzheng; Pu, Yifei

2015-11-01

A random submatrix method (RSM) is proposed to calculate the low-rank decomposition U(m×r)V(n×r)(T) (r < m, n) of the matrix Y∈R(m×n) (assuming m > n generally) with known entry percentage 0 < ρ ≤ 1. RSM is very fast as only O(mr(2)ρ(r)) or O(n(3)ρ(3r)) floating-point operations (flops) are required, compared favorably with O(mnr+r(2)(m+n)) flops required by the state-of-the-art algorithms. Meanwhile, RSM has the advantage of a small memory requirement as only max(n(2),mr+nr) real values need to be saved. With the assumption that known entries are uniformly distributed in Y, submatrices formed by known entries are randomly selected from Y with statistical size k×nρ(k) or mρ(l)×l , where k or l takes r+1 usually. We propose and prove a theorem, under random noises the probability that the subspace associated with a smaller singular value will turn into the space associated to anyone of the r largest singular values is smaller. Based on the theorem, the nρ(k)-k null vectors or the l-r right singular vectors associated with the minor singular values are calculated for each submatrix. The vectors ought to be the null vectors of the submatrix formed by the chosen nρ(k) or l columns of the ground truth of V(T). If enough submatrices are randomly chosen, V and U can be estimated accordingly. The experimental results on random synthetic matrices with sizes such as 13 1072 ×10(24) and on real data sets such as dinosaur indicate that RSM is 4.30 ∼ 197.95 times faster than the state-of-the-art algorithms. It, meanwhile, has considerable high precision achieving or approximating to the best.

Robust inverse kinematics using damped least squares with dynamic weighting

NASA Technical Reports Server (NTRS)

Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.

1994-01-01

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

Nonstationary Dynamics Data Analysis with Wavelet-SVD Filtering

NASA Technical Reports Server (NTRS)

Brenner, Marty; Groutage, Dale; Bessette, Denis (Technical Monitor)

2001-01-01

Nonstationary time-frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time-frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied.

1988 IEEE Aerospace Applications Conference, Park City, UT, Feb. 7-12, 1988, Digest

NASA Astrophysics Data System (ADS)

The conference presents papers on microwave applications, data and signal processing applications, related aerospace applications, and advanced microelectronic products for the aerospace industry. Topics include a high-performance antenna measurement system, microwave power beaming from earth to space, the digital enhancement of microwave component performance, and a GaAs vector processor based on parallel RISC microprocessors. Consideration is also given to unique techniques for reliable SBNR architectures, a linear analysis subsystem for CSSL-IV, and a structured singular value approach to missile autopilot analysis.

Macroscopic theory of dark sector

NASA Astrophysics Data System (ADS)

Meierovich, Boris

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant [1]. Space-like and time-like massive vector fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves [2]. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating non-singular scenarios of evolution of the universe [3]. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerate expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution corresponds to the particular limiting case at the boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows to analyse the main properties of the dark sector analytically and avoid unnecessary model assumptions. It opens a possibility to trace how the additional attraction of the space-like dark matter, dominating in the galaxy scale, transforms into the elastic repulsion of the time-like dark matter, dominating in the scale of the Universe. 1. B. E. Meierovich. "Vector fields in multidimensional cosmology". Phys. Rev. D 84, 064037 (2011). 2. B. E. Meierovich. "Galaxy rotation curves driven by massive vector fields: Key to the theory of the dark sector". Phys. Rev. D 87, 103510, (2013). 3. B. E. Meierovich. "Towards the theory of the evolution of the Universe". Phys. Rev. D 85, 123544 (2012).

Ultra-Dense Quantum Communication Using Integrated Photonic Architecture

DTIC Science & Technology

2012-02-03

and tae have the same right singular vectors , and their singular-value decompositions can be written as tab = uabsabv †, (30) tae = uaesaev †, (31...freedom such as polarization or spatial modes), making its implementation ideal for fiber optics networks. (iii) The protocol promises unprecedented...well as temporal correlations. In particular, using 8 wavelength channels for an additional 3 bpp and two polarization states for one additional bpp

Multifractal vector fields and stochastic Clifford algebra.

PubMed

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition

NASA Astrophysics Data System (ADS)

Kwon, Ohsung; Kweon, Jae Ryong

2018-06-01

In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in R^3. The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a jump discontinuity across there.

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada

In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecturemore » that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.« less

MGRA: Motion Gesture Recognition via Accelerometer.

PubMed

Hong, Feng; You, Shujuan; Wei, Meiyu; Zhang, Yongtuo; Guo, Zhongwen

2016-04-13

Accelerometers have been widely embedded in most current mobile devices, enabling easy and intuitive operations. This paper proposes a Motion Gesture Recognition system (MGRA) based on accelerometer data only, which is entirely implemented on mobile devices and can provide users with real-time interactions. A robust and unique feature set is enumerated through the time domain, the frequency domain and singular value decomposition analysis using our motion gesture set containing 11,110 traces. The best feature vector for classification is selected, taking both static and mobile scenarios into consideration. MGRA exploits support vector machine as the classifier with the best feature vector. Evaluations confirm that MGRA can accommodate a broad set of gesture variations within each class, including execution time, amplitude and non-gestural movement. Extensive evaluations confirm that MGRA achieves higher accuracy under both static and mobile scenarios and costs less computation time and energy on an LG Nexus 5 than previous methods.

Singular value decomposition based feature extraction technique for physiological signal analysis.

PubMed

Chang, Cheng-Ding; Wang, Chien-Chih; Jiang, Bernard C

2012-06-01

Multiscale entropy (MSE) is one of the popular techniques to calculate and describe the complexity of the physiological signal. Many studies use this approach to detect changes in the physiological conditions in the human body. However, MSE results are easily affected by noise and trends, leading to incorrect estimation of MSE values. In this paper, singular value decomposition (SVD) is adopted to replace MSE to extract the features of physiological signals, and adopt the support vector machine (SVM) to classify the different physiological states. A test data set based on the PhysioNet website was used, and the classification results showed that using SVD to extract features of the physiological signal could attain a classification accuracy rate of 89.157%, which is higher than that using the MSE value (71.084%). The results show the proposed analysis procedure is effective and appropriate for distinguishing different physiological states. This promising result could be used as a reference for doctors in diagnosis of congestive heart failure (CHF) disease.

Sensitivity analysis of reactive ecological dynamics.

PubMed

Verdy, Ariane; Caswell, Hal

2008-08-01

Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.

MISR Level 2 TOA/Cloud Versioning

Atmospheric Science Data Center

2017-10-11

... public release. Add trap singular matrix condition. Add test for invalid look vectors. Use different metadata to test for validity of time tags. Fix incorrectly addressed array. Introduced bug ...

The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

Electric and magnetic polarization singularities of first-order Laguerre-Gaussian beams diffracted at a half-plane screen.

PubMed

Luo, Yamei; Gao, Zenghui; Tang, Bihua; Lü, Baida

2013-08-01

Based on the vector Fresnel diffraction integrals, analytical expressions for the electric and magnetic components of first-order Laguerre-Gaussian beams diffracted at a half-plane screen are derived and used to study the electric and magnetic polarization singularities in the diffraction field for both two- and three-dimensional (2D and 3D) cases. It is shown that there exist 2D and 3D electric and magnetic polarization singularities in the diffraction field, which do not coincide each other in general. By suitably varying the waist width ratio, off-axis displacement parameter, amplitude ratio, or propagation distance, the motion, pair-creation, and annihilation of circular polarization singularities, and the motion of linear polarization singularities take place in 2D and 3D electric and magnetic fields. The V point, at which two circular polarization singularities with the same topological charge but opposite handedness collide, appears in the 2D electric field under certain conditions in the diffraction field and free-space propagation. A comparison with the free-space propagation is also made.

Are Bred Vectors The Same As Lyapunov Vectors?

NASA Astrophysics Data System (ADS)

Kalnay, E.; Corazza, M.; Cai, M.

Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the perturbations remain approximately linear (for example, for atmospheric models the interval for rescaling could be varied between a single time step and 1 day without affecting qualitatively the characteristics of the bred vectors. However, the finite-amplitude, finite-time, and lack of orthogonalization of the BVs introduces important differences with LVs: 1) In regions that undergo strong instabilities, the bred vectors tend to be locally domi- 1 nated by simple, low-dimensional structures. Patil et al (2001) showed that the BV-dim (appendix) gives a good estimate of the number of dominant directions (shapes) of the local k bred vectors. For example, if half of them are aligned in one direction, and half in a different direction, the BV-dim is about two. If the majority of the bred vectors are aligned predominantly in one direction and only a few are aligned in a second direction, then the BV-dim is between 1 and 2. Patil et al., (2001) showed that the regions with low dimensionality cover about 20% of the atmosphere. They also found that these low-dimensionality regions have a very well defined vertical structure, and a typical lifetime of 3-7 days. The low dimensionality identifies regions where the in- stability of the basic flow has manifested itself in a low number of preferred directions of perturbation growth. 2) Using a Quasi-Geostrophic simulation system of data assimilation developed by Morss (1999), Corazza et al (2001a, b) found that bred vectors have structures that closely resemble the background (short forecasts used as first guess) errors, which in turn dominate the local analysis errors. This is especially true in regions of low dimensionality, which is not surprising if these are unstable regions where errors grow in preferred shapes. 3) The number of bred vectors needed to represent the unstable subspace in the QG system is small (about 6-10). This was shown by computing the local BV-dim as a function of the number of independent bred vectors. Convergence in the local dimen- sion starts to occur at about 6 BVs, and is essentially complete when the number of vectors is about 10-15 (Corazza et al, 2001a). This should be contrasted with the re- sults of Snyder and Joly (1998) and Palmer et al (1998) who showed that hundreds of Lyapunov vectors with positive Lyapunov exponents are needed to represent the attractor of the system in quasi-geostrophic models. 4) Since only a few bred vectors are needed, and background errors project strongly in the subspace of bred vectors, Corazza et al (2001b) were able to develop cost-efficient methods to improve the 3D-Var data assimilation by adding to the background error covariance terms proportional to the outer product of the bred vectors, thus represent- ing the "errors of the day". This approach led to a reduction of analysis error variance of about 40% at very low cost. 5) The fact that BVs have finite amplitude provides a natural way to filter out instabil- ities present in the system that have fast growth, but saturate nonlinearly at such small amplitudes that they are irrelevant for ensemble perturbations. As shown by Lorenz (1996) Lyapunov vectors (and singular vectors) of models including these physical phenomena would be dominated by the fast but small amplitude instabilities, unless they are explicitly excluded from the linearized models. Bred vectors, on the other 2 hand, through the choice of an appropriate size for the perturbation, provide a natural filter based on nonlinear saturation of fast but irrelevant instabilities. 6) Every bred vector is qualitatively similar to the *leading* LV. LVs beyond the leading LV are obtained by orthogonalization after each time step with respect to the previous LVs subspace. The orthogonalization requires the introduction of a norm. With an enstrophy norm, the successive LVs have larger and larger horizontal scales, and a choice of a stream function norm would lead to successively smaller scales in the LVs. Beyond the first few LVs, there is little qualitative similarity between the background errors and the LVs. In summary, in a system like the atmosphere with enough physical space for several independent local instabilities, BVs and LVs share some properties but they also have significant differences. BV are finite-amplitude, finite-time, and because they are not globally orthogonalized, they have local properties in space. Bred vectors are akin to the leading LV, but bred vectors derived from different arbitrary initial perturba- tions remain distinct from each other, instead of collapsing into a single leading vec- tor, presumably because the nonlinear terms and physical parameterizations introduce sufficient stochastic forcing to avoid such convergence. As a result, there is no need for global orthogonalization, and the number of bred vectors required to describe the natural instabilities in an atmospheric system (from a local point of view) is much smaller than the number of Lyapunov vectors with positive Lyapunov exponents. The BVs are independent of the norm, whereas the LVs beyond the first one do depend on the choice of norm: for example, they become larger in scale with a vorticity norm, and smaller with a stream function norm. These properties of BVs result in significant advantages for data assimilation and en- semble forecasting for the atmosphere. Errors in the analysis have structures very similar to bred vectors, and it is found that they project very strongly on the subspace of a few bred vectors. This is not true for either Lyapunov vectors beyond the lead- ing LVs, or for singular vectors unless they are constructed with a norm based on the analysis error covariance matrix (or a bred vector covariance). The similarity between bred vectors and analysis errors leads to the ability to include "errors of the day" in the background error covariance and a significant improvement of the analysis beyond 3D-Var at a very low cost (Corazza, 2001b). References Alligood K. T., T. D. Sauer and J. A. Yorke, 1996: Chaos: an introduction to dynamical systems. Springer-Verlag, New York. Buizza R., J. Tribbia, F. Molteni and T. Palmer, 1993: Computation of optimal unstable 3 structures for numerical weather prediction models. Tellus, 45A, 388-407. Cai, M., E. Kalnay and Z. Toth, 2001: Potential impact of bred vectors on ensemble forecasting and data assimilation in the Zebiak-Cane model. Submitted to J of Climate. Corazza, M., E. Kalnay, D. J. Patil, R. Morss, M. Cai, I. Szunyogh, B. R. Hunt, E. Ott and J. Yorke, 2001: Use of the breeding technique to determine the structure of the "errors of the day". Submitted to Nonlinear Processes in Geophysics. Corazza, M., E. Kalnay, DJ Patil, E. Ott, J. Yorke, I Szunyogh and M. Cai, 2001: Use of the breeding technique in the estimation of the background error covariance matrix for a quasigeostrophic model. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Farrell, B., 1988: Small error dynamics and the predictability of atmospheric flow, J. Atmos. Sciences, 45, 163-172. Kalnay, E 2002: Atmospheric modeling, data assimilation and predictability. Chapter 6. Cambridge University Press, UK. In press. Kalnay E and Z Toth 1994: Removing growing errors in the analysis. Preprints, Tenth Conference on Numerical Weather Prediction, pp 212-215. Amer. Meteor. Soc., July 18-22, 1994. Lorenz, E.N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 21, 289-307. Lorenz, E.N., 1996: Predictability- A problem partly solved. Proceedings of the ECMWF Seminar on Predictability, Reading, England, Vol. 1 1-18. Molteni F. and TN Palmer, 1993: Predictability and finite-time instability of the north- ern winter circulation. Q. J. Roy. Meteorol. Soc. 119, 269-298. Morss, R.E.: 1999: Adaptive observations: Idealized sampling strategies for improving numerical weather prediction. Ph.D. Thesis, Massachussetts Institute of Technology, 225pp. Ott, E., 1993: Chaos in Dynamical Systems. Cambridge University Press. New York. Palmer, TN, R. Gelaro, J. Barkmeijer and R. Buizza, 1998: Singular vectors, metrics and adaptive observations. J. Atmos Sciences, 55, 633-653. Patil, DJ, BR Hunt, E Kalnay, J. Yorke, and E. Ott, 2001: Local low dimensionality of atmospheric dynamics. Phys. Rev. Lett., 86, 5878. Patil, DJ, I. Szunyogh, BR Hunt, E Kalnay, E Ott, and J. Yorke, 2001: Using large 4 member ensembles to isolate local low dimensionality of atmospheric dynamics. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Snyder, C. and A. Joly, 1998: Development of perturbations within growing baroclinic waves. Q. J. Roy. Meteor. Soc., 124, pp 1961. Szunyogh, I, E. Kalnay and Z. Toth, 1997: A comparison of Lyapunov and Singular vectors in a low resolution GCM. Tellus, 49A, 200-227. Toth, Z and E Kalnay 1993: Ensemble forecasting at NMC - the generation of pertur- bations. Bull. Amer. Meteorol. Soc., 74, 2317-2330. Toth, Z and E Kalnay 1997: Ensemble forecasting at NCEP and the breeding method. Mon Wea Rev, 125, 3297-3319. * Corresponding author address: Eugenia Kalnay, Meteorology Depart- ment, University of Maryland, College Park, MD 20742-2425, USA; email: ekalnay@atmos.umd.edu Appendix: BV-dimension Patil et al., (2001) defined local bred vectors around a point in the 3-dimensional grid of the model by taking the 24 closest horizontal neighbors. If there are k bred vectors available, and N model variables for each grid point, the k local bred vectors form the columns of a 25Nxk matrix B. The kxk covariance matrix is C=B^T B. Its eigen- values are positive, and its eigenvectors v(i) are the singular vectors of the local bred vector subspace. The Bred Vector dimension (BV-dim) measures the local effective dimension: BV-dim[s,s,...,s(k)]={SUM[s(i)]}^2/SUM[s(i)]^2 where s(i) are the square roots of the eigenvalues of the covariance matrix. 5

Normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

Supervised neural network classification of pre-sliced cooked pork ham images using quaternionic singular values.

PubMed

Valous, Nektarios A; Mendoza, Fernando; Sun, Da-Wen; Allen, Paul

2010-03-01

The quaternionic singular value decomposition is a technique to decompose a quaternion matrix (representation of a colour image) into quaternion singular vector and singular value component matrices exposing useful properties. The objective of this study was to use a small portion of uncorrelated singular values, as robust features for the classification of sliced pork ham images, using a supervised artificial neural network classifier. Images were acquired from four qualities of sliced cooked pork ham typically consumed in Ireland (90 slices per quality), having similar appearances. Mahalanobis distances and Pearson product moment correlations were used for feature selection. Six highly discriminating features were used as input to train the neural network. An adaptive feedforward multilayer perceptron classifier was employed to obtain a suitable mapping from the input dataset. The overall correct classification performance for the training, validation and test set were 90.3%, 94.4%, and 86.1%, respectively. The results confirm that the classification performance was satisfactory. Extracting the most informative features led to the recognition of a set of different but visually quite similar textural patterns based on quaternionic singular values. Copyright 2009 Elsevier Ltd. All rights reserved.

Stochastic species abundance models involving special copulas

NASA Astrophysics Data System (ADS)

Huillet, Thierry E.

2018-01-01

Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall-Olkin copula arises in a species extinction model with catastrophe. In a second one, a quasi-copula problem arises in a flagged species abundance model. In a third model, we study completely random species abundance models in the hypercube as those, not of product type, with uniform margins and singular. These can be understood from a singular copula supported by an inflated simplex. An exchangeable singular Dirichlet copula is also introduced, together with its induced completely random species abundance vector.

Modal Filtering for Control of Flexible Aircraft

NASA Technical Reports Server (NTRS)

Suh, Peter M.; Mavris, Dimitri N.

2013-01-01

Modal regulators and deformation trackers are designed for an open-loop fluttering wing model. The regulators are designed with modal coordinate and accelerometer inputs respectively. The modal coordinates are estimated with simulated fiber optics. The robust stability of the closed-loop systems is compared in a structured singular-value vector analysis. Performance is evaluated and compared in a gust alleviation and flutter suppression simulation. For the same wing and flight condition two wing-shape-tracking control architectures are presented, which achieve deformation control at any point on the wing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge upmore » the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.« less

Development of an Efficient Binaural Simulation for the Analysis of Structural Acoustic Data

NASA Technical Reports Server (NTRS)

Lalime, Aimee L.; Johnson, Marty E.; Rizzi, Stephen A. (Technical Monitor)

2002-01-01

Binaural or "virtual acoustic" representation has been proposed as a method of analyzing acoustic and vibroacoustic data. Unfortunately, this binaural representation can require extensive computer power to apply the Head Related Transfer Functions (HRTFs) to a large number of sources, as with a vibrating structure. This work focuses on reducing the number of real-time computations required in this binaural analysis through the use of Singular Value Decomposition (SVD) and Equivalent Source Reduction (ESR). The SVD method reduces the complexity of the HRTF computations by breaking the HRTFs into dominant singular values (and vectors). The ESR method reduces the number of sources to be analyzed in real-time computation by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. It is shown that the effectiveness of the SVD and ESR methods improves as the complexity of the source increases. In addition, preliminary auralization tests have shown that the results from both the SVD and ESR methods are indistinguishable from the results found with the exhaustive method.

Sample-space-based feature extraction and class preserving projection for gene expression data.

PubMed

Wang, Wenjun

2013-01-01

In order to overcome the problems of high computational complexity and serious matrix singularity for feature extraction using Principal Component Analysis (PCA) and Fisher's Linear Discrinimant Analysis (LDA) in high-dimensional data, sample-space-based feature extraction is presented, which transforms the computation procedure of feature extraction from gene space to sample space by representing the optimal transformation vector with the weighted sum of samples. The technique is used in the implementation of PCA, LDA, Class Preserving Projection (CPP) which is a new method for discriminant feature extraction proposed, and the experimental results on gene expression data demonstrate the effectiveness of the method.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

Regularity results for the minimum time function with Hörmander vector fields

NASA Astrophysics Data System (ADS)

Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

2018-03-01

In a bounded domain of Rn with boundary given by a smooth (n - 1)-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields {X1 , … ,XN } subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of {X1 , … ,XN } is a symplectic manifold. We apply our results to several examples.

Efficient subtle motion detection from high-speed video for sound recovery and vibration analysis using singular value decomposition-based approach

NASA Astrophysics Data System (ADS)

Zhang, Dashan; Guo, Jie; Jin, Yi; Zhu, Chang'an

2017-09-01

High-speed cameras provide full field measurement of structure motions and have been applied in nondestructive testing and noncontact structure monitoring. Recently, a phase-based method has been proposed to extract sound-induced vibrations from phase variations in videos, and this method provides insights into the study of remote sound surveillance and material analysis. An efficient singular value decomposition (SVD)-based approach is introduced to detect sound-induced subtle motions from pixel intensities in silent high-speed videos. A high-speed camera is initially applied to capture a video of the vibrating objects stimulated by sound fluctuations. Then, subimages collected from a small region on the captured video are reshaped into vectors and reconstructed to form a matrix. Orthonormal image bases (OIBs) are obtained from the SVD of the matrix; available vibration signal can then be obtained by projecting subsequent subimages onto specific OIBs. A simulation test is initiated to validate the effectiveness and efficiency of the proposed method. Two experiments are conducted to demonstrate the potential applications in sound recovery and material analysis. Results show that the proposed method efficiently detects subtle motions from the video.

FAST TRACK COMMUNICATION: Singularity theorems based on trapped submanifolds of arbitrary co-dimension

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Senovilla, José M. M.

2010-08-01

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to an arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of the co-dimension 1, 2 or n.

Singularity-free spinors in gravity with propagating torsion

NASA Astrophysics Data System (ADS)

Fabbri, Luca

2017-12-01

We consider the most general renormalizable theory of propagating torsion in Einstein gravity for the Dirac matter distribution and we demonstrate that in this case, torsion is a massive axial-vector field whose coupling to the spinor gives rise to conditions in terms of which gravitational singularities are not bound to form; we discuss how our results improve those that are presented in the existing literature, and that no further improvement can be achieved unless one is ready to re-evaluate some considerations on the renormalizability of the theory.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD).

PubMed

Bermúdez Ordoñez, Juan Carlos; Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-05-16

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ 1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)

PubMed Central

Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-01-01

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain. PMID:29772731

Predicting areas of sustainable error growth in quasigeostrophic flows using perturbation alignment properties

NASA Astrophysics Data System (ADS)

Rivière, G.; Hua, B. L.

2004-10-01

A new perturbation initialization method is used to quantify error growth due to inaccuracies of the forecast model initial conditions in a quasigeostrophic box ocean model describing a wind-driven double gyre circulation. This method is based on recent analytical results on Lagrangian alignment dynamics of the perturbation velocity vector in quasigeostrophic flows. More specifically, it consists in initializing a unique perturbation from the sole knowledge of the control flow properties at the initial time of the forecast and whose velocity vector orientation satisfies a Lagrangian equilibrium criterion. This Alignment-based Initialization method is hereafter denoted as the AI method.In terms of spatial distribution of the errors, we have compared favorably the AI error forecast with the mean error obtained with a Monte-Carlo ensemble prediction. It is shown that the AI forecast is on average as efficient as the error forecast initialized with the leading singular vector for the palenstrophy norm, and significantly more efficient than that for total energy and enstrophy norms. Furthermore, a more precise examination shows that the AI forecast is systematically relevant for all control flows whereas the palenstrophy singular vector forecast leads sometimes to very good scores and sometimes to very bad ones.A principal component analysis at the final time of the forecast shows that the AI mode spatial structure is comparable to that of the first eigenvector of the error covariance matrix for a "bred mode" ensemble. Furthermore, the kinetic energy of the AI mode grows at the same constant rate as that of the "bred modes" from the initial time to the final time of the forecast and is therefore characterized by a sustained phase of error growth. In this sense, the AI mode based on Lagrangian dynamics of the perturbation velocity orientation provides a rationale of the "bred mode" behavior.

On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere

NASA Astrophysics Data System (ADS)

Fruman, Mark D.; Remmler, Sebastian; Achatz, Ulrich; Hickel, Stefan

2014-10-01

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear "2.5-D" simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.

Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Variational Mode Decomposition and Multi-Layer Classifier.

PubMed

Huang, Nantian; Chen, Huaijin; Cai, Guowei; Fang, Lihua; Wang, Yuqiang

2016-11-10

Mechanical fault diagnosis of high-voltage circuit breakers (HVCBs) based on vibration signal analysis is one of the most significant issues in improving the reliability and reducing the outage cost for power systems. The limitation of training samples and types of machine faults in HVCBs causes the existing mechanical fault diagnostic methods to recognize new types of machine faults easily without training samples as either a normal condition or a wrong fault type. A new mechanical fault diagnosis method for HVCBs based on variational mode decomposition (VMD) and multi-layer classifier (MLC) is proposed to improve the accuracy of fault diagnosis. First, HVCB vibration signals during operation are measured using an acceleration sensor. Second, a VMD algorithm is used to decompose the vibration signals into several intrinsic mode functions (IMFs). The IMF matrix is divided into submatrices to compute the local singular values (LSV). The maximum singular values of each submatrix are selected as the feature vectors for fault diagnosis. Finally, a MLC composed of two one-class support vector machines (OCSVMs) and a support vector machine (SVM) is constructed to identify the fault type. Two layers of independent OCSVM are adopted to distinguish normal or fault conditions with known or unknown fault types, respectively. On this basis, SVM recognizes the specific fault type. Real diagnostic experiments are conducted with a real SF₆ HVCB with normal and fault states. Three different faults (i.e., jam fault of the iron core, looseness of the base screw, and poor lubrication of the connecting lever) are simulated in a field experiment on a real HVCB to test the feasibility of the proposed method. Results show that the classification accuracy of the new method is superior to other traditional methods.

Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Variational Mode Decomposition and Multi-Layer Classifier

PubMed Central

Huang, Nantian; Chen, Huaijin; Cai, Guowei; Fang, Lihua; Wang, Yuqiang

2016-01-01

Mechanical fault diagnosis of high-voltage circuit breakers (HVCBs) based on vibration signal analysis is one of the most significant issues in improving the reliability and reducing the outage cost for power systems. The limitation of training samples and types of machine faults in HVCBs causes the existing mechanical fault diagnostic methods to recognize new types of machine faults easily without training samples as either a normal condition or a wrong fault type. A new mechanical fault diagnosis method for HVCBs based on variational mode decomposition (VMD) and multi-layer classifier (MLC) is proposed to improve the accuracy of fault diagnosis. First, HVCB vibration signals during operation are measured using an acceleration sensor. Second, a VMD algorithm is used to decompose the vibration signals into several intrinsic mode functions (IMFs). The IMF matrix is divided into submatrices to compute the local singular values (LSV). The maximum singular values of each submatrix are selected as the feature vectors for fault diagnosis. Finally, a MLC composed of two one-class support vector machines (OCSVMs) and a support vector machine (SVM) is constructed to identify the fault type. Two layers of independent OCSVM are adopted to distinguish normal or fault conditions with known or unknown fault types, respectively. On this basis, SVM recognizes the specific fault type. Real diagnostic experiments are conducted with a real SF6 HVCB with normal and fault states. Three different faults (i.e., jam fault of the iron core, looseness of the base screw, and poor lubrication of the connecting lever) are simulated in a field experiment on a real HVCB to test the feasibility of the proposed method. Results show that the classification accuracy of the new method is superior to other traditional methods. PMID:27834902

Comparison Of Eigenvector-Based Statistical Pattern Recognition Algorithms For Hybrid Processing

NASA Astrophysics Data System (ADS)

Tian, Q.; Fainman, Y.; Lee, Sing H.

1989-02-01

The pattern recognition algorithms based on eigenvector analysis (group 2) are theoretically and experimentally compared in this part of the paper. Group 2 consists of Foley-Sammon (F-S) transform, Hotelling trace criterion (HTC), Fukunaga-Koontz (F-K) transform, linear discriminant function (LDF) and generalized matched filter (GMF). It is shown that all eigenvector-based algorithms can be represented in a generalized eigenvector form. However, the calculations of the discriminant vectors are different for different algorithms. Summaries on how to calculate the discriminant functions for the F-S, HTC and F-K transforms are provided. Especially for the more practical, underdetermined case, where the number of training images is less than the number of pixels in each image, the calculations usually require the inversion of a large, singular, pixel correlation (or covariance) matrix. We suggest solving this problem by finding its pseudo-inverse, which requires inverting only the smaller, non-singular image correlation (or covariance) matrix plus multiplying several non-singular matrices. We also compare theoretically the effectiveness for classification with the discriminant functions from F-S, HTC and F-K with LDF and GMF, and between the linear-mapping-based algorithms and the eigenvector-based algorithms. Experimentally, we compare the eigenvector-based algorithms using a set of image data bases each image consisting of 64 x 64 pixels.

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Changing image of correlation optics: introduction.

PubMed

Angelsky, Oleg V; Desyatnikov, Anton S; Gbur, Gregory J; Hanson, Steen G; Lee, Tim; Miyamoto, Yoko; Schneckenburger, Herbert; Wyant, James C

2016-04-20

This feature issue of Applied Optics contains a series of selected papers reflecting recent progress of correlation optics and illustrating current trends in vector singular optics, internal energy flows at light fields, optical science of materials, and new biomedical applications of lasers.

Invariant object recognition based on the generalized discrete radon transform

NASA Astrophysics Data System (ADS)

Easley, Glenn R.; Colonna, Flavia

2004-04-01

We introduce a method for classifying objects based on special cases of the generalized discrete Radon transform. We adjust the transform and the corresponding ridgelet transform by means of circular shifting and a singular value decomposition (SVD) to obtain a translation, rotation and scaling invariant set of feature vectors. We then use a back-propagation neural network to classify the input feature vectors. We conclude with experimental results and compare these with other invariant recognition methods.

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE PAGES

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

2017-04-06

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Generation and dynamics of optical beams with polarization singularities.

PubMed

Cardano, Filippo; Karimi, Ebrahim; Marrucci, Lorenzo; de Lisio, Corrado; Santamato, Enrico

2013-04-08

We present a convenient method to generate vector beams of light having polarization singularities on their axis, via partial spin-to-orbital angular momentum conversion in a suitably patterned liquid crystal cell. The resulting polarization patterns exhibit a C-point on the beam axis and an L-line loop around it, and may have different geometrical structures such as "lemon", "star", and "spiral". Our generation method allows us to control the radius of L-line loop around the central C-point. Moreover, we investigate the free-air propagation of these fields across a Rayleigh range.

Compacted dimensions and singular plasmonic surfaces

NASA Astrophysics Data System (ADS)

Pendry, J. B.; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-01

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

A new feature constituting approach to detection of vocal fold pathology

NASA Astrophysics Data System (ADS)

Hariharan, M.; Polat, Kemal; Yaacob, Sazali

2014-08-01

In the last two decades, non-invasive methods through acoustic analysis of voice signal have been proved to be excellent and reliable tool to diagnose vocal fold pathologies. This paper proposes a new feature vector based on the wavelet packet transform and singular value decomposition for the detection of vocal fold pathology. k-means clustering based feature weighting is proposed to increase the distinguishing performance of the proposed features. In this work, two databases Massachusetts Eye and Ear Infirmary (MEEI) voice disorders database and MAPACI speech pathology database are used. Four different supervised classifiers such as k-nearest neighbour (k-NN), least-square support vector machine, probabilistic neural network and general regression neural network are employed for testing the proposed features. The experimental results uncover that the proposed features give very promising classification accuracy of 100% for both MEEI database and MAPACI speech pathology database.

Operational modal analysis using SVD of power spectral density transmissibility matrices

NASA Astrophysics Data System (ADS)

Araújo, Iván Gómez; Laier, Jose Elias

2014-05-01

This paper proposes the singular value decomposition of power spectrum density transmissibility matrices with different references, (PSDTM-SVD), as an identification method of natural frequencies and mode shapes of a dynamic system subjected to excitations under operational conditions. At the system poles, the rows of the proposed transmissibility matrix converge to the same ratio of amplitudes of vibration modes. As a result, the matrices are linearly dependent on the columns, and their singular values converge to zero. Singular values are used to determine the natural frequencies, and the first left singular vectors are used to estimate mode shapes. A numerical example of the finite element model of a beam subjected to colored noise excitation is analyzed to illustrate the accuracy of the proposed method. Results of the PSDTM-SVD method in the numerical example are compared with obtained using frequency domain decomposition (FDD) and power spectrum density transmissibility (PSDT). It is demonstrated that the proposed method does not depend on the excitation characteristics contrary to the FDD method that assumes white noise excitation, and further reduces the risk to identify extra non-physical poles in comparison to the PSDT method. Furthermore, a case study is performed using data from an operational vibration test of a bridge with a simply supported beam system. The real application of a full-sized bridge has shown that the proposed PSDTM-SVD method is able to identify the operational modal parameter. Operational modal parameters identified by the PSDTM-SVD in the real application agree well those identified by the FDD and PSDT methods.

A Comparison of Nonlinear Filters for Orbit Determination and Estimation

DTIC Science & Technology

1986-06-01

Com- mand uses a nonlinear least squares filter for element set maintenance for all objects orbiting the Earth (3). These objects, including active...initial state vector is the singularly averaged classical orbital element set provided by SPACECOM/DOA. The state vector in this research consists of...GSF (G) - - 26.0 36.7 GSF(A) 32.1 77.4 38.8 59.6 The Air Force Space Command is responsible for main- taining current orbital element sets for about

Automated Change Detection for Synthetic Aperture Sonar

DTIC Science & Technology

2014-01-01

channels, respectively. The canonical coordinates of x and y are defined as u = FHR−1/2xx x v = GHR−1/2yy y where F and G are the mapping matrices...containing the left and right singular vectors of the coherence matrix C, respectively. The canonical coordinate vectors u and v share the diagonal cross...feature set. The coherent change information between canonical coordinates v and u can be calculated using the residual, v −Ku, owing to the fact that

WE-AB-207A-04: Random Undersampled Cone Beam CT: Theoretical Analysis and a Novel Reconstruction Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, C; Chen, L; Jia, X

2016-06-15

Purpose: Reducing x-ray exposure and speeding up data acquisition motived studies on projection data undersampling. It is an important question that for a given undersampling ratio, what the optimal undersampling approach is. In this study, we propose a new undersampling scheme: random-ray undersampling. We will mathematically analyze its projection matrix properties and demonstrate its advantages. We will also propose a new reconstruction method that simultaneously performs CT image reconstruction and projection domain data restoration. Methods: By representing projection operator under the basis of singular vectors of full projection operator, matrix representations for an undersampling case can be generated and numericalmore » singular value decomposition can be performed. We compared properties of matrices among three undersampling approaches: regular-view undersampling, regular-ray undersampling, and the proposed random-ray undersampling. To accomplish CT reconstruction for random undersampling, we developed a novel method that iteratively performs CT reconstruction and missing projection data restoration via regularization approaches. Results: For a given undersampling ratio, random-ray undersampling preserved mathematical properties of full projection operator better than the other two approaches. This translates to advantages of reconstructing CT images at lower errors. Different types of image artifacts were observed depending on undersampling strategies, which were ascribed to the unique singular vectors of the sampling operators in the image domain. We tested the proposed reconstruction algorithm on a Forbid phantom with only 30% of the projection data randomly acquired. Reconstructed image error was reduced from 9.4% in a TV method to 7.6% in the proposed method. Conclusion: The proposed random-ray undersampling is mathematically advantageous over other typical undersampling approaches. It may permit better image reconstruction at the same undersampling ratio. The novel algorithm suitable for this random-ray undersampling was able to reconstruct high-quality images.« less

Nonlinear feedback control for high alpha flight

NASA Technical Reports Server (NTRS)

Stalford, Harold

1990-01-01

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

A Hybrid Short-Term Traffic Flow Prediction Model Based on Singular Spectrum Analysis and Kernel Extreme Learning Machine.

PubMed

Shang, Qiang; Lin, Ciyun; Yang, Zhaosheng; Bing, Qichun; Zhou, Xiyang

2016-01-01

Short-term traffic flow prediction is one of the most important issues in the field of intelligent transport system (ITS). Because of the uncertainty and nonlinearity, short-term traffic flow prediction is a challenging task. In order to improve the accuracy of short-time traffic flow prediction, a hybrid model (SSA-KELM) is proposed based on singular spectrum analysis (SSA) and kernel extreme learning machine (KELM). SSA is used to filter out the noise of traffic flow time series. Then, the filtered traffic flow data is used to train KELM model, the optimal input form of the proposed model is determined by phase space reconstruction, and parameters of the model are optimized by gravitational search algorithm (GSA). Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. And the SSA-KELM model is compared with several well-known prediction models, including support vector machine, extreme learning machine, and single KLEM model. The experimental results demonstrate that performance of the proposed model is superior to that of the comparison models. Apart from accuracy improvement, the proposed model is more robust.

A Hybrid Short-Term Traffic Flow Prediction Model Based on Singular Spectrum Analysis and Kernel Extreme Learning Machine

PubMed Central

Lin, Ciyun; Yang, Zhaosheng; Bing, Qichun; Zhou, Xiyang

2016-01-01

Short-term traffic flow prediction is one of the most important issues in the field of intelligent transport system (ITS). Because of the uncertainty and nonlinearity, short-term traffic flow prediction is a challenging task. In order to improve the accuracy of short-time traffic flow prediction, a hybrid model (SSA-KELM) is proposed based on singular spectrum analysis (SSA) and kernel extreme learning machine (KELM). SSA is used to filter out the noise of traffic flow time series. Then, the filtered traffic flow data is used to train KELM model, the optimal input form of the proposed model is determined by phase space reconstruction, and parameters of the model are optimized by gravitational search algorithm (GSA). Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. And the SSA-KELM model is compared with several well-known prediction models, including support vector machine, extreme learning machine, and single KLEM model. The experimental results demonstrate that performance of the proposed model is superior to that of the comparison models. Apart from accuracy improvement, the proposed model is more robust. PMID:27551829

Unitary Operators on the Document Space.

ERIC Educational Resources Information Center

Hoenkamp, Eduard

2003-01-01

Discusses latent semantic indexing (LSI) that would allow search engines to reduce the dimension of the document space by mapping it into a space spanned by conceptual indices. Topics include vector space models; singular value decomposition (SVD); unitary operators; the Haar transform; and new algorithms. (Author/LRW)

Protein sequence comparison based on K-string dictionary.

PubMed

Yu, Chenglong; He, Rong L; Yau, Stephen S-T

2013-10-25

The current K-string-based protein sequence comparisons require large amounts of computer memory because the dimension of the protein vector representation grows exponentially with K. In this paper, we propose a novel concept, the "K-string dictionary", to solve this high-dimensional problem. It allows us to use a much lower dimensional K-string-based frequency or probability vector to represent a protein, and thus significantly reduce the computer memory requirements for their implementation. Furthermore, based on this new concept, we use Singular Value Decomposition to analyze real protein datasets, and the improved protein vector representation allows us to obtain accurate gene trees. © 2013.

Application of Bred Vectors To Data Assimilation

NASA Astrophysics Data System (ADS)

Corazza, M.; Kalnay, E.; Patil, Dj

We introduced a statistic, the BV-dimension, to measure the effective local finite-time dimensionality of the atmosphere. We show that this dimension is often quite low, and suggest that this finding has important implications for data assimilation and the accuracy of weather forecasting (Patil et al, 2001). The original database for this study was the forecasts of the NCEP global ensemble forecasting system. The initial differences between the control forecast and the per- turbed forecasts are called bred vectors. The control and perturbed initial conditions valid at time t=n(t are evolved using the forecast model until time t=(n+1) (t. The differences between the perturbed and the control forecasts are scaled down to their initial amplitude, and constitute the bred vectors valid at (n+1) (t. Their growth rate is typically about 1.5/day. The bred vectors are similar by construction to leading Lya- punov vectors except that they have small but finite amplitude, and they are valid at finite times. The original NCEP ensemble data set has 5 independent bred vectors. We define a local bred vector at each grid point by choosing the 5 by 5 grid points centered at the grid point (a region of about 1100km by 1100km), and using the north-south and east- west velocity components at 500mb pressure level to form a 50 dimensional column vector. Since we have k=5 global bred vectors, we also have k local bred vectors at each grid point. We estimate the effective dimensionality of the subspace spanned by the local bred vectors by performing a singular value decomposition (EOF analysis). The k local bred vector columns form a 50xk matrix M. The singular values s(i) of M measure the extent to which the k column unit vectors making up the matrix M point in the direction of v(i). We define the bred vector dimension as BVDIM={Sum[s(i)]}^2/{Sum[s(i)]^2} For example, if 4 out of the 5 vectors lie along v, and one lies along v, the BV- dimension would be BVDIM[sqrt(4), 1, 0,0,0]=1.8, less than 2 because one direction is more dominant than the other in representing the original data. The results (Patil et al, 2001) show that there are large regions where the bred vectors span a subspace of substantially lower dimension than that of the full space. These low dimensionality regions are dominant in the baroclinic extratropics, typically have a lifetime of 3-7 days, have a well-defined horizontal and vertical structure that spans 1 most of the atmosphere, and tend to move eastward. New results with a large number of ensemble members confirm these results and indicate that the low dimensionality regions are quite robust, and depend only on the verification time (i.e., the underlying flow). Corazza et al (2001) have performed experiments with a data assimilation system based on a quasi-geostrophic model and simulated observations (Morss, 1999, Hamill et al, 2000). A 3D-variational data assimilation scheme for a quasi-geostrophic chan- nel model is used to study the structure of the background error and its relationship to the corresponding bred vectors. The "true" evolution of the model atmosphere is defined by an integration of the model and "rawinsonde observations" are simulated by randomly perturbing the true state at fixed locations. It is found that after 3-5 days the bred vectors develop well organized structures which are very similar for the two different norms considered in this paper (potential vorticity norm and streamfunction norm). The results show that the bred vectors do indeed represent well the characteristics of the data assimilation forecast errors, and that the subspace of bred vectors contains most of the forecast error, except in areas where the forecast errors are small. For example, the angle between the 6hr forecast error and the subspace spanned by 10 bred vectors is less than 10o over 90% of the domain, indicating a pattern correlation of more than 98.5% between the forecast error and its projection onto the bred vector subspace. The presence of low-dimensional regions in the perturbations of the basic flow has important implications for data assimilation. At any given time, there is a difference between the true atmospheric state and the model forecast. Assuming that model er- rors are not the dominant source of errors, in a region of low BV-dimensionality the difference between the true state and the forecast should lie substantially in the low dimensional unstable subspace of the few bred vectors that contribute most strongly to the low BV-dimension. This information should yield a substantial improvement in the forecast: the data assimilation algorithm should correct the model state by moving it closer to the observations along the unstable subspace, since this is where the true state most likely lies. Preliminary experiments have been conducted with the quasi-geostrophic data assim- ilation system testing whether it is possible to add "errors of the day" based on bred vectors to the standard (constant) 3D-Var background error covariance in order to capture these important errors. The results are extremely encouraging, indicating a significant reduction (about 40%) in the analysis errors at a very low computational cost. References: 2 Corazza, M., E. Kalnay, DJ Patil, R. Morss, M Cai, I. Szunyogh, BR Hunt, E Ott and JA Yorke, 2001: Use of the breeding technique to estimate the structure of the analysis "errors of the day". Submitted to Nonlinear Processes in Geophysics. Hamill, T.M., Snyder, C., and Morss, R.E., 2000: A Comparison of Probabilistic Fore- casts from Bred, Singular-Vector and Perturbed Observation Ensembles, Mon. Wea. Rev., 128, 1835­1851. Kalnay, E., and Z. Toth, 1994: Removing growing errors in the analysis cycle. Preprints of the Tenth Conference on Numerical Weather Prediction, Amer. Meteor. Soc., 1994, 212-215. Morss, R. E., 1999: Adaptive observations: Idealized sampling strategies for improv- ing numerical weather prediction. PHD thesis, Massachussetts Institute of technology, 225pp. Patil, D. J. S., B. R. Hunt, E. Kalnay, J. A. Yorke, and E. Ott., 2001: Local Low Dimensionality of Atmospheric Dynamics. Phys. Rev. Lett., 86, 5878. 3

Method of assessing the state of a rolling bearing based on the relative compensation distance of multiple-domain features and locally linear embedding

NASA Astrophysics Data System (ADS)

Kang, Shouqiang; Ma, Danyang; Wang, Yujing; Lan, Chaofeng; Chen, Qingguo; Mikulovich, V. I.

2017-03-01

To effectively assess different fault locations and different degrees of performance degradation of a rolling bearing with a unified assessment index, a novel state assessment method based on the relative compensation distance of multiple-domain features and locally linear embedding is proposed. First, for a single-sample signal, time-domain and frequency-domain indexes can be calculated for the original vibration signal and each sensitive intrinsic mode function obtained by improved ensemble empirical mode decomposition, and the singular values of the sensitive intrinsic mode function matrix can be extracted by singular value decomposition to construct a high-dimensional hybrid-domain feature vector. Second, a feature matrix can be constructed by arranging each feature vector of multiple samples, the dimensions of each row vector of the feature matrix can be reduced by the locally linear embedding algorithm, and the compensation distance of each fault state of the rolling bearing can be calculated using the support vector machine. Finally, the relative distance between different fault locations and different degrees of performance degradation and the normal-state optimal classification surface can be compensated, and on the basis of the proposed relative compensation distance, the assessment model can be constructed and an assessment curve drawn. Experimental results show that the proposed method can effectively assess different fault locations and different degrees of performance degradation of the rolling bearing under certain conditions.

Binary black hole spacetimes with a helical Killing vector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klein, Christian

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where themore » Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.« less

Normal forms for Hopf-Zero singularities with nonconservative nonlinear part

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh; Sanders, Jan A.

In this paper we are concerned with the simplest normal form computation of the systems x˙=2xf(x,y2+z2), y˙=z+yf(x,y2+z2), z˙=-y+zf(x,y2+z2), where f is a formal function with real coefficients and without any constant term. These are the classical normal forms of a larger family of systems with Hopf-Zero singularity. Indeed, these are defined such that this family would be a Lie subalgebra for the space of all classical normal form vector fields with Hopf-Zero singularity. The simplest normal forms and simplest orbital normal forms of this family with nonzero quadratic part are computed. We also obtain the simplest parametric normal form of any non-degenerate perturbation of this family within the Lie subalgebra. The symmetry group of the simplest normal forms is also discussed. This is a part of our results in decomposing the normal forms of Hopf-Zero singular systems into systems with a first integral and nonconservative systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loef, P.A.; Smed, T.; Andersson, G.

The minimum singular value of the power flow Jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady state voltage stability limit. In this paper a fast method to calculate the minimum singular value and the corresponding (left and right) singular vectors is presented. The main advantages of the developed algorithm are the small amount of computation time needed, and that it only requires information available from an ordinary program for power flow calculations. Furthermore, the proposed method fully utilizes the sparsity of the power flow Jacobian matrixmore » and hence the memory requirements for the computation are low. These advantages are preserved when applied to various submatrices of the Jacobian matrix, which can be useful in constructing special voltage stability indices. The developed algorithm was applied to small test systems as well as to a large (real size) system with over 1000 nodes, with satisfactory results.« less

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Xu, Xiangsheng

2018-04-01

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

Glove-based approach to online signature verification.

PubMed

Kamel, Nidal S; Sayeed, Shohel; Ellis, Grant A

2008-06-01

Utilizing the multiple degrees of freedom offered by the data glove for each finger and the hand, a novel on-line signature verification system using the Singular Value Decomposition (SVD) numerical tool for signature classification and verification is presented. The proposed technique is based on the Singular Value Decomposition in finding r singular vectors sensing the maximal energy of glove data matrix A, called principal subspace, so the effective dimensionality of A can be reduced. Having modeled the data glove signature through its r-principal subspace, signature authentication is performed by finding the angles between the different subspaces. A demonstration of the data glove is presented as an effective high-bandwidth data entry device for signature verification. This SVD-based signature verification technique is tested and its performance is shown to be able to recognize forgery signatures with a false acceptance rate of less than 1.2%.

Singularity in structural optimization

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1993-01-01

The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

ATTITUDE FILTERING ON SO(3)

NASA Technical Reports Server (NTRS)

Markley, F. Landis

2005-01-01

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

Compacted dimensions and singular plasmonic surfaces.

PubMed

Pendry, J B; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-17

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer. Copyright © 2017, American Association for the Advancement of Science.

A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems

PubMed Central

Ran, Changyan; Cheng, Xianghong

2016-01-01

This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method. PMID:27598169

Simplicity and Typical Rank Results for Three-Way Arrays

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2011-01-01

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

A Generalized Method of Image Analysis from an Intercorrelation Matrix which May Be Singular.

ERIC Educational Resources Information Center

Yanai, Haruo; Mukherjee, Bishwa Nath

1987-01-01

This generalized image analysis method is applicable to singular and non-singular correlation matrices (CMs). Using the orthogonal projector and a weaker generalized inverse matrix, image and anti-image covariance matrices can be derived from a singular CM. (SLD)

Topological study of the periodic system.

PubMed

Restrepo, Guillermo; Mesa, Héber; Llanos, Eugenio J; Villaveces, José L

2004-01-01

We carried out a topological study of the Space of Chemical Elements, SCE, based on a clustering analysis of 72 elements, each one defined by a vector of 31 properties. We looked for neighborhoods, boundaries, and other topological properties of the SCE. Among the results one sees the well-known patterns of the Periodic Table and relationships such as the Singularity Principle and the Diagonal Relationship, but there appears also a robustness property of some of the better-known families of elements. Alkaline metals and Noble Gases are sets whose neighborhoods have no other elements besides themselves, whereas the topological boundary of the set of metals is formed by semimetallic elements.

Conical refraction of elastic waves in absorbing crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alshits, V. I., E-mail: alshits@ns.crys.ras.ru; Lyubimov, V. N.

2011-10-15

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after 'switching on' absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincare index n = {+-}1/2, transforms to a planar distribution of ellipses with two singularities n = {+-}1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied.more » The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by {pi}/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.« less

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo; Rivadossi, Luca; Janbozorgi, Mohammad

2018-04-01

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

Gimbal-Angle Vectors of the Nonredundant CMG Cluster

NASA Astrophysics Data System (ADS)

Lee, Donghun; Bang, Hyochoong

2018-05-01

This paper deals with the method using the preferred gimbal angles of a control moment gyro (CMG) cluster for controlling spacecraft attitude. To apply the method to the nonredundant CMG cluster, analytical gimbal-angle solutions for the zero angular momentum state are derived, and the gimbal-angle vectors for the nonzero angular momentum states are studied by a numerical method. It will be shown that the number of the gimbal-angle vectors is determined from the given skew angle and the angular momentum state of the CMG cluster. Through numerical examples, it is shown that the method using the preferred gimbal-angle is an efficient approach to avoid internal singularities for the nonredundant CMG cluster.

A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization

NASA Astrophysics Data System (ADS)

Binz, Ernst; Pods, Sonja

2006-01-01

In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group HX∞. A representation of the C*-group algebra of HX∞ is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.

Treatment of singularities in a middle-crack tension specimen

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1990-01-01

A three-dimensional finite-element analysis of a middle-crack tension specimen subjected to mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed nonsingular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate appears to be an appropriate parameter all along the crack front.

Singularities in Optimal Structural Design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

Singularities in optimal structural design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

Predicting domain-domain interaction based on domain profiles with feature selection and support vector machines

PubMed Central

2010-01-01

Background Protein-protein interaction (PPI) plays essential roles in cellular functions. The cost, time and other limitations associated with the current experimental methods have motivated the development of computational methods for predicting PPIs. As protein interactions generally occur via domains instead of the whole molecules, predicting domain-domain interaction (DDI) is an important step toward PPI prediction. Computational methods developed so far have utilized information from various sources at different levels, from primary sequences, to molecular structures, to evolutionary profiles. Results In this paper, we propose a computational method to predict DDI using support vector machines (SVMs), based on domains represented as interaction profile hidden Markov models (ipHMM) where interacting residues in domains are explicitly modeled according to the three dimensional structural information available at the Protein Data Bank (PDB). Features about the domains are extracted first as the Fisher scores derived from the ipHMM and then selected using singular value decomposition (SVD). Domain pairs are represented by concatenating their selected feature vectors, and classified by a support vector machine trained on these feature vectors. The method is tested by leave-one-out cross validation experiments with a set of interacting protein pairs adopted from the 3DID database. The prediction accuracy has shown significant improvement as compared to InterPreTS (Interaction Prediction through Tertiary Structure), an existing method for PPI prediction that also uses the sequences and complexes of known 3D structure. Conclusions We show that domain-domain interaction prediction can be significantly enhanced by exploiting information inherent in the domain profiles via feature selection based on Fisher scores, singular value decomposition and supervised learning based on support vector machines. Datasets and source code are freely available on the web at http://liao.cis.udel.edu/pub/svdsvm. Implemented in Matlab and supported on Linux and MS Windows. PMID:21034480

Superposition of nonparaxial vectorial complex-source spherically focused beams: Axial Poynting singularity and reverse propagation

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2016-08-01

In this work, counterintuitive effects such as the generation of an axial (i.e., long the direction of wave motion) zero-energy flux density (i.e., axial Poynting singularity) and reverse (i.e., negative) propagation of nonparaxial quasi-Gaussian electromagnetic (EM) beams are examined. Generalized analytical expressions for the EM field's components of a coherent superposition of two high-order quasi-Gaussian vortex beams of opposite handedness and different amplitudes are derived based on the complex-source-point method, stemming from Maxwell's vector equations and the Lorenz gauge condition. The general solutions exhibiting unusual effects satisfy the Helmholtz and Maxwell's equations. The EM beam components are characterized by nonzero integer degree and order (n ,m ) , respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and a weighting (real) factor 0 ≤α ≤1 that describes the transition of the beam from a purely vortex (α =0 ) to a nonvortex (α =1 ) type. An attractive feature for this superposition is the description of strongly focused (or strongly divergent) wave fields. Computations of the EM power density as well as the linear and angular momentum density fluxes illustrate the analysis with particular emphasis on the polarization states of the vector potentials forming the beams and the weight of the coherent beam superposition causing the transition from the vortex to the nonvortex type. Should some conditions determined by the polarization state of the vector potentials and the beam parameters be met, an axial zero-energy flux density is predicted in addition to a negative retrograde propagation effect. Moreover, rotation reversal of the angular momentum flux density with respect to the beam handedness is anticipated, suggesting the possible generation of negative (left-handed) torques. The results are particularly useful in applications involving the design of strongly focused optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque in particle manipulation, and other related topics.

A truncated generalized singular value decomposition algorithm for moving force identification with ill-posed problems

NASA Astrophysics Data System (ADS)

Chen, Zhen; Chan, Tommy H. T.

2017-08-01

This paper proposes a new methodology for moving force identification (MFI) from the responses of bridge deck. Based on the existing time domain method (TDM), the MFI problem eventually becomes solving the linear algebraic equation in the form Ax = b . The vector b is usually contaminated by an unknown error e generating from measurement error, which often called the vector e as ''noise''. With the ill-posed problems that exist in the inverse problem, the identification force would be sensitive to the noise e . The proposed truncated generalized singular value decomposition method (TGSVD) aims at obtaining an acceptable solution and making the noise to be less sensitive to perturbations with the ill-posed problems. The illustrated results show that the TGSVD has many advantages such as higher precision, better adaptability and noise immunity compared with TDM. In addition, choosing a proper regularization matrix L and a truncation parameter k are very useful to improve the identification accuracy and to solve ill-posed problems when it is used to identify the moving force on bridge.

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

NASA Technical Reports Server (NTRS)

Fink, P. W.; Khayat, M. A.; Wilton, D. R.

2005-01-01

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

An integrated analysis-synthesis array system for spatial sound fields.

PubMed

Bai, Mingsian R; Hua, Yi-Hsin; Kuo, Chia-Hao; Hsieh, Yu-Hao

2015-03-01

An integrated recording and reproduction array system for spatial audio is presented within a generic framework akin to the analysis-synthesis filterbanks in discrete time signal processing. In the analysis stage, a microphone array "encodes" the sound field by using the plane-wave decomposition. Direction of arrival of plane-wave components that comprise the sound field of interest are estimated by multiple signal classification. Next, the source signals are extracted by using a deconvolution procedure. In the synthesis stage, a loudspeaker array "decodes" the sound field by reconstructing the plane-wave components obtained in the analysis stage. This synthesis stage is carried out by pressure matching in the interior domain of the loudspeaker array. The deconvolution problem is solved by truncated singular value decomposition or convex optimization algorithms. For high-frequency reproduction that suffers from the spatial aliasing problem, vector panning is utilized. Listening tests are undertaken to evaluate the deconvolution method, vector panning, and a hybrid approach that combines both methods to cover frequency ranges below and above the spatial aliasing frequency. Localization and timbral attributes are considered in the subjective evaluation. The results show that the hybrid approach performs the best in overall preference. In addition, there is a trade-off between reproduction performance and the external radiation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carle, S F

Compositional data are represented as vector variables with individual vector components ranging between zero and a positive maximum value representing a constant sum constraint, usually unity (or 100 percent). The earth sciences are flooded with spatial distributions of compositional data, such as concentrations of major ion constituents in natural waters (e.g. mole, mass, or volume fractions), mineral percentages, ore grades, or proportions of mutually exclusive categories (e.g. a water-oil-rock system). While geostatistical techniques have become popular in earth science applications since the 1970s, very little attention has been paid to the unique mathematical properties of geostatistical formulations involving compositional variables.more » The book 'Geostatistical Analysis of Compositional Data' by Vera Pawlowsky-Glahn and Ricardo Olea (Oxford University Press, 2004), unlike any previous book on geostatistics, directly confronts the mathematical difficulties inherent to applying geostatistics to compositional variables. The book righteously justifies itself with prodigious referencing to previous work addressing nonsensical ranges of estimated values and error, spurious correlation, and singular cross-covariance matrices.« less

The semantic representation of prejudice and stereotypes.

PubMed

Bhatia, Sudeep

2017-07-01

We use a theory of semantic representation to study prejudice and stereotyping. Particularly, we consider large datasets of newspaper articles published in the United States, and apply latent semantic analysis (LSA), a prominent model of human semantic memory, to these datasets to learn representations for common male and female, White, African American, and Latino names. LSA performs a singular value decomposition on word distribution statistics in order to recover word vector representations, and we find that our recovered representations display the types of biases observed in human participants using tasks such as the implicit association test. Importantly, these biases are strongest for vector representations with moderate dimensionality, and weaken or disappear for representations with very high or very low dimensionality. Moderate dimensional LSA models are also the best at learning race, ethnicity, and gender-based categories, suggesting that social category knowledge, acquired through dimensionality reduction on word distribution statistics, can facilitate prejudiced and stereotyped associations. Copyright © 2017 Elsevier B.V. All rights reserved.

Linear discriminant analysis based on L1-norm maximization.

PubMed

Zhong, Fujin; Zhang, Jiashu

2013-08-01

Linear discriminant analysis (LDA) is a well-known dimensionality reduction technique, which is widely used for many purposes. However, conventional LDA is sensitive to outliers because its objective function is based on the distance criterion using L2-norm. This paper proposes a simple but effective robust LDA version based on L1-norm maximization, which learns a set of local optimal projection vectors by maximizing the ratio of the L1-norm-based between-class dispersion and the L1-norm-based within-class dispersion. The proposed method is theoretically proved to be feasible and robust to outliers while overcoming the singular problem of the within-class scatter matrix for conventional LDA. Experiments on artificial datasets, standard classification datasets and three popular image databases demonstrate the efficacy of the proposed method.

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

Constellation of phase singularities in a speckle-like pattern for optical vortex metrology applied to biological kinematic analysis.

PubMed

Wang, Wei; Qiao, Yu; Ishijima, Reika; Yokozeki, Tomoaki; Honda, Daigo; Matsuda, Akihiro; Hanson, Steen G; Takeda, Mitsuo

2008-09-01

A novel technique for biological kinematic analysis is proposed that makes use of the pseudophase singularities in a complex signal generated from a speckle-like pattern. In addition to the information about the locations and the anisotropic core structures of the pseudophase singularities, we also detect the spatial structures of a cluster of phase singularities, which serves as a unique constellation characterizing the mutual position relation between the individual pseudophase singularities. Experimental results of in vivo measurements for a swimming fish along with its kinematic analysis are presented, which demonstrate the validity of the proposed technique.

Exploring the Common Dynamics of Homologous Proteins. Application to the Globin Family

PubMed Central

Maguid, Sandra; Fernandez-Alberti, Sebastian; Ferrelli, Leticia; Echave, Julian

2005-01-01

We present a procedure to explore the global dynamics shared between members of the same protein family. The method allows the comparison of patterns of vibrational motion obtained by Gaussian network model analysis. After the identification of collective coordinates that were conserved during evolution, we quantify the common dynamics within a family. Representative vectors that describe these dynamics are defined using a singular value decomposition approach. As a test case, the globin heme-binding family is considered. The two lowest normal modes are shown to be conserved within this family. Our results encourage the development of models for protein evolution that take into account the conservation of dynamical features. PMID:15749782

Singularity analysis: theory and further developments

NASA Astrophysics Data System (ADS)

Cheng, Qiuming

2015-04-01

Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Failure of geometric electromagnetism in the adiabatic vector Kepler problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anglin, J.R.; Schmiedmayer, J.

2004-02-01

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict themore » precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.« less

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Determination of Rayleigh wave ellipticity using single-station and array-based processing of ambient seismic noise

NASA Astrophysics Data System (ADS)

Workman, Eli Joseph

We present a single-station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 sec the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 sec, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher ( 2%) and significantly higher (>20%), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e., Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves.

Determination of Rayleigh wave ellipticity across the Earthscope Transportable Array using single-station and array-based processing of ambient seismic noise

NASA Astrophysics Data System (ADS)

Workman, Eli; Lin, Fan-Chi; Koper, Keith D.

2017-01-01

We present a single station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 s the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 s, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher (˜2 per cent) and significantly higher (>20 per cent), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e. Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves and tilt noise.

Amino acid "little Big Bang": representing amino acid substitution matrices as dot products of Euclidian vectors.

PubMed

Zimmermann, Karel; Gibrat, Jean-François

2010-01-04

Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.

Scale-invariant streamline equations and strings of singular vorticity for perturbed anisotropic solutions of the Navier-Stokes equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Libin, A., E-mail: a_libin@netvision.net.il

2012-12-15

A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the stringsmore » of singular vorticity.« less

The effect of receiver coil orientations on the imaging performance of magnetic induction tomography

NASA Astrophysics Data System (ADS)

Gürsoy, D.; Scharfetter, H.

2009-10-01

Magnetic induction tomography is an imaging modality which aims to reconstruct the conductivity distribution of the human body. It uses magnetic induction to excite the body and an array of sensor coils to detect the perturbations in the magnetic field. Up to now, much effort has been expended with the aim of finding an efficient coil configuration to extend the dynamic range of the measured signal. However, the merits of different sensor orientations on the imaging performance have not been studied in great detail so far. Therefore, the aim of the study is to fill the void of a systematic investigation of coil orientations on the reconstruction quality of the designs. To this end, a number of alternative receiver array designs with different coil orientations were suggested and the evaluations of the designs were performed based on the singular value decomposition. A generalized class of quality measures, the subclasses of which are linked to both the spatial resolution and uncertainty measures, was used to assess the performance on the radial and axial axes of a cylindrical phantom. The detectability of local conductivity perturbations in the phantom was explored using the reconstructed images. It is possible to draw the conclusion that the proper choice of the coil orientations significantly influences the number of usable singular vectors and accordingly the stability of image reconstruction, although the effect of increased stability on the quality of the reconstructed images was not of paramount importance due to the reduced independent information content of the associated singular vectors.

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Climate and weather across scales: singularities and stochastic Levy-Clifford algebra

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127.

Development of an Efficient Binaural Simulation for the Analysis of Structural Acoustic Data

NASA Technical Reports Server (NTRS)

Johnson, Marty E.; Lalime, Aimee L.; Grosveld, Ferdinand W.; Rizzi, Stephen A.; Sullivan, Brenda M.

2003-01-01

Applying binaural simulation techniques to structural acoustic data can be very computationally intensive as the number of discrete noise sources can be very large. Typically, Head Related Transfer Functions (HRTFs) are used to individually filter the signals from each of the sources in the acoustic field. Therefore, creating a binaural simulation implies the use of potentially hundreds of real time filters. This paper details two methods of reducing the number of real-time computations required by: (i) using the singular value decomposition (SVD) to reduce the complexity of the HRTFs by breaking them into dominant singular values and vectors and (ii) by using equivalent source reduction (ESR) to reduce the number of sources to be analyzed in real-time by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. The ESR and SVD reduction methods can be combined to provide an estimated computation time reduction of 99.4% for the structural acoustic data tested. In addition, preliminary tests have shown that there is a 97% correlation between the results of the combined reduction methods and the results found with the current binaural simulation techniques

Characterizing omega-limit sets which are closed orbits

NASA Astrophysics Data System (ADS)

Bautista, S.; Morales, C.

Let X be a vector field in a compact n-manifold M, n⩾2. Given Σ⊂M we say that q∈M satisfies (P) Σ if the closure of the positive orbit of X through q does not intersect Σ, but, however, there is an open interval I with q as a boundary point such that every positive orbit through I intersects Σ. Among those q having saddle-type hyperbolic omega-limit set ω(q) the ones with ω(q) being a closed orbit satisfy (P) Σ for some closed subset Σ. The converse is true for n=2 but not for n⩾4. Here we prove the converse for n=3. Moreover, we prove for n=3 that if ω(q) is a singular-hyperbolic set [C. Morales, M. Pacifico, E. Pujals, On C robust singular transitive sets for three-dimensional flows, C. R. Acad. Sci. Paris Sér. I 26 (1998) 81-86], [C. Morales, M. Pacifico, E. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Ann. of Math. (2) 160 (2) (2004) 375-432], then ω(q) is a closed orbit if and only if q satisfies (P) Σ for some Σ closed. This result improves [S. Bautista, Sobre conjuntos hiperbólicos-singulares (On singular-hyperbolic sets), thesis Uiversidade Federal do Rio de Janeiro, 2005 (in Portuguese)] and [C. Morales, M. Pacifico, Mixing attractors for 3-flows, Nonlinearity 14 (2001) 359-378].

Rationality of moduli space of torsion-free sheaves over reducible curve

NASA Astrophysics Data System (ADS)

Dey, Arijit; Suhas, B. N.

2018-06-01

Let M(2 , w ̲ , χ) be the moduli space of rank 2 torsion-free sheaves of fixed determinant and odd Euler characteristic over a reducible nodal curve with each irreducible component having utmost two nodal singularities. We show that in each irreducible component of M(2 , w ̲ , χ) , the closure of rank 2 vector bundles is rational.

Diametrical clustering for identifying anti-correlated gene clusters.

PubMed

Dhillon, Inderjit S; Marcotte, Edward M; Roshan, Usman

2003-09-01

Clustering genes based upon their expression patterns allows us to predict gene function. Most existing clustering algorithms cluster genes together when their expression patterns show high positive correlation. However, it has been observed that genes whose expression patterns are strongly anti-correlated can also be functionally similar. Biologically, this is not unintuitive-genes responding to the same stimuli, regardless of the nature of the response, are more likely to operate in the same pathways. We present a new diametrical clustering algorithm that explicitly identifies anti-correlated clusters of genes. Our algorithm proceeds by iteratively (i). re-partitioning the genes and (ii). computing the dominant singular vector of each gene cluster; each singular vector serving as the prototype of a 'diametric' cluster. We empirically show the effectiveness of the algorithm in identifying diametrical or anti-correlated clusters. Testing the algorithm on yeast cell cycle data, fibroblast gene expression data, and DNA microarray data from yeast mutants reveals that opposed cellular pathways can be discovered with this method. We present systems whose mRNA expression patterns, and likely their functions, oppose the yeast ribosome and proteosome, along with evidence for the inverse transcriptional regulation of a number of cellular systems.

Flight-determined stability analysis of multiple-input-multiple-output control systems

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron command-feedback gain by +/- 20 percent. Minimum eigenvalues of the return difference matrix which bound the singular values are also presented. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.

Flight-determined stability analysis of multiple-input-multiple-output control systems

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron-command-feedback gain by +/- 20 percent. Also presented are the minimum eigenvalues of the return difference matrix which bound the singular values. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.

Spectral analysis of two-signed microarray expression data.

PubMed

Higham, Desmond J; Kalna, Gabriela; Vass, J Keith

2007-06-01

We give a simple and informative derivation of a spectral algorithm for clustering and reordering complementary DNA microarray expression data. Here, expression levels of a set of genes are recorded simultaneously across a number of samples, with a positive weight reflecting up-regulation and a negative weight reflecting down-regulation. We give theoretical support for the algorithm based on a biologically justified hypothesis about the structure of the data, and illustrate its use on public domain data in the context of unsupervised tumour classification. The algorithm is derived by considering a discrete optimization problem and then relaxing to the continuous realm. We prove that in the case where the data have an inherent 'checkerboard' sign pattern, the algorithm will automatically reveal that pattern. Further, our derivation shows that the algorithm may be regarded as imposing a random graph model on the expression levels and then clustering from a maximum likelihood perspective. This indicates that the output will be tolerant to perturbations and will reveal 'near-checkerboard' patterns when these are present in the data. It is interesting to note that the checkerboard structure is revealed by the first (dominant) singular vectors--previous work on spectral methods has focussed on the case of nonnegative edge weights, where only the second and higher singular vectors are relevant. We illustrate the algorithm on real and synthetic data, and then use it in a tumour classification context on three different cancer data sets. Our results show that respecting the two-signed nature of the data (thereby distinguishing between up-regulation and down-regulation) reveals structures that cannot be gleaned from the absolute value data (where up- and down-regulation are both regarded as 'changes').

Computation at a coordinate singularity

NASA Astrophysics Data System (ADS)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar singularity are observed to increase with grid resolution. In contrast, test simulations demonstrate robust polar behavior independent of grid resolution.

Analysis of Self-Associating Proteins by Singular Value Decomposition of Solution Scattering Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williamson, Tim E.; Craig, Bruce A.; Kondrashkina, Elena

2008-07-08

We describe a method by which a single experiment can reveal both association model (pathway and constants) and low-resolution structures of a self-associating system. Small-angle scattering data are collected from solutions at a range of concentrations. These scattering data curves are mass-weighted linear combinations of the scattering from each oligomer. Singular value decomposition of the data yields a set of basis vectors from which the scattering curve for each oligomer is reconstructed using coefficients that depend on the association model. A search identifies the association pathway and constants that provide the best agreement between reconstructed and observed data. Using simulatedmore » data with realistic noise, our method finds the correct pathway and association constants. Depending on the simulation parameters, reconstructed curves for each oligomer differ from the ideal by 0.050.99% in median absolute relative deviation. The reconstructed scattering curves are fundamental to further analysis, including interatomic distance distribution calculation and low-resolution ab initio shape reconstruction of each oligomer in solution. This method can be applied to x-ray or neutron scattering data from small angles to moderate (or higher) resolution. Data can be taken under physiological conditions, or particular conditions (e.g., temperature) can be varied to extract fundamental association parameters ({Delta}H{sub ass}, S{sub ass}).« less

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

PubMed

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Dynamic Singularity Spectrum Distribution of Sea Clutter

NASA Astrophysics Data System (ADS)

Xiong, Gang; Yu, Wenxian; Zhang, Shuning

2015-12-01

The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.

Separation of spatial-temporal patterns ('climatic modes') by combined analysis of really measured and generated numerically vector time series

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Volodin, E. M.; Gavrilov, A.; Loskutov, E. M.

2013-12-01

The new method of decomposition of the Earth's climate system into well separated spatial-temporal patterns ('climatic modes') is discussed. The method is based on: (i) generalization of the MSSA (Multichannel Singular Spectral Analysis) [1] for expanding vector (space-distributed) time series in basis of spatial-temporal empirical orthogonal functions (STEOF), which makes allowance delayed correlations of the processes recorded in spatially separated points; (ii) expanding both real SST data, and longer by several times SST data generated numerically, in STEOF basis; (iii) use of the numerically produced STEOF basis for exclusion of 'too slow' (and thus not represented correctly) processes from real data. The application of the method allows by means of vector time series generated numerically by the INM RAS Coupled Climate Model [2] to separate from real SST anomalies data [3] two climatic modes possessing by noticeably different time scales: 3-5 and 9-11 years. Relations of separated modes to ENSO and PDO are investigated. Possible applications of spatial-temporal climatic patterns concept to prognosis of climate system evolution is discussed. 1. Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, et al. (2002) "Advanced spectral methods for climatic time series", Rev. Geophys. 40(1), 3.1-3.41. 2. http://83.149.207.89/GCM_DATA_PLOTTING/GCM_INM_DATA_XY_en.htm 3. http://iridl.ldeo.columbia.edu/SOURCES/.KAPLAN/.EXTENDED/.v2/.ssta/

Tissue multifractality and hidden Markov model based integrated framework for optimum precancer detection

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Sabyasachi; Das, Nandan K.; Kurmi, Indrajit; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.

2017-10-01

We report the application of a hidden Markov model (HMM) on multifractal tissue optical properties derived via the Born approximation-based inverse light scattering method for effective discrimination of precancerous human cervical tissue sites from the normal ones. Two global fractal parameters, generalized Hurst exponent and the corresponding singularity spectrum width, computed by multifractal detrended fluctuation analysis (MFDFA), are used here as potential biomarkers. We develop a methodology that makes use of these multifractal parameters by integrating with different statistical classifiers like the HMM and support vector machine (SVM). It is shown that the MFDFA-HMM integrated model achieves significantly better discrimination between normal and different grades of cancer as compared to the MFDFA-SVM integrated model.

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

NASA Technical Reports Server (NTRS)

Taur, D.-R.; Prussing, J. E.; Coverstone-Carroll, V.

1990-01-01

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Adaptive fault feature extraction from wayside acoustic signals from train bearings

NASA Astrophysics Data System (ADS)

Zhang, Dingcheng; Entezami, Mani; Stewart, Edward; Roberts, Clive; Yu, Dejie

2018-07-01

Wayside acoustic detection of train bearing faults plays a significant role in maintaining safety in the railway transport system. However, the bearing fault information is normally masked by strong background noises and harmonic interferences generated by other components (e.g. axles and gears). In order to extract the bearing fault feature information effectively, a novel method called improved singular value decomposition (ISVD) with resonance-based signal sparse decomposition (RSSD), namely the ISVD-RSSD method, is proposed in this paper. A Savitzky-Golay (S-G) smoothing filter is used to filter singular vectors (SVs) in the ISVD method as an extension of the singular value decomposition (SVD) theorem. Hilbert spectrum entropy and a stepwise optimisation strategy are used to optimize the S-G filter's parameters. The RSSD method is able to nonlinearly decompose the wayside acoustic signal of a faulty train bearing into high and low resonance components, the latter of which contains bearing fault information. However, the high level of noise usually results in poor decomposition results from the RSSD method. Hence, the collected wayside acoustic signal must first be de-noised using the ISVD component of the ISVD-RSSD method. Next, the de-noised signal is decomposed by using the RSSD method. The obtained low resonance component is then demodulated with a Hilbert transform such that the bearing fault can be detected by observing Hilbert envelope spectra. The effectiveness of the ISVD-RSSD method is verified through both laboratory field-based experiments as described in the paper. The results indicate that the proposed method is superior to conventional spectrum analysis and ensemble empirical mode decomposition methods.

Sampling strategies based on singular vectors for assimilated models in ocean forecasting systems

NASA Astrophysics Data System (ADS)

Fattorini, Maria; Brandini, Carlo; Ortolani, Alberto

2016-04-01

Meteorological and oceanographic models do need observations, not only as a ground truth element to verify the quality of the models, but also to keep model forecast error acceptable: through data assimilation techniques which merge measured and modelled data, natural divergence of numerical solutions from reality can be reduced / controlled and a more reliable solution - called analysis - is computed. Although this concept is valid in general, its application, especially in oceanography, raises many problems due to three main reasons: the difficulties that have ocean models in reaching an acceptable state of equilibrium, the high measurements cost and the difficulties in realizing them. The performances of the data assimilation procedures depend on the particular observation networks in use, well beyond the background quality and the used assimilation method. In this study we will present some results concerning the great impact of the dataset configuration, in particular measurements position, on the evaluation of the overall forecasting reliability of an ocean model. The aim consists in identifying operational criteria to support the design of marine observation networks at regional scale. In order to identify the observation network able to minimize the forecast error, a methodology based on Singular Vectors Decomposition of the tangent linear model is proposed. Such a method can give strong indications on the local error dynamics. In addition, for the purpose of avoiding redundancy of information contained in the data, a minimal distance among data positions has been chosen on the base of a spatial correlation analysis of the hydrodynamic fields under investigation. This methodology has been applied for the choice of data positions starting from simplified models, like an ideal double-gyre model and a quasi-geostrophic one. Model configurations and data assimilation are based on available ROMS routines, where a variational assimilation algorithm (4D-var) is included as part of the code These first applications have provided encouraging results in terms of increased predictability time and reduced forecast error, also improving the quality of the analysis used to recover the real circulation patterns from a first guess quite far from the real state.

Two-order parameters theory of the metal-insulator phase transition kinetics in the magnetic field

NASA Astrophysics Data System (ADS)

Dubovskii, L. B.

2018-05-01

The metal-insulator phase transition is considered within the framework of the Ginzburg-Landau approach for the phase transition described with two coupled order parameters. One of the order parameters is the mass density which variation is responsible for the origin of nonzero overlapping of the two different electron bands and the appearance of free electron carriers. This transition is assumed to be a first-order phase one. The free electron carriers are described with the vector-function representing the second-order parameter responsible for the continuous phase transition. This order parameter determines mostly the physical properties of the metal-insulator transition and leads to a singularity of the surface tension at the metal-insulator interface. The magnetic field is involved into the consideration of the system. The magnetic field leads to new singularities of the surface tension at the metal-insulator interface and results in a drastic variation of the phase transition kinetics. A strong singularity in the surface tension results from the Landau diamagnetism and determines anomalous features of the metal-insulator transition kinetics.

Quasinormal Frequencies of D-Dimensional Schwarzschild Black Holes: Evaluation via Continued Fraction Method

NASA Astrophysics Data System (ADS)

Rostworowski, A.

2007-01-01

We adopt Leaver's [E. Leaver, {ITALIC Proc. R. Soc. Lond.} {A402}, 285 (1985)] method to determine quasi normal frequencies of the Schwarzschild black hole in higher (D geq 10) dimensions. In D-dimensional Schwarzschild metric, when D increases, more and more singularities, spaced uniformly on the unit circle |r|=1, approach the horizon at r=rh=1. Thus, a solution satisfying the outgoing wave boundary condition at the horizon must be continued to some mid point and only then the continued fraction condition can be applied. This prescription is general and applies to all cases for which, due to regular singularities on the way from the point of interest to the irregular singularity, Leaver's method in its original setting breaks down. We illustrate the method calculating gravitational vector and tensor quasinormal frequencies of the Schwarzschild black hole in D=11 and D=10 dimensions. We also give the details for the D=9 case, considered in the work of P. Bizoz, T. Chmaj, A. Rostworowski, B.G. Schmidt and Z. Tabor {ITALIC Phys. Rev.}{D72}, 121502(R) (2005) .

Integrating the Gradient of the Thin Wire Kernel

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Wilton, Donald R.

2008-01-01

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

MUSIC algorithm for location searching of dielectric anomalies from S-parameters using microwave imaging

NASA Astrophysics Data System (ADS)

Park, Won-Kwang; Kim, Hwa Pyung; Lee, Kwang-Jae; Son, Seong-Ho

2017-11-01

Motivated by the biomedical engineering used in early-stage breast cancer detection, we investigated the use of MUltiple SIgnal Classification (MUSIC) algorithm for location searching of small anomalies using S-parameters. We considered the application of MUSIC to functional imaging where a small number of dipole antennas are used. Our approach is based on the application of Born approximation or physical factorization. We analyzed cases in which the anomaly is respectively small and large in relation to the wavelength, and the structure of the left-singular vectors is linked to the nonzero singular values of a Multi-Static Response (MSR) matrix whose elements are the S-parameters. Using simulations, we demonstrated the strengths and weaknesses of the MUSIC algorithm in detecting both small and extended anomalies.

Attitude control with realization of linear error dynamics

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Bach, Ralph E.

1993-01-01

An attitude control law is derived to realize linear unforced error dynamics with the attitude error defined in terms of rotation group algebra (rather than vector algebra). Euler parameters are used in the rotational dynamics model because they are globally nonsingular, but only the minimal three Euler parameters are used in the error dynamics model because they have no nonlinear mathematical constraints to prevent the realization of linear error dynamics. The control law is singular only when the attitude error angle is exactly pi rad about any eigenaxis, and a simple intuitive modification at the singularity allows the control law to be used globally. The forced error dynamics are nonlinear but stable. Numerical simulation tests show that the control law performs robustly for both initial attitude acquisition and attitude control.

Implementation of hierarchical clustering using k-mer sparse matrix to analyze MERS-CoV genetic relationship

NASA Astrophysics Data System (ADS)

Bustamam, A.; Ulul, E. D.; Hura, H. F. A.; Siswantining, T.

2017-07-01

Hierarchical clustering is one of effective methods in creating a phylogenetic tree based on the distance matrix between DNA (deoxyribonucleic acid) sequences. One of the well-known methods to calculate the distance matrix is k-mer method. Generally, k-mer is more efficient than some distance matrix calculation techniques. The steps of k-mer method are started from creating k-mer sparse matrix, and followed by creating k-mer singular value vectors. The last step is computing the distance amongst vectors. In this paper, we analyze the sequences of MERS-CoV (Middle East Respiratory Syndrome - Coronavirus) DNA by implementing hierarchical clustering using k-mer sparse matrix in order to perform the phylogenetic analysis. Our results show that the ancestor of our MERS-CoV is coming from Egypt. Moreover, we found that the MERS-CoV infection that occurs in one country may not necessarily come from the same country of origin. This suggests that the process of MERS-CoV mutation might not only be influenced by geographical factor.

Introduction to Adjoint Models

NASA Technical Reports Server (NTRS)

Errico, Ronald M.

2015-01-01

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

The role of model errors represented by nonlinear forcing singular vector tendency error in causing the "spring predictability barrier" within ENSO predictions

NASA Astrophysics Data System (ADS)

Duan, Wansuo; Zhao, Peng

2017-04-01

Within the Zebiak-Cane model, the nonlinear forcing singular vector (NFSV) approach is used to investigate the role of model errors in the "Spring Predictability Barrier" (SPB) phenomenon within ENSO predictions. NFSV-related errors have the largest negative effect on the uncertainties of El Niño predictions. NFSV errors can be classified into two types: the first is characterized by a zonal dipolar pattern of SST anomalies (SSTA), with the western poles centered in the equatorial central-western Pacific exhibiting positive anomalies and the eastern poles in the equatorial eastern Pacific exhibiting negative anomalies; and the second is characterized by a pattern almost opposite the first type. The first type of error tends to have the worst effects on El Niño growth-phase predictions, whereas the latter often yields the largest negative effects on decaying-phase predictions. The evolution of prediction errors caused by NFSV-related errors exhibits prominent seasonality, with the fastest error growth in the spring and/or summer seasons; hence, these errors result in a significant SPB related to El Niño events. The linear counterpart of NFSVs, the (linear) forcing singular vector (FSV), induces a less significant SPB because it contains smaller prediction errors. Random errors cannot generate a SPB for El Niño events. These results show that the occurrence of an SPB is related to the spatial patterns of tendency errors. The NFSV tendency errors cause the most significant SPB for El Niño events. In addition, NFSVs often concentrate these large value errors in a few areas within the equatorial eastern and central-western Pacific, which likely represent those areas sensitive to El Niño predictions associated with model errors. Meanwhile, these areas are also exactly consistent with the sensitive areas related to initial errors determined by previous studies. This implies that additional observations in the sensitive areas would not only improve the accuracy of the initial field but also promote the reduction of model errors to greatly improve ENSO forecasts.

Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.

PubMed

Okimoto, Gordon; Zeinalzadeh, Ashkan; Wenska, Tom; Loomis, Michael; Nation, James B; Fabre, Tiphaine; Tiirikainen, Maarit; Hernandez, Brenda; Chan, Owen; Wong, Linda; Kwee, Sandi

2016-01-01

Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1. The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation. We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology. Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.

A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method

NASA Astrophysics Data System (ADS)

Chen, Leilei; Zheng, Changjun; Chen, Haibo

2013-09-01

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

Lefschetz thimbles in fermionic effective models with repulsive vector-field

NASA Astrophysics Data System (ADS)

Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira

2018-06-01

We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion bilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This "auxiliary" sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.

The double universal joint wrist on a manipulator: Solution of inverse position kinematics and singularity analysis

NASA Technical Reports Server (NTRS)

Williams, Robert L., III

1992-01-01

This paper presents three methods to solve the inverse position kinematics position problem of the double universal joint attached to a manipulator: (1) an analytical solution for two specific cases; (2) an approximate closed form solution based on ignoring the wrist offset; and (3) an iterative method which repeats closed form position and orientation calculations until the solution is achieved. Several manipulators are used to demonstrate the solution methods: cartesian, cylindrical, spherical, and an anthropomorphic articulated arm, based on the Flight Telerobotic Servicer (FTS) arm. A singularity analysis is presented for the double universal joint wrist attached to the above manipulator arms. While the double universal joint wrist standing alone is singularity-free in orientation, the singularity analysis indicates the presence of coupled position/orientation singularities of the spherical and articulated manipulators with the wrist. The cartesian and cylindrical manipulators with the double universal joint wrist were found to be singularity-free. The methods of this paper can be implemented in a real-time controller for manipulators with the double universal joint wrist. Such mechanically dextrous systems could be used in telerobotic and industrial applications, but further work is required to avoid the singularities.

Signature of phase singularities in diffusive regimes in disordered waveguide lattices: interplay and qualitative analysis

NASA Astrophysics Data System (ADS)

Ghosh, Somnath

2018-05-01

Co-existence and interplay between mesoscopic light dynamics with singular optics in spatially random but temporally coherent disordered waveguide lattices is reported. Two CW light beams of 1.55 micron operating wavelength are launched as inputs to 1D waveguide lattices with controllable weak disorder in refractive index profile. Direct observation of phase singularities in the speckle pattern along the length is numerically demonstrated. Quantitative analysis of onset of such singular behavior and diffusive wave propagation is analyzed for the first time.

Complex numbers in chemometrics: examples from multivariate impedance measurements on lipid monolayers.

PubMed

Geladi, Paul; Nelson, Andrew; Lindholm-Sethson, Britta

2007-07-09

Electrical impedance gives multivariate complex number data as results. Two examples of multivariate electrical impedance data measured on lipid monolayers in different solutions give rise to matrices (16x50 and 38x50) of complex numbers. Multivariate data analysis by principal component analysis (PCA) or singular value decomposition (SVD) can be used for complex data and the necessary equations are given. The scores and loadings obtained are vectors of complex numbers. It is shown that the complex number PCA and SVD are better at concentrating information in a few components than the naïve juxtaposition method and that Argand diagrams can replace score and loading plots. Different concentrations of Magainin and Gramicidin A give different responses and also the role of the electrolyte medium can be studied. An interaction of Gramicidin A in the solution with the monolayer over time can be observed.

Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Correlation between solar flare productivity and photospheric vector magnetic fields

NASA Astrophysics Data System (ADS)

Cui, Yanmei; Wang, Huaning

2008-11-01

Studying the statistical correlation between the solar flare productivity and photospheric magnetic fields is very important and necessary. It is helpful to set up a practical flare forecast model based on magnetic properties and improve the physical understanding of solar flare eruptions. In the previous study ([Cui, Y.M., Li, R., Zhang, L.Y., He, Y.L., Wang, H.N. Correlation between solar flare productivity and photospheric magnetic field properties 1. Maximum horizontal gradient, length of neutral line, number of singular points. Sol. Phys. 237, 45 59, 2006]; from now on we refer to this paper as ‘Paper I’), three measures of the maximum horizontal gradient, the length of the neutral line, and the number of singular points are computed from 23990 SOHO/MDI longitudinal magnetograms. The statistical relationship between the solar flare productivity and these three measures is well fitted with sigmoid functions. In the current work, the three measures of the length of strong-shear neutral line, total unsigned current, and total unsigned current helicity are computed from 1353 vector magnetograms observed at Huairou Solar Observing Station. The relationship between the solar flare productivity and the current three measures can also be well fitted with sigmoid functions. These results are expected to be beneficial to future operational flare forecasting models.

Design of 2D time-varying vector fields.

PubMed

Chen, Guoning; Kwatra, Vivek; Wei, Li-Yi; Hansen, Charles D; Zhang, Eugene

2012-10-01

Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects.

Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate.

PubMed

Liu, Gui-Geng; Wang, Ke; Lee, Yun-Han; Wang, Dan; Li, Ping-Ping; Gou, Fangwang; Li, Yongnan; Tu, Chenghou; Wu, Shin-Tson; Wang, Hui-Tian

2018-02-15

Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into ±1 orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

Signature of phase singularities in diffusive regimes in disordered waveguide lattices: interplay and qualitative analysis.

PubMed

Ghosh, Somnath

2018-05-10

Coexistence and interplay between mesoscopic light dynamics with singular optics in spatially disordered waveguide lattices are reported. Two CW light beams of a 1.55 μm operating wavelength are launched as inputs to 1D waveguide lattices with controllable weak disorder in a complex refractive index profile. Direct observation of phase singularities in the speckle pattern along the length is numerically demonstrated. Quantitative analysis of the onset of such singular behavior and diffusive wave propagation is analyzed for the first time, to the best of our knowledge.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Crews, J. H., Jr.

1981-01-01

A quasi-three-dimensional finite-element analysis was used to analyze the edge-stress problem in four-ply, composite laminates. The seven laminates that were considered belong to the laminate family where the outer ply angle is between 0 and 90 deg. Systematic convergence studies were made to explore the existence of stress singularities near the free edge. The present analysis appears to confirm the existence of stress singularities at the intersection of the interface and the free edge. The power of the stress singularity was the same for all seven laminates considered.

An Improved Wavefront Control Algorithm for Large Space Telescopes

NASA Technical Reports Server (NTRS)

Sidick, Erkin; Basinger, Scott A.; Redding, David C.

2008-01-01

Wavefront sensing and control is required throughout the mission lifecycle of large space telescopes such as James Webb Space Telescope (JWST). When an optic of such a telescope is controlled with both surface-deforming and rigid-body actuators, the sensitivity-matrix obtained from the exit pupil wavefront vector divided by the corresponding actuator command value can sometimes become singular due to difference in actuator types and in actuator command values. In this paper, we propose a simple approach for preventing a sensitivity-matrix from singularity. We also introduce a new "minimum-wavefront and optimal control compensator". It uses an optimal control gain matrix obtained by feeding back the actuator commands along with the measured or estimated wavefront phase information to the estimator, thus eliminating the actuator modes that are not observable in the wavefront sensing process.

Forecasting electric vehicles sales with univariate and multivariate time series models: The case of China.

PubMed

Zhang, Yong; Zhong, Miner; Geng, Nana; Jiang, Yunjian

2017-01-01

The market demand for electric vehicles (EVs) has increased in recent years. Suitable models are necessary to understand and forecast EV sales. This study presents a singular spectrum analysis (SSA) as a univariate time-series model and vector autoregressive model (VAR) as a multivariate model. Empirical results suggest that SSA satisfactorily indicates the evolving trend and provides reasonable results. The VAR model, which comprised exogenous parameters related to the market on a monthly basis, can significantly improve the prediction accuracy. The EV sales in China, which are categorized into battery and plug-in EVs, are predicted in both short term (up to December 2017) and long term (up to 2020), as statistical proofs of the growth of the Chinese EV industry.

Forecasting electric vehicles sales with univariate and multivariate time series models: The case of China

PubMed Central

Zhang, Yong; Zhong, Miner; Geng, Nana; Jiang, Yunjian

2017-01-01

The market demand for electric vehicles (EVs) has increased in recent years. Suitable models are necessary to understand and forecast EV sales. This study presents a singular spectrum analysis (SSA) as a univariate time-series model and vector autoregressive model (VAR) as a multivariate model. Empirical results suggest that SSA satisfactorily indicates the evolving trend and provides reasonable results. The VAR model, which comprised exogenous parameters related to the market on a monthly basis, can significantly improve the prediction accuracy. The EV sales in China, which are categorized into battery and plug-in EVs, are predicted in both short term (up to December 2017) and long term (up to 2020), as statistical proofs of the growth of the Chinese EV industry. PMID:28459872

Development of the Nonstationary Incremental Analysis Update Algorithm for Sequential Data Assimilation System

NASA Astrophysics Data System (ADS)

Ham, Yoo-Geun; Song, Hyo-Jong; Jung, Jaehee; Lim, Gyu-Ho

2017-04-01

This study introduces a altered version of the incremental analysis updates (IAU), called the nonstationary IAU (NIAU) method, to enhance the assimilation accuracy of the IAU while retaining the continuity of the analysis. Analogous to the IAU, the NIAU is designed to add analysis increments at every model time step to improve the continuity in the intermittent data assimilation. Still, unlike the IAU, the NIAU method applies time-evolved forcing employing the forward operator as rectifications to the model. The solution of the NIAU is better than that of the IAU, of which analysis is performed at the start of the time window for adding the IAU forcing, in terms of the accuracy of the analysis field. It is because, in the linear systems, the NIAU solution equals that in an intermittent data assimilation method at the end of the assimilation interval. To have the filtering property in the NIAU, a forward operator to propagate the increment is reconstructed with only dominant singular vectors. An illustration of those advantages of the NIAU is given using the simple 40-variable Lorenz model.

Analysis and design of nonlinear resonances via singularity theory

NASA Astrophysics Data System (ADS)

Cirillo, G. I.; Habib, G.; Kerschen, G.; Sepulchre, R.

2017-03-01

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.

Singular spectrum analysis of sleep EEG in insomnia.

PubMed

Aydın, Serap; Saraoǧlu, Hamdi Melih; Kara, Sadık

2011-08-01

In the present study, the Singular Spectrum Analysis (SSA) is applied to sleep EEG segments collected from healthy volunteers and patients diagnosed by either psycho physiological insomnia or paradoxical insomnia. Then, the resulting singular spectra computed for both C3 and C4 recordings are assigned as the features to the Artificial Neural Network (ANN) architectures for EEG classification in diagnose. In tests, singular spectrum of particular sleep stages such as awake, REM, stage1 and stage2, are considered. Three clinical groups are successfully classified by using one hidden layer ANN architecture with respect to their singular spectra. The results show that the SSA can be applied to sleep EEG series to support the clinical findings in insomnia if ten trials are available for the specific sleep stages. In conclusion, the SSA can detect the oscillatory variations on sleep EEG. Therefore, different sleep stages meet different singular spectra. In addition, different healthy conditions generate different singular spectra for each sleep stage. In summary, the SSA can be proposed for EEG discrimination to support the clinical findings for psycho-psychological disorders.

MUFACT: An Algorithm for Multiple Factor Analyses of Singular and Nonsingular Data with Orthogonal and Oblique Transformation Solutions

ERIC Educational Resources Information Center

Hofmann, Richard J.

1978-01-01

A general factor analysis computer algorithm is briefly discussed. The algorithm is highly transportable with minimum limitations on the number of observations. Both singular and non-singular data can be analyzed. (Author/JKS)

Singularity Analysis: a powerful image processing tool in remote sensing of the oceans

NASA Astrophysics Data System (ADS)

Turiel, A.; Umbert, M.; Hoareau, N.; Ballabrera-Poy, J.; Portabella, M.

2012-04-01

The study of fully developed turbulence has given rise to the development of new methods to describe real data of scalars submitted to the action of a turbulent flow. The application of this brand of methodologies (known as Microcanonical Multifractal Formalism, MMF) on remote sensing ocean maps open new ways to exploit those data for oceanographic purposes. The main technique in MMF is that of Singularity Analysis (SA). By means of SA a singularity exponents is assigned to each point of a given image. The singularity exponent of a given point is a dimensionless measure of the regularity or irregularity of the scalar at that point. Singularity exponents arrange in singularity lines, which accurately track the flow streamlines from any scalar, as we have verified with remote sensing and simulated data. Applications of SA include quality assessment of different products, the estimation of surface velocities, the development of fusion techniques for different types of scalars, comparison with measures of ocean mixing, and improvement in assimilation schemes.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

A two-dimensional cascade solution using minimized surface singularity density distributions - with application to film cooled turbine blades

NASA Technical Reports Server (NTRS)

Mcfarland, E.; Tabakoff, W.; Hamed, A.

1977-01-01

An investigation of the effects of coolant injection on the aerodynamic performance of cooled turbine blades is presented. The coolant injection is modeled in the inviscid irrotational adiabatic flow analysis through the cascade using the distributed singularities approach. The resulting integral equations are solved using a minimized surface singularity density criteria. The aerodynamic performance was evaluated using this solution in conjunction with an existing mixing theory analysis. The results of the present analysis are compared with experimental measurements in cold flow tests.

A geometric approach to problems in birational geometry.

PubMed

Chi, Chen-Yu; Yau, Shing-Tung

2008-12-02

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties. A fundamental question is the following: Given two mildly singular projective varieties with some of the first variety's pseudonormed spaces being isometric to the corresponding ones of the second variety's, can one construct a birational map between them that induces these isometries? In this work, a positive answer to this question is given for varieties of general type. This can be thought of as a theorem of Torelli type for birational equivalence.

Semiclassical analysis of spectral singularities and their applications in optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mostafazadeh, Ali

2011-08-15

Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain coefficient varies due to the exponential decay of the intensity of the pumping beam inside the medium. For both singly and doublypumped samples, we obtain universal upper bounds on the decay constant beyond which no lasing occurs. Furthermore, we show that the dependence of the wavelength of the spectral singularities on the value of the decay constant is extremely mild. This is an indication ofmore » the stability of optical spectral singularities.« less

Registration algorithm of point clouds based on multiscale normal features

NASA Astrophysics Data System (ADS)

Lu, Jun; Peng, Zhongtao; Su, Hang; Xia, GuiHua

2015-01-01

The point cloud registration technology for obtaining a three-dimensional digital model is widely applied in many areas. To improve the accuracy and speed of point cloud registration, a registration method based on multiscale normal vectors is proposed. The proposed registration method mainly includes three parts: the selection of key points, the calculation of feature descriptors, and the determining and optimization of correspondences. First, key points are selected from the point cloud based on the changes of magnitude of multiscale curvatures obtained by using principal components analysis. Then the feature descriptor of each key point is proposed, which consists of 21 elements based on multiscale normal vectors and curvatures. The correspondences in a pair of two point clouds are determined according to the descriptor's similarity of key points in the source point cloud and target point cloud. Correspondences are optimized by using a random sampling consistency algorithm and clustering technology. Finally, singular value decomposition is applied to optimized correspondences so that the rigid transformation matrix between two point clouds is obtained. Experimental results show that the proposed point cloud registration algorithm has a faster calculation speed, higher registration accuracy, and better antinoise performance.

Topology of three-dimensional separated flows

NASA Technical Reports Server (NTRS)

Tobak, M.; Peake, D. J.

1981-01-01

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Statistical analysis of effective singular values in matrix rank determination

NASA Technical Reports Server (NTRS)

Konstantinides, Konstantinos; Yao, Kung

1988-01-01

A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inomata, A.; Junker, G.; Wilson, R.

1993-08-01

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bahn problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. 32 refs.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

NASA Astrophysics Data System (ADS)

Wang, L.-P.; Ochoa-Rodríguez, S.; Onof, C.; Willems, P.

2015-09-01

Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system's dynamics, particularly of peak runoff flows.

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Crews, J. H., Jr.

1980-01-01

A quasi three dimensional finite element analysis was used to analyze the edge stress problem in four-ply, composite laminates. Convergence studies were made to explore the existence of stress singularities near the free edge. The existence of stress singularities at the intersection of the interface and the free edge is confirmed.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Characterization of agricultural land using singular value decomposition

NASA Astrophysics Data System (ADS)

Herries, Graham M.; Danaher, Sean; Selige, Thomas

1995-11-01

A method is defined and tested for the characterization of agricultural land from multi-spectral imagery, based on singular value decomposition (SVD) and key vector analysis. The SVD technique, which bears a close resemblance to multivariate statistic techniques, has previously been successfully applied to problems of signal extraction for marine data and forestry species classification. In this study the SVD technique is used as a classifier for agricultural regions, using airborne Daedalus ATM data, with 1 m resolution. The specific region chosen is an experimental research farm in Bavaria, Germany. This farm has a large number of crops, within a very small region and hence is not amenable to existing techniques. There are a number of other significant factors which render existing techniques such as the maximum likelihood algorithm less suitable for this area. These include a very dynamic terrain and tessellated pattern soil differences, which together cause large variations in the growth characteristics of the crops. The SVD technique is applied to this data set using a multi-stage classification approach, removing unwanted land-cover classes one step at a time. Typical classification accuracy's for SVD are of the order of 85-100%. Preliminary results indicate that it is a fast and efficient classifier with the ability to differentiate between crop types such as wheat, rye, potatoes and clover. The results of characterizing 3 sub-classes of Winter Wheat are also shown.

Quantum Linear System Algorithm for Dense Matrices.

PubMed

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-02

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that Ax=b. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O(κ^{2}sqrt[n]polylog(n)/ε) for an n×n dimensional A with bounded spectral norm, where κ denotes the condition number of A, and ε is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A.

How long the singular value decomposed entropy predicts the stock market? - Evidence from the Dow Jones Industrial Average Index

NASA Astrophysics Data System (ADS)

Gu, Rongbao; Shao, Yanmin

2016-07-01

In this paper, a new concept of multi-scales singular value decomposition entropy based on DCCA cross correlation analysis is proposed and its predictive power for the Dow Jones Industrial Average Index is studied. Using Granger causality analysis with different time scales, it is found that, the singular value decomposition entropy has predictive power for the Dow Jones Industrial Average Index for period less than one month, but not for more than one month. This shows how long the singular value decomposition entropy predicts the stock market that extends Caraiani's result obtained in Caraiani (2014). On the other hand, the result also shows an essential characteristic of stock market as a chaotic dynamic system.

Investigations on the hierarchy of reference frames in geodesy and geodynamics

NASA Technical Reports Server (NTRS)

Grafarend, E. W.; Mueller, I. I.; Papo, H. B.; Richter, B.

1979-01-01

Problems related to reference directions were investigated. Space and time variant angular parameters are illustrated in hierarchic structures or towers. Using least squares techniques, model towers of triads are presented which allow the formation of linear observation equations. Translational and rotational degrees of freedom (origin and orientation) are discussed along with and the notion of length and scale degrees of freedom. According to the notion of scale parallelism, scale factors with respect to a unit length are given. Three-dimensional geodesy was constructed from the set of three base vectors (gravity, earth-rotation and the ecliptic normal vector). Space and time variations are given with respect to a polar and singular value decomposition or in terms of changes in translation, rotation, deformation (shear, dilatation or angular and scale distortions).

Local sensitivity analysis for inverse problems solved by singular value decomposition

USGS Publications Warehouse

Hill, M.C.; Nolan, B.T.

2010-01-01

Local sensitivity analysis provides computationally frugal ways to evaluate models commonly used for resource management, risk assessment, and so on. This includes diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data likely to reduce model uncertainty. Here, we consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration. The statistics considered include the PEST identifiability statistic, and combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC). The statistics are complimentary in that the identifiability statistic integrates the effects of parameter sensitivity and interdependence, while CSS and PCC provide individual measures of sensitivity and interdependence. PCC quantifies correlations between pairs or larger sets of parameters; when a set of parameters is intercorrelated, the absolute value of PCC is close to 1.00 for all pairs in the set. The number of singular vectors to include in the calculation of the identifiability statistic is somewhat subjective and influences the statistic. To demonstrate the statistics, we use the USDA’s Root Zone Water Quality Model to simulate nitrogen fate and transport in the unsaturated zone of the Merced River Basin, CA. There are 16 log-transformed process-model parameters, including water content at field capacity (WFC) and bulk density (BD) for each of five soil layers. Calibration data consisted of 1,670 observations comprising soil moisture, soil water tension, aqueous nitrate and bromide concentrations, soil nitrate concentration, and organic matter content. All 16 of the SVD parameters could be estimated by regression based on the range of singular values. Identifiability statistic results varied based on the number of SVD parameters included. Identifiability statistics calculated for four SVD parameters indicate the same three most important process-model parameters as CSS/PCC (WFC1, WFC2, and BD2), but the order differed. Additionally, the identifiability statistic showed that BD1 was almost as dominant as WFC1. The CSS/PCC analysis showed that this results from its high correlation with WCF1 (-0.94), and not its individual sensitivity. Such distinctions, combined with analysis of how high correlations and(or) sensitivities result from the constructed model, can produce important insights into, for example, the use of sensitivity analysis to design monitoring networks. In conclusion, the statistics considered identified similar important parameters. They differ because (1) with CSS/PCC can be more awkward because sensitivity and interdependence are considered separately and (2) identifiability requires consideration of how many SVD parameters to include. A continuing challenge is to understand how these computationally efficient methods compare with computationally demanding global methods like Markov-Chain Monte Carlo given common nonlinear processes and the often even more nonlinear models.

Singular boundary method for wave propagation analysis in periodic structures

NASA Astrophysics Data System (ADS)

Fu, Zhuojia; Chen, Wen; Wen, Pihua; Zhang, Chuanzeng

2018-07-01

A strong-form boundary collocation method, the singular boundary method (SBM), is developed in this paper for the wave propagation analysis at low and moderate wavenumbers in periodic structures. The SBM is of several advantages including mathematically simple, easy-to-program, meshless with the application of the concept of origin intensity factors in order to eliminate the singularity of the fundamental solutions and avoid the numerical evaluation of the singular integrals in the boundary element method. Due to the periodic behaviors of the structures, the SBM coefficient matrix can be represented as a block Toeplitz matrix. By employing three different fast Toeplitz-matrix solvers, the computational time and storage requirements are significantly reduced in the proposed SBM analysis. To demonstrate the effectiveness of the proposed SBM formulation for wave propagation analysis in periodic structures, several benchmark examples are presented and discussed The proposed SBM results are compared with the analytical solutions, the reference results and the COMSOL software.

CP Symmetry, Lee-Yang zeros and Phase Transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2011-05-23

We analyze the analytic properties of {theta}-vacuum in QCD and its connection with spontaneous symmetry breaking of CP symmetry. A loss of analyticity in the {theta}-vacuum energy density can only be due to the accumulation of Lee-Yang zeros at some real values of {theta}. In the case of first order transitions these singularities are always associated to and cusp singularities and never to or cusps, which in the case {theta} = 0 are incompatible with the Vafa-Witten diamagnetic inequality This fact provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories like QCD.more » The argument is very similar to that used in the derivation of Bank-Casher formula for chiral symmetry breaking. However, the and behavior does not exclude the existence of a first phase transition at {theta} = {pi}, where a and cusp singularity is not forbidden by any inequality; in this case the topological charge condensate is proportional to the density of Lee-Yang zeros at {theta} = {pi}. Moreover, Lee-Yang zeros could give rise to a second order phase transition at {theta} = 0, which might be very relevant for the interpretation of the anomalous behavior of the topological susceptibility in the CP{sup 1} sigma model.« less

Aircraft Range Optimization Using Singular Perturbations

NASA Technical Reports Server (NTRS)

Oconnor, Joseph Taffe

1973-01-01

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Characteristic classes of gauge systems

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2004-12-01

We define and study invariants which can be uniformly constructed for any gauge system. By a gauge system we understand an (anti-)Poisson supermanifold provided with an odd Hamiltonian self-commuting vector field called a homological vector field. This definition encompasses all the cases usually included into the notion of a gauge theory in physics as well as some other similar (but different) structures like Lie or Courant algebroids. For Lagrangian gauge theories or Hamiltonian first class constrained systems, the homological vector field is identified with the classical BRST transformation operator. We define characteristic classes of a gauge system as universal cohomology classes of the homological vector field, which are uniformly constructed in terms of this vector field itself. Not striving to exhaustively classify all the characteristic classes in this work, we compute those invariants which are built up in terms of the first derivatives of the homological vector field. We also consider the cohomological operations in the space of all the characteristic classes. In particular, we show that the (anti-)Poisson bracket becomes trivial when applied to the space of all the characteristic classes, instead the latter space can be endowed with another Lie bracket operation. Making use of this Lie bracket one can generate new characteristic classes involving higher derivatives of the homological vector field. The simplest characteristic classes are illustrated by the examples relating them to anomalies in the traditional BV or BFV-BRST theory and to characteristic classes of (singular) foliations.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

[Surface electromyography signal classification using gray system theory].

PubMed

Xie, Hongbo; Ma, Congbin; Wang, Zhizhong; Huang, Hai

2004-12-01

A new method based on gray correlation was introduced to improve the identification rate in artificial limb. The electromyography (EMG) signal was first transformed into time-frequency domain by wavelet transform. Singular value decomposition (SVD) was then used to extract feature vector from the wavelet coefficient for pattern recognition. The decision was made according to the maximum gray correlation coefficient. Compared with neural network recognition, this robust method has an almost equivalent recognition rate but much lower computation costs and less training samples.

Development and Applications of the FV3 GEOS-5 Adjoint Modeling System

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kim, Jong G.; Lin, Shian-Jiann; Errico, Ron; Gelaro, Ron; Kent, James; Coy, Larry; Doyle, Jim; Goldstein, Alex

2017-01-01

GMAO has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR. In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

A two-stage linear discriminant analysis via QR-decomposition.

PubMed

Ye, Jieping; Li, Qi

2005-06-01

Linear Discriminant Analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the so-called singularity problems; that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the singularity problems. Among these extensions, PCA+LDA, a two-stage method, received relatively more attention. In PCA+LDA, the LDA stage is preceded by an intermediate dimension reduction stage using Principal Component Analysis (PCA). Most previous LDA extensions are computationally expensive, and not scalable, due to the use of Singular Value Decomposition or Generalized Singular Value Decomposition. In this paper, we propose a two-stage LDA method, namely LDA/QR, which aims to overcome the singularity problems of classical LDA, while achieving efficiency and scalability simultaneously. The key difference between LDA/QR and PCA+LDA lies in the first stage, where LDA/QR applies QR decomposition to a small matrix involving the class centroids, while PCA+LDA applies PCA to the total scatter matrix involving all training data points. We further justify the proposed algorithm by showing the relationship among LDA/QR and previous LDA methods. Extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm.

Exotic singularities and spatially curved loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Parampreet; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5; Vidotto, Francesca

2011-03-15

We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k={+-}1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the nontrivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities, are ignored by quantum gravity when spatial curvature is negative, as was previouslymore » found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with nonzero spatial curvature.« less

Redundant single gimbal control moment gyroscope singularity analysis

NASA Technical Reports Server (NTRS)

Bedrossian, Nazareth S.; Paradiso, Joseph; Bergmann, Edward V.; Rowell, Derek

1990-01-01

The robotic manipulator is proposed as the mechanical analog to single gimbal control moment gyroscope systems, and it is shown that both systems share similar difficulties with singular configurations. This analogy is used to group gimbal angles corresponding to any momentum state into different families. The singularity problem associated with these systems is examined in detail. In particular, a method is presented to test for the possibility of nontorque-producing gimbal motion at a singular configuration, as well as to determine the admissible motions in the case when this is possible. Sufficient conditions are derived for instances where the singular system can be reconfigured into a nonsingular state by these nontorque-producing motions.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

New trend in electron holography

NASA Astrophysics Data System (ADS)

Tanigaki, Toshiaki; Harada, Ken; Murakami, Yasukazu; Niitsu, Kodai; Akashi, Tetsuya; Takahashi, Yoshio; Sugawara, Akira; Shindo, Daisuke

2016-06-01

Electron holography using a coherent electron wave is a promising technique for high-resolution visualization of electromagnetic fields in and around objects. The capability of electron holography has been enhanced by the development of new technologies and has thus become an even more powerful tool for exploring scientific frontiers. This review introduces these technologies including split-illumination electron holography and vector-field electron tomography. Split-illumination electron holography, which uses separated coherent waves, overcomes the limits imposed by the lateral coherence requirement for electron waves in electron holography. Areas that are difficult to observe using conventional electron holography are now observable. Exemplified applications include observing a singular magnetic domain wall in electrical steel sheets, local magnetizations at anti-phase boundaries, and electrostatic potentials in metal-oxide-semiconductor field-effect transistors. Vector-field electron tomography can be used to visualize magnetic vectors in three dimensions. Two components of the vectors are reconstructed using dual-axis tomography, and the remaining one is calculated using div B   =  0. A high-voltage electron microscope can be used to achieve precise magnetic reconstruction. For example, magnetic vortices have been visualized using a 1 MV holography electron microscope.

Joint Smoothed l₀-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar.

PubMed

Liu, Jing; Zhou, Weidong; Juwono, Filbert H

2017-05-08

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed l 0 -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed l 0 -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the l 1 -norm minimization based methods, such as l 1 -SVD (singular value decomposition), RV (real-valued) l 1 -SVD and RV l 1 -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.

All That Glisters Is Not Gold: Sampling-Process Uncertainty in Disease-Vector Surveys with False-Negative and False-Positive Detections

PubMed Central

Abad-Franch, Fernando; Valença-Barbosa, Carolina; Sarquis, Otília; Lima, Marli M.

2014-01-01

Background Vector-borne diseases are major public health concerns worldwide. For many of them, vector control is still key to primary prevention, with control actions planned and evaluated using vector occurrence records. Yet vectors can be difficult to detect, and vector occurrence indices will be biased whenever spurious detection/non-detection records arise during surveys. Here, we investigate the process of Chagas disease vector detection, assessing the performance of the surveillance method used in most control programs – active triatomine-bug searches by trained health agents. Methodology/Principal Findings Control agents conducted triplicate vector searches in 414 man-made ecotopes of two rural localities. Ecotope-specific ‘detection histories’ (vectors or their traces detected or not in each individual search) were analyzed using ordinary methods that disregard detection failures and multiple detection-state site-occupancy models that accommodate false-negative and false-positive detections. Mean (±SE) vector-search sensitivity was ∼0.283±0.057. Vector-detection odds increased as bug colonies grew denser, and were lower in houses than in most peridomestic structures, particularly woodpiles. False-positive detections (non-vector fecal streaks misidentified as signs of vector presence) occurred with probability ∼0.011±0.008. The model-averaged estimate of infestation (44.5±6.4%) was ∼2.4–3.9 times higher than naïve indices computed assuming perfect detection after single vector searches (11.4–18.8%); about 106–137 infestation foci went undetected during such standard searches. Conclusions/Significance We illustrate a relatively straightforward approach to addressing vector detection uncertainty under realistic field survey conditions. Standard vector searches had low sensitivity except in certain singular circumstances. Our findings suggest that many infestation foci may go undetected during routine surveys, especially when vector density is low. Undetected foci can cause control failures and induce bias in entomological indices; this may confound disease risk assessment and mislead program managers into flawed decision making. By helping correct bias in naïve indices, the approach we illustrate has potential to critically strengthen vector-borne disease control-surveillance systems. PMID:25233352

New classification methods on singularity of mechanism

NASA Astrophysics Data System (ADS)

Luo, Jianguo; Han, Jianyou

2010-07-01

Based on the analysis of base and methods of singularity of mechanism, four methods obtained according to the factors of moving states of mechanism and cause of singularity and property of linear complex of singularity and methods in studying singularity, these bases and methods can't reflect the direct property and systematic property and controllable property of the structure of mechanism in macro, thus can't play an excellent role in guiding to evade the configuration before the appearance of singularity. In view of the shortcomings of forementioned four bases and methods, six new methods combined with the structure and exterior phenomena and motion control of mechanism directly and closely, classfication carried out based on the factors of moving base and joint component and executor and branch and acutating source and input parameters, these factors display the systemic property in macro, excellent guiding performance can be expected in singularity evasion and machine design and machine control based on these new bases and methods.

Steering Law Design for Redundant Single Gimbal Control Moment Gyro Systems. M.S. Thesis - Massachusetts Inst. of Technology.

NASA Technical Reports Server (NTRS)

Bedrossian, Nazareth Sarkis

1987-01-01

The correspondence between robotic manipulators and single gimbal Control Moment Gyro (CMG) systems was exploited to aid in the understanding and design of single gimbal CMG Steering laws. A test for null motion near a singular CMG configuration was derived which is able to distinguish between escapable and unescapable singular states. Detailed analysis of the Jacobian matrix null-space was performed and results were used to develop and test a variety of single gimbal CMG steering laws. Computer simulations showed that all existing singularity avoidance methods are unable to avoid Elliptic internal singularities. A new null motion algorithm using the Moore-Penrose pseudoinverse, however, was shown by simulation to avoid Elliptic type singularities under certain conditions. The SR-inverse, with appropriate null motion was proposed as a general approach to singularity avoidance, because of its ability to avoid singularities through limited introduction of torque error. Simulation results confirmed the superior performance of this method compared to the other available and proposed pseudoinverse-based Steering laws.

Higher Order Bases in a 2D Hybrid BEM/FEM Formulation

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.

2002-01-01

The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions.

svdPPCS: an effective singular value decomposition-based method for conserved and divergent co-expression gene module identification.

PubMed

Zhang, Wensheng; Edwards, Andrea; Fan, Wei; Zhu, Dongxiao; Zhang, Kun

2010-06-22

Comparative analysis of gene expression profiling of multiple biological categories, such as different species of organisms or different kinds of tissue, promises to enhance the fundamental understanding of the universality as well as the specialization of mechanisms and related biological themes. Grouping genes with a similar expression pattern or exhibiting co-expression together is a starting point in understanding and analyzing gene expression data. In recent literature, gene module level analysis is advocated in order to understand biological network design and system behaviors in disease and life processes; however, practical difficulties often lie in the implementation of existing methods. Using the singular value decomposition (SVD) technique, we developed a new computational tool, named svdPPCS (SVD-based Pattern Pairing and Chart Splitting), to identify conserved and divergent co-expression modules of two sets of microarray experiments. In the proposed methods, gene modules are identified by splitting the two-way chart coordinated with a pair of left singular vectors factorized from the gene expression matrices of the two biological categories. Importantly, the cutoffs are determined by a data-driven algorithm using the well-defined statistic, SVD-p. The implementation was illustrated on two time series microarray data sets generated from the samples of accessory gland (ACG) and malpighian tubule (MT) tissues of the line W118 of M. drosophila. Two conserved modules and six divergent modules, each of which has a unique characteristic profile across tissue kinds and aging processes, were identified. The number of genes contained in these models ranged from five to a few hundred. Three to over a hundred GO terms were over-represented in individual modules with FDR < 0.1. One divergent module suggested the tissue-specific relationship between the expressions of mitochondrion-related genes and the aging process. This finding, together with others, may be of biological significance. The validity of the proposed SVD-based method was further verified by a simulation study, as well as the comparisons with regression analysis and cubic spline regression analysis plus PAM based clustering. svdPPCS is a novel computational tool for the comparative analysis of transcriptional profiling. It especially fits the comparison of time series data of related organisms or different tissues of the same organism under equivalent or similar experimental conditions. The general scheme can be directly extended to the comparisons of multiple data sets. It also can be applied to the integration of data sets from different platforms and of different sources.

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1990-01-01

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1989-01-01

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

Sensitivity analysis of automatic flight control systems using singular value concepts

NASA Technical Reports Server (NTRS)

Herrera-Vaillard, A.; Paduano, J.; Downing, D.

1985-01-01

A sensitivity analysis is presented that can be used to judge the impact of vehicle dynamic model variations on the relative stability of multivariable continuous closed-loop control systems. The sensitivity analysis uses and extends the singular-value concept by developing expressions for the gradients of the singular value with respect to variations in the vehicle dynamic model and the controller design. Combined with a priori estimates of the accuracy of the model, the gradients are used to identify the elements in the vehicle dynamic model and controller that could severely impact the system's relative stability. The technique is demonstrated for a yaw/roll damper stability augmentation designed for a business jet.

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

1992-01-01

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Continuations of the nonlinear Schrödinger equation beyond the singularity

NASA Astrophysics Data System (ADS)

Fibich, G.; Klein, M.

2011-07-01

We present four continuations of the critical nonlinear Schrödinger equation (NLS) beyond the singularity: (1) a sub-threshold power continuation, (2) a shrinking-hole continuation for ring-type solutions, (3) a vanishing nonlinear-damping continuation and (4) a complex Ginzburg-Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. These calculations show that for generic initial data that lead to a loglog collapse, the sub-threshold power limit is a Bourgain-Wang solution, both before and after the singularity, and the vanishing nonlinear-damping and CGL limits are a loglog solution before the singularity, and have an infinite-velocity expanding core after the singularity. Our results suggest that all NLS continuations share the universal feature that after the singularity time Tc, the phase of the singular core is only determined up to multiplication by eiθ. As a result, interactions between post-collapse beams (filaments) become chaotic. We also show that when the continuation model leads to a point singularity and preserves the NLS invariance under the transformation t → -t and ψ → ψ*, the singular core of the weak solution is symmetric with respect to Tc. Therefore, the sub-threshold power and the shrinking-hole continuations are symmetric with respect to Tc, but continuations which are based on perturbations of the NLS equation are generically asymmetric.

Deep Restricted Kernel Machines Using Conjugate Feature Duality.

PubMed

Suykens, Johan A K

2017-08-01

The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel machines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are characterized by visible and hidden units in a bipartite graph without hidden-to-hidden connections and deep learning extensions as deep belief networks and deep Boltzmann machines. From the viewpoint of kernel machines, it includes least squares support vector machines for classification and regression, kernel principal component analysis (PCA), matrix singular value decomposition, and Parzen-type models. A key element is to first characterize these kernel machines in terms of so-called conjugate feature duality, yielding a representation with visible and hidden units. It is shown how this is related to the energy form in restricted Boltzmann machines, with continuous variables in a nonprobabilistic setting. In this new framework of so-called restricted kernel machine (RKM) representations, the dual variables correspond to hidden features. Deep RKM are obtained by coupling the RKMs. The method is illustrated for deep RKM, consisting of three levels with a least squares support vector machine regression level and two kernel PCA levels. In its primal form also deep feedforward neural networks can be trained within this framework.

Second-order QCD effects in Higgs boson production through vector boson fusion

NASA Astrophysics Data System (ADS)

Cruz-Martinez, J.; Gehrmann, T.; Glover, E. W. N.; Huss, A.

2018-06-01

We compute the factorising second-order QCD corrections to the electroweak production of a Higgs boson through vector boson fusion. Our calculation is fully differential in the kinematics of the Higgs boson and of the final state jets, and uses the antenna subtraction method to handle infrared singular configurations in the different parton-level contributions. Our results allow us to reassess the impact of the next-to-leading order (NLO) QCD corrections to electroweak Higgs-plus-three-jet production and of the next-to-next-to-leading order (NNLO) QCD corrections to electroweak Higgs-plus-two-jet production. The NNLO corrections are found to be limited in magnitude to around ± 5% and are uniform in several of the kinematical variables, displaying a kinematical dependence only in the transverse momenta and rapidity separation of the two tagging jets.

Fixed points, stable manifolds, weather regimes, and their predictability

DOE PAGES

Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael

2009-10-27

In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemblemore » forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.« less

Spinor Geometry and Signal Transmission in Three-Space

NASA Astrophysics Data System (ADS)

Binz, Ernst; Pods, Sonja; Schempp, Walter

2002-09-01

For a singularity free gradient field in an open set of an oriented Euclidean space of dimension three we define a natural principal bundle out of an immanent complex line bundle. The elements of both bundles are called internal variables. Several other natural bundles are associated with the principal bundle and, in turn, determine the vector field. Two examples are given and it is shown that for a constant vector field circular polarized waves travelling along a field line can be considered as waves of internal variables. Einstein's equation epsilon = m [middle dot] c2 is derived from the geometry of the principal bundle. On SU(2) a relation between spin representations and Schrodinger representations is established. The link between the spin 1/2-model and the Schrodinger representations yields a connection between a microscopic and a macroscopic viewpoint.

Fixed points, stable manifolds, weather regimes, and their predictability.

PubMed

Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael

2009-12-01

In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes." To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, "bred vectors" and singular vectors. These results are then verified in the framework of ensemble forecasts issued from "clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.

Singularity and Nonnormality in the Classification of Compositional Data

USGS Publications Warehouse

Bohling, Geoffrey C.; Davis, J.C.; Olea, R.A.; Harff, Jan

1998-01-01

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore-Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

Integrable mappings and the notion of anticonfinement

NASA Astrophysics Data System (ADS)

Mase, T.; Willox, R.; Ramani, A.; Grammaticos, B.

2018-06-01

We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward iterations of a mapping, with only a finite number of iterates taking regular values in between. We show through several concrete examples that the behaviour of some anticonfined singularities is strongly related to the integrability properties of the discrete mappings in which they arise, and we explain how to use this information to decide on the integrability or non-integrability of the mapping.

On the initial singularity problem in rainbow cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Santos, Grasiele; Gubitosi, Giulia; Amelino-Camelia, Giovanni, E-mail: grasiele.dossantos@icranet.org, E-mail: g.gubitosi@imperial.ac.uk, E-mail: giovanni.amelino-camelia@roma1.infn.it

2015-08-01

It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ('rainbow') spacetime metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbowmore » metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.« less

Soliton structure versus singularity analysis: Third-order completely intergrable nonlinear differential equations in 1 + 1-dimensions

NASA Astrophysics Data System (ADS)

Fuchssteiner, Benno; Carillo, Sandra

1989-01-01

Bäcklund transformations between all known completely integrable third-order differential equations in (1 + 1)-dimensions are established and the corresponding transformations formulas for their hereditary operators and Hamiltonian formulations are exhibited. Some of these Bäcklund transformations are not injective; therefore additional non-commutative symmetry groups are found for some equations. These non-commutative symmetry groups are classified as having a semisimple part isomorphic to the affine algebra A(1)1. New completely integrable third-order integro-differential equations, some depending explicitly on x, are given. These new equations give rise to nonin equation. Connections between the singularity equations (from the Painlevé analysis) and the nonlinear equations for interacting solitons are established. A common approach to singularity analysis and soliton structure is introduced. The Painlevé analysis is modified in such a sense that it carries over directly and without difficulty to the time evolution of singularity manifolds of equations like the sine-Gordon and nonlinear Schrödinger equation. A method to recover the Painlevé series from its constant level term is exhibit. The soliton-singularity transform is recognized to be connected to the Möbius group. This gives rise to a Darboux-like result for the spectral properties of the recursion operator. These connections are used in order to explain why poles of soliton equations move like trajectories of interacting solitons. Furthermore it is explicitly computed how solitons of singularity equations behave under the effect of this soliton-singularity transform. This then leads to the result that only for scaling degrees α = -1 and α = -2 the usual Painlevé analysis can be carried out. A new invariance principle, connected to kernels of differential operators is discovered. This new invariance, for example, connects the explicit solutions of the Liouville equation with the Miura transform. Simple methods are exhibited which allow to compute out of N-soliton solutions of the KdV (Bargman potentials) explicit solutions of equations like the Harry Dym equation. Certain solutions are plotted.

Singularity-free interpretation of the thermodynamics of supercooled water

NASA Astrophysics Data System (ADS)

Sastry, Srikanth; Debenedetti, Pablo G.; Sciortino, Francesco; Stanley, H. E.

1996-06-01

The pronounced increases in isothermal compressibility, isobaric heat capacity, and in the magnitude of the thermal expansion coefficient of liquid water upon supercooling have been interpreted either in terms of a continuous, retracing spinodal curve bounding the superheated, stretched, and supercooled states of liquid water, or in terms of a metastable, low-temperature critical point. Common to these two scenarios is the existence of singularities associated with diverging density fluctuations at low temperature. We show that the increase in compressibility upon lowering the temperature of a liquid that expands on cooling, like water, is not contingent on any singular behavior, but rather is a thermodynamic necessity. We perform a thermodynamic analysis for an anomalous liquid (i.e., one that expands when cooled) in the absence of a retracing spinodal and show that one may in general expect a locus of compressibility extrema in the anomalous regime. Our analysis suggests that the simplest interpretation of the behavior of supercooled water consistent with experimental observations is free of singularities. We then develop a waterlike lattice model that exhibits no singular behavior, while capturing qualitative aspects of the thermodynamics of water.

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

NASA Astrophysics Data System (ADS)

Biswas, Sounak; Damle, Kedar

2018-02-01

A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : <σz(R ⃗) σz(0 ) > ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

Energy flow of electric dipole radiation in between parallel mirrors

NASA Astrophysics Data System (ADS)

Xu, Zhangjin; Arnoldus, Henk F.

2017-11-01

We have studied the energy flow patterns of the radiation emitted by an electric dipole located in between parallel mirrors. It appears that the field lines of the Poynting vector (the flow lines of energy) can have very intricate structures, including many singularities and vortices. The flow line patterns depend on the distance between the mirrors, the distance of the dipole to one of the mirrors and the angle of oscillation of the dipole moment with respect to the normal of the mirror surfaces. Already for the simplest case of a dipole moment oscillating perpendicular to the mirrors, singularities appear at regular intervals along the direction of propagation (parallel to the mirrors). For a parallel dipole, vortices appear in the neighbourhood of the dipole. For a dipole oscillating under a finite angle with the surface normal, the radiating tends to swirl around the dipole before travelling off parallel to the mirrors. For relatively large mirror separations, vortices appear in the pattern. When the dipole is off-centred with respect to the midway point between the mirrors, the flow line structure becomes even more complicated, with numerous vortices in the pattern, and tiny loops near the dipole. We have also investigated the locations of the vortices and singularities, and these can be found without any specific knowledge about the flow lines. This provides an independent means of studying the propagation of dipole radiation between mirrors.

An approach toward the numerical evaluation of multi-loop Feynman diagrams

NASA Astrophysics Data System (ADS)

Passarino, Giampiero

2001-12-01

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model. As a first step an algorithm, proposed by F.V. Tkachov and based on the so-called generalized Bernstein functional relation, is applied to one-loop multi-leg diagrams with particular emphasis to the presence of infrared singularities, to the problem of tensorial reduction and to the classification of all singularities of a given diagram. Successively, the extension of the algorithm to two-loop diagrams is examined. The proposed solution consists in applying the functional relation to the one-loop sub-diagram which has the largest number of internal lines. In this way the integrand can be made smooth, a part from a factor which is a polynomial in xS, the vector of Feynman parameters needed for the complementary sub-diagram with the smallest number of internal lines. Since the procedure does not introduce new singularities one can distort the xS-integration hyper-contour into the complex hyper-plane, thus achieving numerical stability. The algorithm is then modified to deal with numerical evaluation around normal thresholds. Concise and practical formulas are assembled and presented, numerical results and comparisons with the available literature are shown and discussed for the so-called sunset topology.

Electromagnetic fields and potentials generated by massless charged particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azzurli, Francesco, E-mail: francesco.azzurli@gmail.com; Lechner, Kurt, E-mail: lechner@pd.infn.it; INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova

2014-10-15

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates amore » planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.« less

Visualization of x-ray computer tomography using computer-generated holography

NASA Astrophysics Data System (ADS)

Daibo, Masahiro; Tayama, Norio

1998-09-01

The theory converted from x-ray projection data to the hologram directly by combining the computer tomography (CT) with the computer generated hologram (CGH), is proposed. The purpose of this study is to offer the theory for realizing the all- electronic and high-speed seeing through 3D visualization system, which is for the application to medical diagnosis and non- destructive testing. First, the CT is expressed using the pseudo- inverse matrix which is obtained by the singular value decomposition. CGH is expressed in the matrix style. Next, `projection to hologram conversion' (PTHC) matrix is calculated by the multiplication of phase matrix of CGH with pseudo-inverse matrix of the CT. Finally, the projection vector is converted to the hologram vector directly, by multiplication of the PTHC matrix with the projection vector. Incorporating holographic analog computation into CT reconstruction, it becomes possible that the calculation amount is drastically reduced. We demonstrate the CT cross section which is reconstituted by He-Ne laser in the 3D space from the real x-ray projection data acquired by x-ray television equipment, using our direct conversion technique.

Quantum Linear System Algorithm for Dense Matrices

NASA Astrophysics Data System (ADS)

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-01

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that A x =b . We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O (κ2√{n }polylog(n )/ɛ ) for an n ×n dimensional A with bounded spectral norm, where κ denotes the condition number of A , and ɛ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A .

Role of a triangle singularity in the π N (1535 ) contribution to γ p →p π0η

NASA Astrophysics Data System (ADS)

Debastiani, V. R.; Sakai, S.; Oset, E.

2017-08-01

We have studied the γ p →p π0η reaction paying attention to the two main mechanisms at low energies, the γ p →Δ (1700 )→η Δ (1232 ) and the γ p →Δ (1700 )→π N (1535 ) . Both are driven by the photoexcitation of the Δ (1700 ) and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for this process and show that it agrees with the experimental determination. Yet there are some differences with the standard partial wave analysis which does not include explicitly the triangle singularity. The exercise also shows the convenience of exploring possible triangle singularities in other reactions and how a standard partial wave analysis can be extended to accommodate them.

Estimation and Control with Relative Measurements: Algorithms and Scaling Laws

DTIC Science & Technology

2007-09-01

eigenvector of L −1 corre- sponding to its largest eigenvalue. Since L−1 is a positive matrix, Perron - Frobenius theory tells us that |u1| := {|u11...the Frobenius norm of a matrix, and a linear vector space SV as the space of all bounded node-functions with respect to the above defined 144 norm...je‖2F where Eu is the set edges in E that are incident on u. It can be shown from the relationship between the Frobenius norm and the singular

Optical Signal Processing.

DTIC Science & Technology

1983-11-30

be large if s is highly negative, which is the Poynting vector, the same singularity function can be case for TeO2 operated in the slow-shear mode...we give the values of the elastic coefficients for PbMoO 4 and TeO2 from which we calculate that s = -0.176 for PbMoO 4 and s = 0.274 for TeO 2. Our...lowest for TeO2 and highest for PbMoO 4; the rate for fused quartz is nearly halfway between these two values. The diffraction patterns produced by

Segmented strings coupled to a B-field

NASA Astrophysics Data System (ADS)

Vegh, David

2018-04-01

In this paper we study segmented strings in AdS3 coupled to a background two-form whose field strength is proportional to the volume form. By changing the coupling, the theory interpolates between the Nambu-Goto string and the SL(2, ℝ) Wess-Zumino-Witten model. In terms of the kink momentum vectors, the action is independent of the coupling and the classical theory reduces to a single discrete-time Toda-type theory. The WZW model is a singular point in coupling space where the map into Toda variables degenerates.

Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2018-02-01

After surveying analyses of the 3D Euler equations using the Clebsch potentials scattered over the literature, we report some preliminary new results. 1. Assuming that flow fields are free from nulls of the impulse and the vorticity fields, we study how constraints imposed by the Clebsch potentials lead to a degenerate geometrical structure, typically in the form of depletion of nonlinearity. We consider a vorticity surface spanned by \\boldsymbol ω and another material vector \\boldsymbol {W} such that \\boldsymbol γ=\\boldsymbol ω× \\boldsymbol {W}, where \\boldsymbol γ is the impulse variable in geometric gauge. We identify dual mechanism for geometric depletion and show that at least of one them is acting if \\boldsymbol {W} does not develop a null. This suggests that formation of singularity in flows endowed with Clebsch potentials is less likely to happen than in more general flows. Some arguments are given towards exclusion of ‘type I’ blowup. A mathematical challenge remains to rule out singularity formation for flows which have Clebsch potentials everywhere. 2. We exploit classical differential geometry kinematically to write down the Gauss-Weingarten equations for the vorticity surface of the Clebsch potential in terms of fluid dynamical variables, as are the first, second and third fundamental forms. In particular, we derive a constraint on the size of the Gaussian curvature near the point of a possible singularity. On the other hand, an application of the Gauss-Bonnet theorem reveals that the tangential curvature of the surface becomes large in the neighborhood of near-singularity. 3. Using spatially-periodic flows with highly-symmetry, i.e. initial conditions of the Taylor-Green vortex and the Kida-Pelz flow, we present explicit formulas of the Clebsch potentials with exceptional singular surfaces where the Clebsch potentials are undefined. This is done by connecting the known expressions with the solenoidal impulse variable (i.e. the incompressible velocity) using suitable canonical transforms. By a simple argument we show that they keep forming material separatrices under the time evolution of the 3D Euler equations. We argue on this basis that a singularity, if developed, will be associated with these exceptional material surfaces. The difficulty of having Clebsch potentials globally on all of space have been with us for a long time. The proposal rather seeks to turn the difficulty into an advantage by using their absence to identify and locate possible singularities.

Evolution of coherence singularities of Schell-model beams.

PubMed

Rodrigo, José A; Alieva, Tatiana

2015-08-01

We show that the propagation of the widely used Schell-model partially coherent light can be easily understood using the ambiguity function. This approach is especially beneficial for the analysis of the mutual intensity of Schell-model beams (SMBs), which are associated with stable coherent beams such as Laguerre-, Hermite-, and Ince-Gaussian. We study the evolution of the coherence singularities during the SMB propagation. It is demonstrated that the distance of singularity formation depends on the coherence degree of the input beam. Moreover, it is proved that the shape, position, and number of singularity curves in far field are defined by the associated coherent beam.

Analysis on singular spaces: Lie manifolds and operator algebras

NASA Astrophysics Data System (ADS)

Nistor, Victor

2016-07-01

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called ;Lie manifolds; -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaufmann, Ralph M., E-mail: rkaufman@math.purdue.edu; Khlebnikov, Sergei, E-mail: skhleb@physics.purdue.edu; Wehefritz-Kaufmann, Birgit, E-mail: ebkaufma@math.purdue.edu

2012-11-15

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians,more » such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties. - Highlights: Black-Right-Pointing-Pointer New method for analytically finding Dirac points. Black-Right-Pointing-Pointer Novel relation of level crossings to singularity theory. Black-Right-Pointing-Pointer More precise version of the von-Neumann-Wigner theorem for arbitrary smooth families of Hamiltonians of fixed size. Black-Right-Pointing-Pointer Analytical proof of the existence of Dirac points for the Gyroid wire network.« less

Applications of singular value analysis and partial-step algorithm for nonlinear orbit determination

NASA Technical Reports Server (NTRS)

Ryne, Mark S.; Wang, Tseng-Chan

1991-01-01

An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.

Indirect detection constraints on s- and t-channel simplified models of dark matter

NASA Astrophysics Data System (ADS)

Carpenter, Linda M.; Colburn, Russell; Goodman, Jessica; Linden, Tim

2016-09-01

Recent Fermi-LAT observations of dwarf spheroidal galaxies in the Milky Way have placed strong limits on the gamma-ray flux from dark matter annihilation. In order to produce the strongest limit on the dark matter annihilation cross section, the observations of each dwarf galaxy have typically been "stacked" in a joint-likelihood analysis, utilizing optical observations to constrain the dark matter density profile in each dwarf. These limits have typically been computed only for singular annihilation final states, such as b b ¯ or τ+τ- . In this paper, we generalize this approach by producing an independent joint-likelihood analysis to set constraints on models where the dark matter particle annihilates to multiple final-state fermions. We interpret these results in the context of the most popular simplified models, including those with s- and t-channel dark matter annihilation through scalar and vector mediators. We present our results as constraints on the minimum dark matter mass and the mediator sector parameters. Additionally, we compare our simplified model results to those of effective field theory contact interactions in the high-mass limit.

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Analysis of regional crustal magnetization in Vector Cartesian Harmonics

NASA Astrophysics Data System (ADS)

Gubbins, D.; Ivers, D. J.; Williams, S.

2017-12-01

We introduce a set of basis functions for analysing magnetization in a plane layer, called Vector Cartesian Harmonics, that separate the part of the magnetization responsible for generating the external potential field from the part that generates no observable field. They are counterparts of similar functions defined on a sphere, Vector Spherical Harmonics, which we introduced earlier for magnetization in a spherical shell. We expand four example magnetizations in these functions and determine which parts are responsible for the observed magnetic field above the layer. For a point dipole, the component of magnetization responsible for the external potential field is the sum of a point dipole of half strength and a distributed magnetization that gives the same field. The dipping prism has no magnetic field if magnetized along strike; otherwise it, like the point dipole, has the correct dipping structure but of half the correct intensity accompanied by a distributed magnetization producing the same magnetic field. Interestingly, the distributed magnetization has singularities at the edges of the dipping slab. The buried cube is done numerically and again only a fraction of the true magnetization appears along with distributed magnetizations, strongest at the edges of the cube, making up the rest of the field. The Bishop model, a model of magnetization often used to test analysis methods, behaves similarly. In cases where the magnetization is induced by a known, non-horizontal field it is always possible to recover the vertically averaged susceptibility except for its horizontal average. Simple damped inversion of magnetic data will return only the harmonics responsible for the external field, so the analysis gives a clear indication of how any combination of induced and remanent magnetization would be returned. In practice, most interpretations of magnetic surveys are done in combination with other geological data and insights. We propose using this prior information to construct a quantitative magnetization that can be expanded in Vector Cartesian Harmonics to determine the part that generates the observed magnetic anomalies; this part can be refined to fit the data while the remaining part can only be improved using different information. The separation is simple and fast to implement using standard software because it involves only elementary manipulations of 2-dimensional Fourier transforms.

Modern CACSD using the Robust-Control Toolbox

NASA Technical Reports Server (NTRS)

Chiang, Richard Y.; Safonov, Michael G.

1989-01-01

The Robust-Control Toolbox is a collection of 40 M-files which extend the capability of PC/PRO-MATLAB to do modern multivariable robust control system design. Included are robust analysis tools like singular values and structured singular values, robust synthesis tools like continuous/discrete H(exp 2)/H infinity synthesis and Linear Quadratic Gaussian Loop Transfer Recovery methods and a variety of robust model reduction tools such as Hankel approximation, balanced truncation and balanced stochastic truncation, etc. The capabilities of the toolbox are described and illustated with examples to show how easily they can be used in practice. Examples include structured singular value analysis, H infinity loop-shaping and large space structure model reduction.

Development of a sensitivity analysis technique for multiloop flight control systems

NASA Technical Reports Server (NTRS)

Vaillard, A. H.; Paduano, J.; Downing, D. R.

1985-01-01

This report presents the development and application of a sensitivity analysis technique for multiloop flight control systems. This analysis yields very useful information on the sensitivity of the relative-stability criteria of the control system, with variations or uncertainties in the system and controller elements. The sensitivity analysis technique developed is based on the computation of the singular values and singular-value gradients of a feedback-control system. The method is applicable to single-input/single-output as well as multiloop continuous-control systems. Application to sampled-data systems is also explored. The sensitivity analysis technique was applied to a continuous yaw/roll damper stability augmentation system of a typical business jet, and the results show that the analysis is very useful in determining the system elements which have the largest effect on the relative stability of the closed-loop system. As a secondary product of the research reported here, the relative stability criteria based on the concept of singular values were explored.

Predictability Experiments With the Navy Operational Global Atmospheric Prediction System

NASA Astrophysics Data System (ADS)

Reynolds, C. A.; Gelaro, R.; Rosmond, T. E.

2003-12-01

There are several areas of research in numerical weather prediction and atmospheric predictability, such as targeted observations and ensemble perturbation generation, where it is desirable to combine information about the uncertainty of the initial state with information about potential rapid perturbation growth. Singular vectors (SVs) provide a framework to accomplish this task in a mathematically rigorous and computationally feasible manner. In this study, SVs are calculated using the tangent and adjoint models of the Navy Operational Global Atmospheric Prediction System (NOGAPS). The analysis error variance information produced by the NRL Atmospheric Variational Data Assimilation System is used as the initial-time SV norm. These VAR SVs are compared to SVs for which total energy is both the initial and final time norms (TE SVs). The incorporation of analysis error variance information has a significant impact on the structure and location of the SVs. This in turn has a significant impact on targeted observing applications. The utility and implications of such experiments in assessing the analysis error variance estimates will be explored. Computing support has been provided by the Department of Defense High Performance Computing Center at the Naval Oceanographic Office Major Shared Resource Center at Stennis, Mississippi.

Hard sphere perturbation theory of dense fluids with singular perturbation

NASA Astrophysics Data System (ADS)

Mon, K. K.

2000-02-01

Hard sphere perturbation theories (HSPT) played a significant role in the fundamental understanding of fluids and continues to be a popular method in a wide range of applications. The possibility of difficulty with singular perturbation for some classical soft core model fluids appears to have been overlooked or ignored in the literature. We address this issue in this short note and show by analysis that a region of phase space has been neglected in the standard application of HSPT involving singular perturbation.

Development of the triplet singularity for the analysis of wings and bodies in supersonic flow

NASA Technical Reports Server (NTRS)

Woodward, F. A.

1981-01-01

A supersonic triplet singularity was developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which gives directional properties to the perturbation flow field surrounding the panel. The theoretical development of the triplet singularity is described together with its application to the calculation of surface pressures on wings and bodies. Examples are presented comparing the results of the new method with other supersonic methods and with experimental data.

Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds.

PubMed

Herlin, Antoine; Jacquemet, Vincent

2012-05-01

Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.

A novel finite element analysis of three-dimensional circular crack

NASA Astrophysics Data System (ADS)

Ping, X. C.; Wang, C. G.; Cheng, L. P.

2018-06-01

A novel singular element containing a part of the circular crack front is established to solve the singular stress fields of circular cracks by using the numerical series eigensolutions of singular stress fields. The element is derived from the Hellinger-Reissner variational principle and can be directly incorporated into existing 3D brick elements. The singular stress fields are determined as the system unknowns appearing as displacement nodal values. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of circular cracks. The usage of the novel singular element can avoid mesh refinement near the crack front domain without loss of calculation accuracy and velocity of convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated structures with a large number of elements.

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Liu, Kuojuey Ray

1990-01-01

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Singular value decomposition: a diagnostic tool for ill-posed inverse problems in optical computed tomography

NASA Astrophysics Data System (ADS)

Lanen, Theo A.; Watt, David W.

1995-10-01

Singular value decomposition has served as a diagnostic tool in optical computed tomography by using its capability to provide insight into the condition of ill-posed inverse problems. Various tomographic geometries are compared to one another through the singular value spectrum of their weight matrices. The number of significant singular values in the singular value spectrum of a weight matrix is a quantitative measure of the condition of the system of linear equations defined by a tomographic geometery. The analysis involves variation of the following five parameters, characterizing a tomographic geometry: 1) the spatial resolution of the reconstruction domain, 2) the number of views, 3) the number of projection rays per view, 4) the total observation angle spanned by the views, and 5) the selected basis function. Five local basis functions are considered: the square pulse, the triangle, the cubic B-spline, the Hanning window, and the Gaussian distribution. Also items like the presence of noise in the views, the coding accuracy of the weight matrix, as well as the accuracy of the accuracy of the singular value decomposition procedure itself are assessed.

Kinematically Optimal Robust Control of Redundant Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2017-12-01

This work deals with the problem of the robust optimal task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the endeffector. Furthermore, the movement is to be accomplished in such a way as to minimize both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of chattering-free robust kinematically optimal controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Robust Task Space Trajectory Tracking Control of Robotic Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2016-08-01

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Class of regular bouncing cosmologies

NASA Astrophysics Data System (ADS)

Vasilić, Milovan

2017-06-01

In this paper, I construct a class of everywhere regular geometric sigma models that possess bouncing solutions. Precisely, I show that every bouncing metric can be made a solution of such a model. My previous attempt to do so by employing one scalar field has failed due to the appearance of harmful singularities near the bounce. In this work, I use four scalar fields to construct a class of geometric sigma models which are free of singularities. The models within the class are parametrized by their background geometries. I prove that, whatever background is chosen, the dynamics of its small perturbations is classically stable on the whole time axis. Contrary to what one expects from the structure of the initial Lagrangian, the physics of background fluctuations is found to carry two tensor, two vector, and two scalar degrees of freedom. The graviton mass, which naturally appears in these models, is shown to be several orders of magnitude smaller than its experimental bound. I provide three simple examples to demonstrate how this is done in practice. In particular, I show that graviton mass can be made arbitrarily small.

Analysis of a New Variational Model to Restore Point-Like and Curve-Like Singularities in Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aubert, Gilles, E-mail: gaubert@unice.fr; Blanc-Feraud, Laure, E-mail: Laure.Blanc-Feraud@inria.fr; Graziani, Daniele, E-mail: Daniele.Graziani@inria.fr

2013-02-15

The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme.

Application of a sensitivity analysis technique to high-order digital flight control systems

NASA Technical Reports Server (NTRS)

Paduano, James D.; Downing, David R.

1987-01-01

A sensitivity analysis technique for multiloop flight control systems is studied. This technique uses the scaled singular values of the return difference matrix as a measure of the relative stability of a control system. It then uses the gradients of these singular values with respect to system and controller parameters to judge sensitivity. The sensitivity analysis technique is first reviewed; then it is extended to include digital systems, through the derivation of singular-value gradient equations. Gradients with respect to parameters which do not appear explicitly as control-system matrix elements are also derived, so that high-order systems can be studied. A complete review of the integrated technique is given by way of a simple example: the inverted pendulum problem. The technique is then demonstrated on the X-29 control laws. Results show linear models of real systems can be analyzed by this sensitivity technique, if it is applied with care. A computer program called SVA was written to accomplish the singular-value sensitivity analysis techniques. Thus computational methods and considerations form an integral part of many of the discussions. A user's guide to the program is included. The SVA is a fully public domain program, running on the NASA/Dryden Elxsi computer.

The Tangent Linear and Adjoint of the FV3 Dynamical Core: Development and Applications

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2018-01-01

GMAO (NASA's Global Modeling and Assimilation Office) has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR (4-Dimensional Variational Assimilation). In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Quantum Gravity and Cosmology: an intimate interplay

NASA Astrophysics Data System (ADS)

Sakellariadou, Mairi

2017-08-01

I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Fuel optimal maneuvers of spacecraft about a circular orbit

NASA Technical Reports Server (NTRS)

Carter, T. E.

1982-01-01

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Classical and quantum analysis of repulsive singularities in four-dimensional extended supergravity

NASA Astrophysics Data System (ADS)

Gaida, I.; Hollmann, H. R.; Stewart, J. M.

1999-07-01

Non-minimal repulsive singularities (`repulsons') in extended supergravity theories are investigated. The short-distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar test-particle. Using a partial wave expansion it is shown that the particle is totally reflected at the origin. A high-frequency incoming particle undergoes a phase shift of icons/Journals/Common/pi" ALT="pi" ALIGN="TOP"/>/2. However, the phase shift for a low-frequency particle depends upon the physical data of the repulson. The curvature singularity at a finite distance rh turns out to be transparent for the scalar test-particle and the coordinate singularity at the origin serves as the repulsive barrier to bounce back the particles.

The fields of a naked singularity and a black hole in mutual equilibrium

NASA Astrophysics Data System (ADS)

Paolino, Armando; Pizzi, Marco

2008-01-01

Recently Alekseev and Belinski have presented a new exact solution of the Einstein-Maxwell equation which describes two Reissner-Nordstrom (RN) sources in reciprocal equilibrium (no struts nor strings) one source is a naked singularity, the other is a black hole. In this paper we use the Alekseev-Belinki solution in the special case in which the charge of the black hole is zero-therefore we have a naked singularity near a neutral black hole. We give the plots of the electric force lines in both the cases in which the naked singularity has a mass comparable with the black hole and in which it is much smaller. The analysis of this latter case confirm the goodness of the Hanni-Ruffini approximation.

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

NASA Astrophysics Data System (ADS)

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

Extracting semantic representations from word co-occurrence statistics: stop-lists, stemming, and SVD.

PubMed

Bullinaria, John A; Levy, Joseph P

2012-09-01

In a previous article, we presented a systematic computational study of the extraction of semantic representations from the word-word co-occurrence statistics of large text corpora. The conclusion was that semantic vectors of pointwise mutual information values from very small co-occurrence windows, together with a cosine distance measure, consistently resulted in the best representations across a range of psychologically relevant semantic tasks. This article extends that study by investigating the use of three further factors--namely, the application of stop-lists, word stemming, and dimensionality reduction using singular value decomposition (SVD)--that have been used to provide improved performance elsewhere. It also introduces an additional semantic task and explores the advantages of using a much larger corpus. This leads to the discovery and analysis of improved SVD-based methods for generating semantic representations (that provide new state-of-the-art performance on a standard TOEFL task) and the identification and discussion of problems and misleading results that can arise without a full systematic study.

Precoded spatial multiplexing MIMO system with spatial component interleaver.

PubMed

Gao, Xiang; Wu, Zhanji

In this paper, the performance of precoded bit-interleaved coded modulation (BICM) spatial multiplexing multiple-input multiple-output (MIMO) system with spatial component interleaver is investigated. For the ideal precoded spatial multiplexing MIMO system with spatial component interleaver based on singular value decomposition (SVD) of the MIMO channel, the average pairwise error probability (PEP) of coded bits is derived. Based on the PEP analysis, the optimum spatial Q-component interleaver design criterion is provided to achieve the minimum error probability. For the limited feedback precoded proposed scheme with linear zero forcing (ZF) receiver, in order to minimize a bound on the average probability of a symbol vector error, a novel effective signal-to-noise ratio (SNR)-based precoding matrix selection criterion and a simplified criterion are proposed. Based on the average mutual information (AMI)-maximization criterion, the optimal constellation rotation angles are investigated. Simulation results indicate that the optimized spatial multiplexing MIMO system with spatial component interleaver can achieve significant performance advantages compared to the conventional spatial multiplexing MIMO system.

Analysis of protein circular dichroism spectra for secondary structure using a simple matrix multiplication.

PubMed

Compton, L A; Johnson, W C

1986-05-15

Inverse circular dichroism (CD) spectra are presented for each of the five major secondary structures of proteins: alpha-helix, antiparallel and parallel beta-sheet, beta-turn, and other (random) structures. The fraction of the each secondary structure in a protein is predicted by forming the dot product of the corresponding inverse CD spectrum, expressed as a vector, with the CD spectrum of the protein digitized in the same way. We show how this method is based on the construction of the generalized inverse from the singular value decomposition of a set of CD spectra corresponding to proteins whose secondary structures are known from X-ray crystallography. These inverse spectra compute secondary structure directly from protein CD spectra without resorting to least-squares fitting and standard matrix inversion techniques. In addition, spectra corresponding to the individual secondary structures, analogous to the CD spectra of synthetic polypeptides, are generated from the five most significant CD eigenvectors.

EDITORIAL: The plurality of optical singularities

NASA Astrophysics Data System (ADS)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the electric (or magnetic) polarization ellipse is purely circular (C lines) or purely linear (L lines). The patterns of ellipse-fields are different for purely paraxial and fully three-dimensional fields. White-light diffraction generates richly coloured vortices—the colours of dark light. The description of these chromatic effects, and also those associated with polarization singularities, leads to new applications of coherence theory. For non-monochromatic light, it is natural to seek singularities of the full electromagnetic field, rather than of the electric or magnetic field separately. Such electromagnetic singularities are the Riemann-Silberstein vortices; these are relativistically covariant nodal lines of a complex scalar field constructed from the electromagnetic field. Optical fields have dynamical aspects, particularly those associated with angular momentum. Although angular momentum is not inevitably associated with optical singularities, in practice the two phenomena can occur together. Orbital angular momentum is associated with the spatial structure of light, and in beams with optical vortices it can be used to rotate particles in the field. Spin angular momentum is associated with the polarization structure of the light. There are tricky questions associated with the angular momentum of light in a refracting medium, echoing the Abraham-Minkowski controversy about linear momentum. In optically nonlinear materials (leading to second-harmonic generation, for example), new classes of phenomena can occur, such as, for example, dynamical interaction between vortex lines, whose stability needs to be considered. At a more fundamental level, it is important to investigate quantum effects associated with optical singularities, and a start has been made. The dark centre of an optical vortex can be regarded as a window onto the vacuum fluctuations of quantum optics, with the quantum core emerging as a distinct entity when the classical light is intense. And for light in a rapidly and inhomogeneously flowing material, horizons can develop, analogous to those surrounding black holes in general relativity, and these new optical singularities can be regarded as wave catastrophes, and new associated quantum effects anticipated. Three decades after wave dislocations were introduced as ‘a new concept in ... wave theory’, these phase singularities have been extensively explored and are now familiar. New ideas—in addition to those described in this special issue—continue to emerge. For example, x-ray vortices were observed recently; there is a proposal to create lenses to form atomic beams containing vortices; and astrophysical applications have been suggested for both photon orbital angular momentum and optical vortices. We can safely assume that the science of wave singularities will develop further, and diffuse into new areas of physics.

A singular value decomposition approach for improved taxonomic classification of biological sequences

PubMed Central

2011-01-01

Background Singular value decomposition (SVD) is a powerful technique for information retrieval; it helps uncover relationships between elements that are not prima facie related. SVD was initially developed to reduce the time needed for information retrieval and analysis of very large data sets in the complex internet environment. Since information retrieval from large-scale genome and proteome data sets has a similar level of complexity, SVD-based methods could also facilitate data analysis in this research area. Results We found that SVD applied to amino acid sequences demonstrates relationships and provides a basis for producing clusters and cladograms, demonstrating evolutionary relatedness of species that correlates well with Linnaean taxonomy. The choice of a reasonable number of singular values is crucial for SVD-based studies. We found that fewer singular values are needed to produce biologically significant clusters when SVD is employed. Subsequently, we developed a method to determine the lowest number of singular values and fewest clusters needed to guarantee biological significance; this system was developed and validated by comparison with Linnaean taxonomic classification. Conclusions By using SVD, we can reduce uncertainty concerning the appropriate rank value necessary to perform accurate information retrieval analyses. In tests, clusters that we developed with SVD perfectly matched what was expected based on Linnaean taxonomy. PMID:22369633

The Zel'dovich approximation: key to understanding cosmic web complexity

NASA Astrophysics Data System (ADS)

Hidding, Johan; Shandarin, Sergei F.; van de Weygaert, Rien

2014-02-01

We describe how the dynamics of cosmic structure formation defines the intricate geometric structure of the spine of the cosmic web. The Zel'dovich approximation is used to model the backbone of the cosmic web in terms of its singularity structure. The description by Arnold et al. in terms of catastrophe theory forms the basis of our analysis. This two-dimensional analysis involves a profound assessment of the Lagrangian and Eulerian projections of the gravitationally evolving four-dimensional phase-space manifold. It involves the identification of the complete family of singularity classes, and the corresponding caustics that we see emerging as structure in Eulerian space evolves. In particular, as it is instrumental in outlining the spatial network of the cosmic web, we investigate the nature of spatial connections between these singularities. The major finding of our study is that all singularities are located on a set of lines in Lagrangian space. All dynamical processes related to the caustics are concentrated near these lines. We demonstrate and discuss extensively how all 2D singularities are to be found on these lines. When mapping this spatial pattern of lines to Eulerian space, we find a growing connectedness between initially disjoint lines, resulting in a percolating network. In other words, the lines form the blueprint for the global geometric evolution of the cosmic web.

Inferring mixed-culture growth from total biomass data in a wavelet approach

NASA Astrophysics Data System (ADS)

Ibarra-Junquera, V.; Escalante-Minakata, P.; Murguía, J. S.; Rosu, H. C.

2006-10-01

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Hölder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Hölder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Hölder exponent is no longer a useful parameter.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

NASA Astrophysics Data System (ADS)

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

2017-04-01

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

Stable computations with flat radial basis functions using vector-valued rational approximations

NASA Astrophysics Data System (ADS)

Wright, Grady B.; Fornberg, Bengt

2017-02-01

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Gravitational radiation from a cylindrical naked singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakao, Ken-ichi; Morisawa, Yoshiyuki

We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that allmore » the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and the final singularity will be a conical one. Weyl curvature is completely released from the collapsed dust.« less

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandel, Ilya

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holesmore » into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a 'radiation-reaction field'. (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves--sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.« less

A Linear Stochastic Dynamical Model of ENSO. Part II: Analysis.

NASA Astrophysics Data System (ADS)

Thompson, C. J.; Battisti, D. S.

2001-02-01

In this study the behavior of a linear, intermediate model of ENSO is examined under stochastic forcing. The model was developed in a companion paper (Part I) and is derived from the Zebiak-Cane ENSO model. Four variants of the model are used whose stabilities range from slightly damped to moderately damped. Each model is run as a simulation while being perturbed by noise that is uncorrelated (white) in space and time. The statistics of the model output show the moderately damped models to be more realistic than the slightly damped models. The moderately damped models have power spectra that are quantitatively quite similar to observations, and a seasonal pattern of variance that is qualitatively similar to observations. All models produce ENSOs that are phase locked to the annual cycle, and all display the `spring barrier' characteristic in their autocorrelation patterns, though in the models this `barrier' occurs during the summer and is less intense than in the observations (inclusion of nonlinear effects is shown to partially remedy this deficiency). The more realistic models also show a decadal variability in the lagged autocorrelation pattern that is qualitatively similar to observations.Analysis of the models shows that the greatest part of the variability comes from perturbations that project onto the first singular vector, which then grow rapidly into the ENSO mode. Essentially, the model output represents many instances of the ENSO mode, with random phase and amplitude, stimulated by the noise through the optimal transient growth of the singular vectors.The limit of predictability for each model is calculated and it is shown that the more realistic (moderately damped) models have worse potential predictability (9-15 months) than the deterministic chaotic models that have been studied widely in the literature. The predictability limits are strongly correlated with the stability of the models' ENSO mode-the more highly damped models having much shorter limits of predictability. A comparison of the two most realistic models shows that even though these models have similar statistics, they have very different predictability limits. The models have a strong seasonal dependence to their predictability limits.The results of this study (with the companion paper) suggest that the linear, stable dynamical model of ENSO is indeed a plausible hypothesis for the observed ENSO. With very reasonable levels of stochastic forcing, the model produces realistic levels of variance, has a realistic spectrum, and qualitatively reproduces the observed seasonal pattern of variance, the autocorrelation pattern, and the ENSO-like decadal variability.

Theory of bright-field scanning transmission electron microscopy for tomography

NASA Astrophysics Data System (ADS)

Levine, Zachary H.

2005-02-01

Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elastic scattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of 300-keV electrons through aluminum foils up to 25μm thick. For thin films, the theory gives a validity condition for Beer's law. For thick films, a variant of Molière's theory [V. G. Molière, Z. Naturforschg. 3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as [tln(e1-2γt/τ)]-1 where t is the path length of the beam, τ is the mean free path for elastic scattering, and γ is Euler's constant. The Goudsmit-Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elastic scattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elastic scattering cross sections minus a delta function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.

Recurrence quantity analysis based on singular value decomposition

NASA Astrophysics Data System (ADS)

Bian, Songhan; Shang, Pengjian

2017-05-01

Recurrence plot (RP) has turned into a powerful tool in many different sciences in the last three decades. To quantify the complexity and structure of RP, recurrence quantification analysis (RQA) has been developed based on the measures of recurrence density, diagonal lines, vertical lines and horizontal lines. This paper will study the RP based on singular value decomposition which is a new perspective of RP study. Principal singular value proportion (PSVP) will be proposed as one new RQA measure and bigger PSVP means higher complexity for one system. In contrast, smaller PSVP reflects a regular and stable system. Considering the advantage of this method in detecting the complexity and periodicity of systems, several simulation and real data experiments are chosen to examine the performance of this new RQA.

C-point and V-point singularity lattice formation and index sign conversion methods

NASA Astrophysics Data System (ADS)

Kumar Pal, Sushanta; Ruchi; Senthilkumaran, P.

2017-06-01

The generic singularities in an ellipse field are C-points namely stars, lemons and monstars in a polarization distribution with C-point indices (-1/2), (+1/2) and (+1/2) respectively. Similar to C-point singularities, there are V-point singularities that occur in a vector field and are characterized by Poincare-Hopf index of integer values. In this paper we show that the superposition of three homogenously polarized beams in different linear states leads to the formation of polarization singularity lattice. Three point sources at the focal plane of the lens are used to create three interfering plane waves. A radial/azimuthal polarization converter (S-wave plate) placed near the focal plane modulates the polarization states of the three beams. The interference pattern is found to host C-points and V-points in a hexagonal lattice. The C-points occur at intensity maxima and V-points occur at intensity minima. Modulating the state of polarization (SOP) of three plane waves from radial to azimuthal does not essentially change the nature of polarization singularity lattice as the Poincare-Hopf index for both radial and azimuthal polarization distributions is (+1). Hence a transformation from a star to a lemon is not trivial, as such a transformation requires not a single SOP change, but a change in whole spatial SOP distribution. Further there is no change in the lattice structure and the C- and V-points appear at locations where they were present earlier. Hence to convert an interlacing star and V-point lattice into an interlacing lemon and V-point lattice, the interferometer requires modification. We show for the first time a method to change the polarity of C-point and V-point indices. This means that lemons can be converted into stars and stars can be converted into lemons. Similarly the positive V-point can be converted to negative V-point and vice versa. The intensity distribution in all these lattices is invariant as the SOPs of the three beams are changed in an orderly fashion. It shows degeneracy as long as the SOPs of the three beams are drawn from polarization distributions that have Poincare-Hopf index of same magnitude. Various topological aspects of these lattices are presented with the help of Stokes field S12, which is constructed using generalized Stokes parameters of a fully polarized light. We envisage that such polarization lattice structure may lead to novel concept of structured polarization illumination methods in super resolution microscopy.

Noise Removal on Ocean Scalars by Means of Singularity-Based Fusion

NASA Astrophysics Data System (ADS)

Umbert, M.; Turiel, A.; Hoareau, N.; Ballabrera, J.; Martinez, J.; guimbard, S.; Font, J.

2013-12-01

Thanks to new remote sensing platforms as SMOS and Aquarius we have now access to synoptic maps of Sea Surface Salinity (SSS) at global scale. Both missions require a non-negligible amount of development in order to meet pre-launch requirements on the quality of the retrieved variables. Development efforts have been so far mainly concentrated in improving the accuracy of the acquired signals from the radiometric point of view, which is a point-wise characteristic, that is, the qualities of each point in the snapshot or swath are considered separately. However, some spatial redundancy (i.e., spatial correlation) is implicit in geophysical signals, and particularly in SSS. This redundancy is known since the beginning of the remote sensing age: eddies and fronts are visually evident in images of different variables, including Sea Surface Temperature (SST), Sea Surface Height (SSH), Ocean Color (OC), Synthetic Aperture Radars (SAR) and Brightness Temperatures (BT) at different bands. An assessment on the quality of SSS products accounting for this kind of spatial redundancy would be very interesting. So far, the structure of those correlations have been evidenced using correlation functions, but correlation functions vary from one variable to other; additionally, they are not characteristic to the points of the image but to a given large enough area. The introduction of singularity analysis for remote sensing maps of the ocean has shown that the correspondence among different scalars can be rigorously stated in terms of the correspondence of the values of their associated singularity exponents. The singularity exponents of a scalar at a given point is a unitless measure of the degree of regularity or irregularity of this function at that given point. Hence, singularity exponents can be directly compared disregarding the physical meaning of the variable from which they were derived. Using singularity analysis we can assess the quality of any scalar, as singularity exponents align in fronts following the streamlines of the flow, while noise breaks up the coherence of singularity fronts. The analysis of the output of numerical models show that up to the numerical accuracy singularity exponents of different scalars take the same values at every point. Taking the correspondence of the singularity exponents into account, it can be proved that two scalars having the same singularity exponents have a relation of functional dependence (a matricial identity involving their gradients). That functional relation can be approximated by a local linear regression under some hypothesis, which simplifies and speeds up the calculations and leads to a simple algorithm to reduce noise on a given ocean scalar using another higher- quality variable as template. This simple algorithm has been applied to SMOS data with a considerable quality gain. As a template, high-level SST maps from different sources have been used, while SMOS L2 and L3 SSS maps, and even brightness temperature maps play the role of the noisy data to be corrected. In all instances the noise level is divided by a factor of two at least. This quality gain opens the use of SMOS data for new applications, including the instant identification of ocean fronts, rain lenses, hurricane tracks, etc.

A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms

PubMed Central

Ponnapalli, Sri Priya; Saunders, Michael A.; Van Loan, Charles F.; Alter, Orly

2011-01-01

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices , each with full column rank. Each matrix is exactly factored as Di = UiΣiVT, where V, identical in all factorizations, is obtained from the eigensystem SV = VΛ of the arithmetic mean S of all pairwise quotients of the matrices , i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λk≥1. Equality holds if and only if the corresponding eigenvector vk is a right basis vector of equal significance in all matrices Di and Dj, that is σi,k/σj,k = 1 for all i and j, and the corresponding left basis vector ui,k is orthogonal to all other vectors in Ui for all i. The eigenvalues λk = 1, therefore, define the “common HO GSVD subspace.” We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified. PMID:22216090

Oscillatory singular integrals and harmonic analysis on nilpotent groups

PubMed Central

Ricci, F.; Stein, E. M.

1986-01-01

Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i) oscillatory factors that are exponentials of imaginary polynomials, (ii) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii) validity in the general context not requiring the existence of dilations that are automorphisms. PMID:16593640

Automatic classification of singular elements for the electrostatic analysis of microelectromechanical systems

NASA Astrophysics Data System (ADS)

Su, Y.; Ong, E. T.; Lee, K. H.

2002-05-01

The past decade has seen an accelerated growth of technology in the field of microelectromechanical systems (MEMS). The development of MEMS products has generated the need for efficient analytical and simulation methods for minimizing the requirement for actual prototyping. The boundary element method is widely used in the electrostatic analysis for MEMS devices. However, singular elements are needed to accurately capture the behavior at singular regions, such as sharp corners and edges, where standard elements fail to give an accurate result. The manual classification of boundary elements based on their singularity conditions is an immensely laborious task, especially when the boundary element model is large. This process can be automated by querying the geometric model of the MEMS device for convex edges based on geometric information of the model. The associated nodes of the boundary elements on these edges can then be retrieved. The whole process is implemented in the MSC/PATRAN platform using the Patran Command Language (the source code is available as supplementary data in the electronic version of this journal issue).

A rapid local singularity analysis algorithm with applications

NASA Astrophysics Data System (ADS)

Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits

2015-04-01

The local singularity model developed by Cheng is fast gaining popularity in characterizing mineralization and detecting anomalies of geochemical, geophysical and remote sensing data. However in one of the conventional algorithms involving the moving average values with different scales is time-consuming especially while analyzing a large dataset. Summed area table (SAT), also called as integral image, is a fast algorithm used within the Viola-Jones object detection framework in computer vision area. Historically, the principle of SAT is well-known in the study of multi-dimensional probability distribution functions, namely in computing 2D (or ND) probabilities (area under the probability distribution) from the respective cumulative distribution functions. We introduce SAT and it's variation Rotated Summed Area Table in the isotropic, anisotropic or directional local singularity mapping in this study. Once computed using SAT, any one of the rectangular sum can be computed at any scale or location in constant time. The area for any rectangular region in the image can be computed by using only 4 array accesses in constant time independently of the size of the region; effectively reducing the time complexity from O(n) to O(1). New programs using Python, Julia, matlab and C++ are implemented respectively to satisfy different applications, especially to the big data analysis. Several large geochemical and remote sensing datasets are tested. A wide variety of scale changes (linear spacing or log spacing) for non-iterative or iterative approach are adopted to calculate the singularity index values and compare the results. The results indicate that the local singularity analysis with SAT is more robust and superior to traditional approach in identifying anomalies.

Absolute and convective instabilities of a film flow down a vertical fiber subjected to a radial electric field

NASA Astrophysics Data System (ADS)

Liu, Rong; Chen, Xue; Ding, Zijing

2018-01-01

We consider the motion of a gravity-driven flow down a vertical fiber subjected to a radial electric field. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the Maxwell stress at the interface. A spatiotemporal stability analysis is performed to investigate the effect of electric field on the absolute-convective instability (AI-CI) characteristics. We performed a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. The numerical results are in excellent agreement with the spatiotemporal stability analysis. The blowup behavior of nonlinear simulation predicts the formation of touchdown singularity of the interface due to the effect of electric field. We try to connect the blowup behavior with the AI-CI characteristics. It is found that the singularities mainly occur in the AI regime. The results indicate that the film may have a tendency to form very sharp tips due to the enhancement of the absolute instability induced by the electric field. We perform a theoretical analysis to study the behaviors of the singularities. The results show that there exists a self-similarity between the temporal and spatial distances from the singularities.

Caustic Singularities Of High-Gain, Dual-Shaped Reflectors

NASA Technical Reports Server (NTRS)

Galindo, Victor; Veruttipong, Thavath W.; Imbriale, William A.; Rengarajan, Sambiam

1991-01-01

Report presents study of some sources of error in analysis, by geometric theory of diffraction (GTD), of performance of high-gain, dual-shaped antenna reflector. Study probes into underlying analytic causes of singularity, with view toward devising and testing practical methods to avoid problems caused by singularity. Hybrid physical optics (PO) approach used to study near-field spillover or noise-temperature characteristics of high-gain relector antenna efficiently and accurately. Report illustrates this approach and underlying principles by presenting numerical results, for both offset and symmetrical reflector systems, computed by GTD, PO, and PO/GO methods.

The Zeldovich & Adhesion approximations and applications to the local universe

NASA Astrophysics Data System (ADS)

Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei

2016-10-01

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.

Singularity detection in FOG-based pavement data by wavelet transform

NASA Astrophysics Data System (ADS)

Yang, Dandan; Wang, Lixin; Hu, Wenbin; Zhang, Zhen; Fu, Jinghua; Gan, Weibing

2017-04-01

The angular velocity data of Fiber-Optic Gyro (FOG) has been analyzed to locate the singularity by the wavelet transform (WT) method. By using WT analysis method to decompose and reconstruct the signal of pavement data collecting by the FOG, the different types of pavement singularities can be extracted. The experiments are conducted on different road surfaces. The experimental results show that the locations of bumps and expansion joints have been obtained, with a relative precision of 0.5 m and an absolute precision of 2 m over 2.4 km. The characteristic of the pavement roughness can also be identified.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Segmentation of singularity maps in the context of soil porosity

NASA Astrophysics Data System (ADS)

Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

2016-04-01

Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in porphyry Cu deposits by fractal concentration-volume modeling. Journal of Geochemical Exploration, 108, 220-232. Martín-Sotoca, J. J., Tarquis, A. M., Saa-Requejo, A. and Grau, J. B. (2015). Pore detection in Computed Tomography (CT) soil images through singularity map analysis. Oral Presentation in PedoFract VIII Congress (June, La Coruña - Spain).

Decomposition of the Multistatic Response Matrix and Target Characterization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chambers, D H

2008-02-14

Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In this paper we review the analysis of the time-reversal operator (TRO), or equivalently the multistatic response matrix (MRM), of an array system and a small target. We begin with two-dimensional scattering from a small cylinder then show the results formore » a small non-spherical target in three dimensions. We show that the number and magnitudes of the singular values contain information about target composition, shape, and orientation.« less

IUTAM Symposium and NATO Advanced Research Workshop on Interpretation of Time Series from Nonlinear Mechanical Systems Held in Coventry, England on 26-30 August 1991. Conference Abstracts

DTIC Science & Technology

1991-08-01

day oscillation in the extratropical atmosphere as identified by multi-channel singular spectrum analysis 10:25 Coffee Break 10:50 Read Chaotic...day oscillation in the extratropical atmosphere as identified by multi-channel singular spectrum analysis M. Kimoto, M. Ghil and K.-C. Mo ABSTRACT...The three-dimensional spatial structure of an oscillatory mode in the Northern Hemisphere (NH) extratropics will be describe.d The oscillation is

Experimental Modal Analysis and Dynamic Component Synthesis. Volume 3. Modal Parameter Estimation

DTIC Science & Technology

1987-12-01

residues as well as poles is achieved. A singular value decomposition method has been used to develop a complex mode indicator function ( CMIF )[70...which can be used to help determine the number of poles before the analysis. The CMIF is formed by performing a singular value decomposition of all of...servo systems which can include both low and high damping modes. "• CMIF can be used to indicate close or repeated eigenvalues before the parameter

Cost Prediction via Quantitative Analysis of Complexity in U.S. Navy Shipbuilding

DTIC Science & Technology

2014-06-01

in regards to the analysis of advanced sensors and weaponry, the summation of singular values via a singular value decomposition will be used in the...In the DDG 51 class, the Main Reduction Gear (MRG) reduces the 3600-RPM produced by the LM-2500 gas turbines to approximately 168-RPM (at full...RDT&E efforts are currently underway to reduce complexity of the MCS by developing a wireless approach that will concurrently boost the host ship’s

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

Theory and investigation of acoustic multiple-input multiple-output systems based on spherical arrays in a room.

PubMed

Morgenstern, Hai; Rafaely, Boaz; Zotter, Franz

2015-11-01

Spatial attributes of room acoustics have been widely studied using microphone and loudspeaker arrays. However, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have only been studied to a limited degree in this context. These systems can potentially provide a powerful tool for room acoustics analysis due to the ability to simultaneously control both arrays. This paper offers a theoretical framework for the spatial analysis of enclosed sound fields using a MIMO system comprising spherical loudspeaker and microphone arrays. A system transfer function is formulated in matrix form for free-field conditions, and its properties are studied using tools from linear algebra. The system is shown to have unit-rank, regardless of the array types, and its singular vectors are related to the directions of arrival and radiation at the microphone and loudspeaker arrays, respectively. The formulation is then generalized to apply to rooms, using an image source method. In this case, the rank of the system is related to the number of significant reflections. The paper ends with simulation studies, which support the developed theory, and with an extensive reflection analysis of a room impulse response, using the platform of a MIMO system.

Singular perturbation, state aggregation and nonlinear filtering

NASA Technical Reports Server (NTRS)

Hijab, O.; Sastry, S.

1981-01-01

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

DOE PAGES

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; ...

2017-01-25

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to notmore » only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. Furthermore, the algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.« less

Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics.

PubMed

Kisdi, Éva

2015-04-01

Evolutionary singularities are central to the adaptive dynamics of evolving traits. The evolutionary singularities are strongly affected by the shape of any trade-off functions a model assumes, yet the trade-off functions are often chosen in an ad hoc manner, which may unjustifiably constrain the evolutionary dynamics exhibited by the model. To avoid this problem, critical function analysis has been used to find a trade-off function that yields a certain evolutionary singularity such as an evolutionary branching point. Here I extend this method to multiple trade-offs parameterized with a scalar strategy. I show that the trade-off functions can be chosen such that an arbitrary point in the viability domain of the trait space is a singularity of an arbitrary type, provided (next to certain non-degeneracy conditions) that the model has at least two environmental feedback variables and at least as many trade-offs as feedback variables. The proof is constructive, i.e., it provides an algorithm to find trade-off functions that yield the desired singularity. I illustrate the construction of trade-offs with an example where the virulence of a pathogen evolves in a small ecosystem of a host, its pathogen, a predator that attacks the host and an alternative prey of the predator.

Singularities in Dromo formulation. Analysis of deep flybys

NASA Astrophysics Data System (ADS)

Roa, Javier; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-08-01

The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very specific situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric flybys. The performance of Dromo is evaluated in different scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical flybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the flyby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.

Kinematic rate control of simulated robot hand at or near wrist singularity

NASA Technical Reports Server (NTRS)

Barker, K.; Houck, J. A.; Carzoo, S. W.

1985-01-01

A robot hand should obey movement commands from an operator on a computer program as closely as possible. However, when two of the three rotational axes of the robot wrist are colinear, the wrist loses a degree of freedom, and the usual resolved rate equations (used to move the hand in response to an operator's inputs) are indeterminant. Furthermore, rate limiting occurs in close vicinity to this singularity. An analysis shows that rate limiting occurs not only in the vicinity of this singularity but also substantially away from it, even when the operator commands rotational rates of the robot hand that are only a small percentage of the operational joint rate limits. Therefore, joint angle rates are scaled when they exceed operational limits in a real time simulation of a robot arm. Simulation results show that a small dead band avoids the wrist singularity in the resolved rate equations but can introduce a high frequency oscillation close to the singularity. However, when a coordinated wrist movement is used in conjunction with the resolved rate equations, the high frequency oscillation disappears.

Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography

PubMed Central

Leblond, Frederic; Tichauer, Kenneth M.; Pogue, Brian W.

2010-01-01

The spatial resolution and recovered contrast of images reconstructed from diffuse fluorescence tomography data are limited by the high scattering properties of light propagation in biological tissue. As a result, the image reconstruction process can be exceedingly vulnerable to inaccurate prior knowledge of tissue optical properties and stochastic noise. In light of these limitations, the optimal source-detector geometry for a fluorescence tomography system is non-trivial, requiring analytical methods to guide design. Analysis of the singular value decomposition of the matrix to be inverted for image reconstruction is one potential approach, providing key quantitative metrics, such as singular image mode spatial resolution and singular data mode frequency as a function of singular mode. In the present study, these metrics are used to analyze the effects of different sources of noise and model errors as related to image quality in the form of spatial resolution and contrast recovery. The image quality is demonstrated to be inherently noise-limited even when detection geometries were increased in complexity to allow maximal tissue sampling, suggesting that detection noise characteristics outweigh detection geometry for achieving optimal reconstructions. PMID:21258566

Nonequilibrium dynamics of the O( N ) model on dS3 and AdS crunches

NASA Astrophysics Data System (ADS)

Kumar, S. Prem; Vaganov, Vladislav

2018-03-01

We study the nonperturbative quantum evolution of the interacting O( N ) vector model at large- N , formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called "E-frame" theory, is related via a conformal transformation to the interacting O( N ) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large- N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical "end of time". With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.

The magnetic field of a permanent hollow cylindrical magnet

NASA Astrophysics Data System (ADS)

Reich, Felix A.; Stahn, Oliver; Müller, Wolfgang H.

2016-09-01

Based on the rational version of M AXWELL's equations according to T RUESDELL and T OUPIN or KOVETZ, cf. (Kovetz in Electromagnetic theory, Oxford University Press, Oxford, 2000; Truesdell and Toupin in Handbuch der Physik, Bd. III/1, Springer, Berlin, pp 226-793; appendix, pp 794-858, 2000), we present, for stationary processes, a closed-form solution for the magnetic flux density of a hollow cylindrical magnet. Its magnetization is constant in axial direction. We consider M AXWELL's equations in regular and singular points that are obtained by rational electrodynamics, adapted to stationary processes. The magnetic flux density is calculated analytically by means of a vector potential. We obtain a solution in terms of complete elliptic integrals. Therefore, numerical evaluation can be performed in a computationally efficient manner. The solution is written in dimensionless form and can easily be applied to cylinders of arbitrary shape. The relation between the magnetic flux density and the magnetic field is linear, and an explicit relation for the field is presented. With a slight modification the result can be used to obtain the field of a solid cylindrical magnet. The mathematical structure of the solution and, in particular, singularities are discussed.

Charged black holes in compactified spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karlovini, Max; Unge, Rikard von

2005-11-15

We construct and investigate a compactified version of the four-dimensional Reissner-Nordstroem-Taub-NUT solution, generalizing the compactified Schwarzschild black hole that has been previously studied by several workers. Our approach to compactification is based on dimensional reduction with respect to the stationary Killing vector, resulting in three-dimensional gravity coupled to a nonlinear sigma model. Knowing that the original noncompactified solution corresponds to a target space geodesic, the problem can be linearized much in the same way as in the case of no electric or Taub-NUT charge. An interesting feature of the solution family is that, for nonzero electric charge but vanishing Taub-NUTmore » charge, the solution has a curvature singularity on a torus that surrounds the event horizon, but this singularity is removed when the Taub-NUT charge is switched on. We also treat the Schwarzschild case in a more complete way than has been done previously. In particular, the asymptotic solution (the Levi-Civita solution with the height coordinate made periodic) has to our knowledge only been calculated up to a determination of the mass parameter. The periodic Levi-Civita solution contains three essential parameters, however, and the remaining two are explicitly calculated here.« less

Complex mode indication function and its applications to spatial domain parameter estimation

NASA Astrophysics Data System (ADS)

Shih, C. Y.; Tsuei, Y. G.; Allemang, R. J.; Brown, D. L.

1988-10-01

This paper introduces the concept of the Complex Mode Indication Function (CMIF) and its application in spatial domain parameter estimation. The concept of CMIF is developed by performing singular value decomposition (SVD) of the Frequency Response Function (FRF) matrix at each spectral line. The CMIF is defined as the eigenvalues, which are the square of the singular values, solved from the normal matrix formed from the FRF matrix, [ H( jω)] H[ H( jω)], at each spectral line. The CMIF appears to be a simple and efficient method for identifying the modes of the complex system. The CMIF identifies modes by showing the physical magnitude of each mode and the damped natural frequency for each root. Since multiple reference data is applied in CMIF, repeated roots can be detected. The CMIF also gives global modal parameters, such as damped natural frequencies, mode shapes and modal participation vectors. Since CMIF works in the spatial domain, uneven frequency spacing data such as data from spatial sine testing can be used. A second-stage procedure for accurate damped natural frequency and damping estimation as well as mode shape scaling is also discussed in this paper.

On the use of the singular value decomposition for text retrieval

DOE Office of Scientific and Technical Information (OSTI.GOV)

Husbands, P.; Simon, H.D.; Ding, C.

2000-12-04

The use of the Singular Value Decomposition (SVD) has been proposed for text retrieval in several recent works. This technique uses the SVD to project very high dimensional document and query vectors into a low dimensional space. In this new space it is hoped that the underlying structure of the collection is revealed thus enhancing retrieval performance. Theoretical results have provided some evidence for this claim and to some extent experiments have confirmed this. However, these studies have mostly used small test collections and simplified document models. In this work we investigate the use of the SVD on large documentmore » collections. We show that, if interpreted as a mechanism for representing the terms of the collection, this technique alone is insufficient for dealing with the variability in term occurrence. Section 2 introduces the text retrieval concepts necessary for our work. A short description of our experimental architecture is presented in Section 3. Section 4 describes how term occurrence variability affects the SVD and then shows how the decomposition influences retrieval performance. A possible way of improving SVD-based techniques is presented in Section 5 and concluded in Section 6.« less

Charged anti-de Sitter BTZ black holes in Maxwell-f(T) gravity

NASA Astrophysics Data System (ADS)

Nashed, G. G. L.; Capozziello, S.

2018-05-01

Inspired by the Bañados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-f(T) gravity in (2 + 1) dimensions. The main task is to derive exact solutions for a special form of f(T) = T + 𝜖T2, with T being the torsion scalar of Weitzenböck geometry. To this end, a triad field is applied to the equations of motion of charged f(T) and sets of circularly symmetric noncharged and charged solutions have been derived. We show that, in the charged case, the monopole-like and the ln terms are linked by a correlative constant despite the known results in teleparallel geometry and its extensions.39 Furthermore, it is possible to show that the event horizon is not identical with the Cauchy horizon due to such a constant. The singularities and the horizons of these black holes are examined: they are new and have no analogue in the literature due to the fact that their curvature singularities are soft. We calculate the energy content of these solutions by using the general vector form of the energy-momentum within the framework of f(T) gravity. Finally, some thermodynamical quantities, like entropy and Hawking temperature, are derived.

Orbital theory in terms of KS elements with luni-solar perturbations

NASA Astrophysics Data System (ADS)

Sellamuthu, Harishkumar; Sharma, Ram

2016-07-01

Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

Analysis of the Fisher solution

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-01

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the “scalar charge” Σ. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,Σ) maps the exterior region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its “big bang” and “big crunch.” The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are “dual to the horizon.”

Analysis of the Fisher solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-15

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the 'scalar charge' {Sigma}. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,{Sigma}) maps the exteriormore » region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its 'big bang' and 'big crunch'. The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are 'dual to the horizon'.« less

Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells

PubMed Central

Taniguchi, Daisuke; Ishihara, Shuji; Oonuki, Takehiko; Honda-Kitahara, Mai; Kaneko, Kunihiko; Sawai, Satoshi

2013-01-01

In both randomly moving Dictyostelium and mammalian cells, phosphatidylinositol (3,4,5)-trisphosphate and F-actin are known to propagate as waves at the membrane and act to push out the protruding edge. To date, however, the relationship between the wave geometry and the patterns of amoeboid shape change remains elusive. Here, by using phase map analysis, we show that morphology dynamics of randomly moving Dictyostelium discoideum cells can be characterized by the number, topology, and position of spatial phase singularities, i.e., points that represent organizing centers of rotating waves. A single isolated singularity near the cellular edge induced a rotational protrusion, whereas a pair of singularities supported a symmetric extension. These singularities appeared by strong phase resetting due to de novo nucleation at the back of preexisting waves. Analysis of a theoretical model indicated excitability of the system that is governed by positive feedback from phosphatidylinositol (3,4,5)-trisphosphate to PI3-kinase activation, and we showed experimentally that this requires F-actin. Furthermore, by incorporating membrane deformation into the model, we demonstrated that geometries of competing waves explain most of the observed semiperiodic changes in amoeboid morphology. PMID:23479620

Inflection point caustic problems and solutions for high-gain dual-shaped reflectors

NASA Technical Reports Server (NTRS)

Galindo-Israel, Victor; Veruttipong, Thavath; Imbriale, William; Rengarajan, Sembiam

1990-01-01

The singular nature of the uniform geometrical theory of diffraction (UTD) subreflector scattered field at the vicinity of the main reflector edge (for a high-gain antenna design) is investigated. It is shown that the singularity in the UTD edge-diffracted and slope-diffracted fields is due to the reflection distance parameter approaching infinity in the transition functions. While the geometrical optics (GO) and UTD edge-diffracted fields exhibit singularities of the same order, the edge slope-diffracted field singularity is more significant and is substantial for greater subreflector edge tapers. The diffraction analysis of such a subreflector in the vicinity of the main reflector edge has been carried out efficiently and accurately by a stationary phase evaluation of the phi-integral, whereas the theta-integral is carried out numerically. Computational results from UTD and physical optics (PO) analysis of a 34-m ground station dual-shaped reflector confirm the analytical formulations for both circularly symmetric and offset asymmetric subreflectors. It is concluded that the proposed PO(theta)GO(phi) technique can be used to study the spillover or noise temperature characteristics of a high-gain reflector antenna efficiently and accurately.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Sufficient condition for a finite-time singularity in a high-symmetry Euler flow: Analysis and statistics

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

1996-08-01

A sufficient condition is obtained for the development of a finite-time singularity in a highly symmetric Euler flow, first proposed by Kida [J. Phys. Soc. Jpn. 54, 2132 (1995)] and recently simulated by Boratav and Pelz [Phys. Fluids 6, 2757 (1994)]. It is shown that if the second-order spatial derivative of the pressure (pxx) is positive following a Lagrangian element (on the x axis), then a finite-time singularity must occur. Under some assumptions, this Lagrangian sufficient condition can be reduced to an Eulerian sufficient condition which requires that the fourth-order spatial derivative of the pressure (pxxxx) at the origin be positive for all times leading up to the singularity. Analytical as well as direct numerical evaluation over a large ensemble of initial conditions demonstrate that for fixed total energy, pxxxx is predominantly positive with the average value growing with the numbers of modes.

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

NASA Astrophysics Data System (ADS)

Bao, J.; Lin, Z.; Lu, Z. X.

2018-02-01

A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from the drift kinetic equation is used to time advance the electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, the shear Alfvén wave dispersion relation in the shearless slab and continuum damping in the sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in the conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also avoids the problem in the conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

Improved quantitative analysis of spectra using a new method of obtaining derivative spectra based on a singular perturbation technique.

PubMed

Li, Zhigang; Wang, Qiaoyun; Lv, Jiangtao; Ma, Zhenhe; Yang, Linjuan

2015-06-01

Spectroscopy is often applied when a rapid quantitative analysis is required, but one challenge is the translation of raw spectra into a final analysis. Derivative spectra are often used as a preliminary preprocessing step to resolve overlapping signals, enhance signal properties, and suppress unwanted spectral features that arise due to non-ideal instrument and sample properties. In this study, to improve quantitative analysis of near-infrared spectra, derivatives of noisy raw spectral data need to be estimated with high accuracy. A new spectral estimator based on singular perturbation technique, called the singular perturbation spectra estimator (SPSE), is presented, and the stability analysis of the estimator is given. Theoretical analysis and simulation experimental results confirm that the derivatives can be estimated with high accuracy using this estimator. Furthermore, the effectiveness of the estimator for processing noisy infrared spectra is evaluated using the analysis of beer spectra. The derivative spectra of the beer and the marzipan are used to build the calibration model using partial least squares (PLS) modeling. The results show that the PLS based on the new estimator can achieve better performance compared with the Savitzky-Golay algorithm and can serve as an alternative choice for quantitative analytical applications.

Multilayer neural networks for reduced-rank approximation.

PubMed

Diamantaras, K I; Kung, S Y

1994-01-01

This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non-invertible autocorrelation matrix. Previous identification methods usually rely on the invertibility assumption of the input autocorrelation, therefore they can not be applied to this case.

Structure and propagation of supersonic singularities from helicoidal sources

NASA Technical Reports Server (NTRS)

Myers, M. K.; Farassat, F.

1987-01-01

An asymptotic analysis of the acoustic field radiated by a supersonic helicoidal line source distribution is given. The asymptotic results are valid in the vicinity of the Mach surfaces associated with the moving sources. Particular attention is paid to the singular nature of the field on the Mach surfaces, which the analysis describes exactly. In addition, it is found that the asymptotic approximation predicts numerical values of the pressure with considerable accuracy. Some details on the field of a single source are derived as a special case.

Application of Artificial Neural Networks and Singular-Spectral Analysis in Forecasting the Daily Traffic in the Moscow Metro

NASA Astrophysics Data System (ADS)

Ivanov, Victor; Osetrov, Evgenii

2018-02-01

In this paper, we investigate the possibility of applying various approaches to solving the problem of medium-term forecasting of daily passenger traffic volumes in the Moscow metro (MM): 1) on the basis of artificial neural networks (ANN); 2) using the singular-spectral analysis implemented in the package "Caterpillar"-SSA; 3) sharing the ANN and the "Caterpillar"-SSA approach. We demonstrate that the developed methods and algorithms allow us to conduct medium-term forecasting of passenger traffic in the MM with reasonable accuracy.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

Elementary exact calculations of degree growth and entropy for discrete equations.

PubMed

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Computation of ancestry scores with mixed families and unrelated individuals.

PubMed

Zhou, Yi-Hui; Marron, James S; Wright, Fred A

2018-03-01

The issue of robustness to family relationships in computing genotype ancestry scores such as eigenvector projections has received increased attention in genetic association, and is particularly challenging when sets of both unrelated individuals and closely related family members are included. The current standard is to compute loadings (left singular vectors) using unrelated individuals and to compute projected scores for remaining family members. However, projected ancestry scores from this approach suffer from shrinkage toward zero. We consider two main novel strategies: (i) matrix substitution based on decomposition of a target family-orthogonalized covariance matrix, and (ii) using family-averaged data to obtain loadings. We illustrate the performance via simulations, including resampling from 1000 Genomes Project data, and analysis of a cystic fibrosis dataset. The matrix substitution approach has similar performance to the current standard, but is simple and uses only a genotype covariance matrix, while the family-average method shows superior performance. Our approaches are accompanied by novel ancillary approaches that provide considerable insight, including individual-specific eigenvalue scree plots. © 2017 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

SH c realization of minimal model CFT: triality, poset and Burge condition

NASA Astrophysics Data System (ADS)

Fukuda, M.; Nakamura, S.; Matsuo, Y.; Zhu, R.-D.

2015-11-01

Recently an orthogonal basis of {{W}}_N -algebra (AFLT basis) labeled by N-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH c which is universal for any N. We show that it has an {{S}}_3 automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by N or M Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH c . Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the N-Burge condition in the Hilbert space.

Electromagnetic analysis of arbitrarily shaped pinched carpets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupont, Guillaume; Guenneau, Sebastien; Enoch, Stefan

2010-09-15

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and permeability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map an arbitrary region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components. Moreover, a reduced set of parameters leads to nonmagnetic two-dimensional carpets in p polarization (i.e., for a magnetic field orthogonal to the plane containing the carpet). Such an arbitrarily shaped carpet is shown to work over amore » finite bandwidth when it is approximated by a checkerboard with 190 homogeneous cells of piecewise constant anisotropic permittivity. We finally perform some finite element computations in the full vector three-dimensional case for a plane wave in normal incidence and a Gaussian beam in oblique incidence. The latter requires perfectly matched layers set in a rotated coordinate axis which exemplifies the role played by geometric transforms in computational electromagnetism.« less

Analysis of Drude model using fractional derivatives without singular kernels

NASA Astrophysics Data System (ADS)

Jiménez, Leonardo Martínez; García, J. Juan Rosales; Contreras, Abraham Ortega; Baleanu, Dumitru

2017-11-01

We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.

Beyond singular values and loop shapes

NASA Technical Reports Server (NTRS)

Stein, G.

1985-01-01

The status of singular value loop-shaping as a design paradigm for multivariable feedback systems is reviewed. It shows that this paradigm is an effective design tool whenever the problem specifications are spacially round. The tool can be arbitrarily conservative, however, when they are not. This happens because singular value conditions for robust performance are not tight (necessary and sufficient) and can severely overstate actual requirements. An alternate paradign is discussed which overcomes these limitations. The alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The state of the art currently permits analysis of feedback systems within this new paradigm. Synthesis remains a subject of research.

Singular instantons in Eddington-inspired-Born-Infeld gravity

DOE PAGES

Arroja, Frederico; Chen, Che -Yu; Chen, Pisin; ...

2017-03-23

In this study, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but theremore » is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

Singularity-free dynamic equations of spacecraft-manipulator systems

NASA Astrophysics Data System (ADS)

From, Pål J.; Ytterstad Pettersen, Kristin; Gravdahl, Jan T.

2011-12-01

In this paper we derive the singularity-free dynamic equations of spacecraft-manipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. This paper represents the first detailed study of modeling of spacecraft-manipulator systems with a focus on a singularity free formulation using the proposed framework.

Singularity-free extraction of a quaternion from a direction-cosine matrix. [for spacecraft control and guidance

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1976-01-01

A computer algorithm for extracting a quaternion from a direction-cosine matrix (DCM) is described. The quaternion provides a four-parameter representation of rotation, as against the nine-parameter representation afforded by a DCM. Commanded attitude in space shuttle steering is conveniently computed by DCM, while actual attitude is computed most compactly as a quaternion, as is attitude error. The unit length of the rotation quaternion, and interchangeable of a quaternion and its negative, are used to advantage in the extraction algorithm. Protection of the algorithm against square root failure and division overflow are considered. Necessary and sufficient conditions for handling the rotation vector element of largest magnitude are discussed

Lyapounov Functions of Closed Cone Fields: From Conley Theory to Time Functions

NASA Astrophysics Data System (ADS)

Bernard, Patrick; Suhr, Stefan

2018-03-01

We propose a theory "à la Conley" for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of closed (or equivalently semi-continuous) cone fields with singularities. This setting contains (for questions which are parametrization independent such as the existence of Lyapounov functions) the case of continuous vector-fields on manifolds, of differential inclusions, of Lorentzian metrics, and of continuous cone fields. We generalize to this setting the equivalence between stable causality and the existence of temporal functions. We also generalize the equivalence between global hyperbolicity and the existence of a steep temporal function.

Hyperasymptotics and quark-hadron duality violations in QCD

NASA Astrophysics Data System (ADS)

Boito, Diogo; Caprini, Irinel; Golterman, Maarten; Maltman, Kim; Peris, Santiago

2018-03-01

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex q2 plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality-violating contributions. Starting with the assumption that for QCD at Nc=∞ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite Nc.

Evaluation of constraint stabilization procedures for multibody dynamical systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.

1987-01-01

Comparative numerical studies of four constraint treatment techniques for the simulation of general multibody dynamic systems are presented, and results are presented for the example of a classical crank mechanism and for a simplified version of the seven-link manipulator deployment problem. The staggered stabilization technique (Park, 1986) is found to yield improved accuracy and robustness over Baumgarte's (1972) technique, the singular decomposition technique (Walton and Steeves, 1969), and the penalty technique (Lotstedt, 1979). Furthermore, the staggered stabilization technique offers software modularity, and the only data each solution module needs to exchange with the other is a set of vectors plus a common module to generate the gradient matrix of the constraints, B.

Unimodularity criteria for Poisson structures on foliated manifolds

NASA Astrophysics Data System (ADS)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

SU-G-JeP4-03: Anomaly Detection of Respiratory Motion by Use of Singular Spectrum Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotoku, J; Kumagai, S; Nakabayashi, S

Purpose: The implementation and realization of automatic anomaly detection of respiratory motion is a very important technique to prevent accidental damage during radiation therapy. Here, we propose an automatic anomaly detection method using singular value decomposition analysis. Methods: The anomaly detection procedure consists of four parts:1) measurement of normal respiratory motion data of a patient2) calculation of a trajectory matrix representing normal time-series feature3) real-time monitoring and calculation of a trajectory matrix of real-time data.4) calculation of an anomaly score from the similarity of the two feature matrices. Patient motion was observed by a marker-less tracking system using a depthmore » camera. Results: Two types of motion e.g. cough and sudden stop of breathing were successfully detected in our real-time application. Conclusion: Automatic anomaly detection of respiratory motion using singular spectrum analysis was successful in the cough and sudden stop of breathing. The clinical use of this algorithm will be very hopeful. This work was supported by JSPS KAKENHI Grant Number 15K08703.« less

Singularity analysis based on wavelet transform of fractal measures for identifying geochemical anomaly in mineral exploration

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2016-02-01

Multi-resolution and scale-invariance have been increasingly recognized as two closely related intrinsic properties endowed in geofields such as geochemical and geophysical anomalies, and they are commonly investigated by using multiscale- and scaling-analysis methods. In this paper, the wavelet-based multiscale decomposition (WMD) method was proposed to investigate the multiscale natures of geochemical pattern from large scale to small scale. In the light of the wavelet transformation of fractal measures, we demonstrated that the wavelet approximation operator provides a generalization of box-counting method for scaling analysis of geochemical patterns. Specifically, the approximation coefficient acts as the generalized density-value in density-area fractal modeling of singular geochemical distributions. Accordingly, we presented a novel local singularity analysis (LSA) using the WMD algorithm which extends the conventional moving averaging to a kernel-based operator for implementing LSA. Finally, the novel LSA was validated using a case study dealing with geochemical data (Fe2O3) in stream sediments for mineral exploration in Inner Mongolia, China. In comparison with the LSA implemented using the moving averaging method the novel LSA using WMD identified improved weak geochemical anomalies associated with mineralization in covered area.

Finite-time singularities in the dynamics of hyperinflation in an economy

NASA Astrophysics Data System (ADS)

Szybisz, Martín A.; Szybisz, Leszek

2009-08-01

The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective “adaptive inflation expectations” with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t) , changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time tc . By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t)≈(tc-t)-α (with α>0 ) and the other exhibits a logarithmic divergence, p(t)≈ln[1/(tc-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.

[Formula: see text] regularity properties of singular parameterizations in isogeometric analysis.

PubMed

Takacs, T; Jüttler, B

2012-11-01

Isogeometric analysis (IGA) is a numerical simulation method which is directly based on the NURBS-based representation of CAD models. It exploits the tensor-product structure of 2- or 3-dimensional NURBS objects to parameterize the physical domain. Hence the physical domain is parameterized with respect to a rectangle or to a cube. Consequently, singularly parameterized NURBS surfaces and NURBS volumes are needed in order to represent non-quadrangular or non-hexahedral domains without splitting, thereby producing a very compact and convenient representation. The Galerkin projection introduces finite-dimensional spaces of test functions in the weak formulation of partial differential equations. In particular, the test functions used in isogeometric analysis are obtained by composing the inverse of the domain parameterization with the NURBS basis functions. In the case of singular parameterizations, however, some of the resulting test functions do not necessarily fulfill the required regularity properties. Consequently, numerical methods for the solution of partial differential equations cannot be applied properly. We discuss the regularity properties of the test functions. For one- and two-dimensional domains we consider several important classes of singularities of NURBS parameterizations. For specific cases we derive additional conditions which guarantee the regularity of the test functions. In addition we present a modification scheme for the discretized function space in case of insufficient regularity. It is also shown how these results can be applied for computational domains in higher dimensions that can be parameterized via sweeping.

Improvements in surface singularity analysis and design methods. [applicable to airfoils

NASA Technical Reports Server (NTRS)

Bristow, D. R.

1979-01-01

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Strong lensing probability in TeVeS (tensor-vector-scalar) theory

NASA Astrophysics Data System (ADS)

Chen, Da-Ming

2008-01-01

We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with Ωb = 0.04 and ΩΛ = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We compare our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function μ(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.

Global-Local Finite Element Analysis for Thermo-Mechanical Stresses in Bonded Joints

NASA Technical Reports Server (NTRS)

Shkarayev, S.; Madenci, Erdogan; Camarda, C. J.

1997-01-01

An analysis of adhesively bonded joints using conventional finite elements does not capture the singular behavior of the stress field in regions where two or three dissimilar materials form a junction with or without free edges. However, these regions are characteristic of the bonded joints and are prone to failure initiation. This study presents a method to capture the singular stress field arising from the geometric and material discontinuities in bonded composites. It is achieved by coupling the local (conventional) elements with global (special) elements whose interpolation functions are constructed from the asymptotic solution.

Structural singularities in Ge(x)Te(100-x) films.

PubMed

Piarristeguy, A A; Micoulaut, M; Escalier, R; Jóvári, P; Kaban, I; van Eijk, J; Luckas, J; Ravindren, S; Boolchand, P; Pradel, A

2015-08-21

Structural and calorimetric investigation of Ge(x)Te(100-x) films over wide range of concentration 10 < x < 50 led to evidence two structural singularities at x ∼ 22 at. % and x ∼ 33-35 at. %. Analysis of bond distribution, bond variability, and glass thermal stability led to conclude to the origin of the first singularity being the flexible/rigid transition proposed in the framework of rigidity model and the origin of the second one being the disappearance of the undercooled region resulting in amorphous materials with statistical distributions of bonds. While the first singularity signs the onset of the Ge-Ge homopolar bonds, the second is related to compositions where enhanced Ge-Ge correlations at intermediate lengthscales (7.7 Å) are observed. These two threshold compositions correspond to recently reported resistance drift threshold compositions, an important support for models pointing the breaking of homopolar Ge-Ge bonds as the main phenomenon behind the ageing of phase change materials.

Analysis of singular interface stresses in dissimilar material joints for plasma facing components

NASA Astrophysics Data System (ADS)

You, J. H.; Bolt, H.

2001-10-01

Duplex joint structures are typical material combinations for the actively cooled plasma facing components of fusion devices. The structural integrity under the incident heat loads from the plasma is one of the most crucial issues in the technology of these components. The most critical domain in a duplex joint component is the free surface edge of the bond interface between heterogeneous materials. This is due to the fact that the thermal stress usually shows a singular intensification in this region. If the plasma facing armour tile consists of a brittle material, the existence of the stress singularity can be a direct cause of failure. The present work introduces a comprehensive analytical tool to estimate the impact of the stress singularity for duplex PFC design and quantifies the relative stress intensification in various materials joints by use of a model formulated by Munz and Yang. Several candidate material combinations of plasma facing armour and metallic heat sink are analysed and the results are compared with each other.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.; Rubiera-Garcia, Diego

2017-10-01

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

Aerodynamic influence coefficient method using singularity splines

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1974-01-01

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Transverse cracking and stiffness reduction in composite laminates

NASA Technical Reports Server (NTRS)

Yuan, F. G.; Selek, M. C.

1993-01-01

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J.

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of themore » gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.« less

Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory

NASA Astrophysics Data System (ADS)

Taylor, Jamie M.

2016-09-01

This paper is concerned with an investigation into a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability distributions on a state space, defined so that it corresponds to the maximum possible entropy given known observed statistical averages, although non-classical entropy-like objective functions will also be considered. First the set of admissible moments must be established, and under the conditions presented in this work the set is open, bounded and convex allowing a description in terms of supporting hyperplanes, which provides estimates on the development of singularities for related probability distributions. Under appropriate conditions it is shown that the singular potential is strictly convex, as differentiable as the microscopic entropy, and blows up uniformly as the macroscopic variable tends to the boundary of the set of admissible moments. Applications of the singular potential are then discussed, and particular consideration will be given to certain free-energy functionals typical in mean-field theory, demonstrating an equivalence between certain microscopic and macroscopic free-energy functionals. This allows statements about L^1-local minimisers of Onsager's free energy to be obtained which cannot be given by two-sided variations, and overcomes the need to ensure local minimisers are bounded away from zero and +∞ before taking L^∞ variations. The analysis also permits the definition of a dual order parameter for which Onsager's free energy allows an explicit representation. Also, the difficulties in approximating the singular potential by everywhere defined functions, in particular by polynomial functions, are addressed, with examples demonstrating the failure of the Taylor approximation to preserve relevant shape properties of the singular potential.

Phononic band gaps and phase singularities in the ultrasonic response from toughened composites

NASA Astrophysics Data System (ADS)

Smith, Robert A.; Nelson, Luke J.; Mienczakowski, Martin J.

2018-04-01

Ultrasonic 3D characterization of ply-level features in layered composites, such as out-of-plane wrinkles and ply drops, is now possible with carefully applied analytic-signal analysis. Study of instantaneous amplitude, phase and frequency in the ultrasonic response has revealed some interesting effects, which become more problematic for 3D characterization as the inter-ply resin-layer thicknesses increase. In modern particle-toughened laminates, the thicker resin layers cause phase singularities to be observed; these are locations where the instantaneous amplitude is zero, so the instantaneous phase is undefined. The depth at which these occur has been observed experimentally to vary with resin- layer thickness, such that a phase-singularity surface is formed; beyond this surface, the ultrasonic response is reduced and significantly more difficult to interpret, so a method for removing the effect would be advantageous. The underlying physics has been studied using an analytical one-dimensional multi-layer model. This has been sufficient to determine that the cause is linked to a phononic band gap in the ultrasound transmitted through multiple equally-spaced partial reflectors. As a result, the phase singularity also depends on input-pulse center frequency and bandwidth. Various methods for overcoming the confusing effects in the data have been proposed and subsequently investigated using the analytical model. This paper will show experimental and modelled evidence of phase-singularities and phase-singularity surfaces, as well as the success of methods for reducing their effects.

Singularity detection by wavelet approach: application to electrocardiogram signal

NASA Astrophysics Data System (ADS)

Jalil, Bushra; Beya, Ouadi; Fauvet, Eric; Laligant, Olivier

2010-01-01

In signal processing, the region of abrupt changes contains the most of the useful information about the nature of the signal. The region or the points where these changes occurred are often termed as singular point or singular region. The singularity is considered to be an important character of the signal, as it refers to the discontinuity and interruption present in the signal and the main purpose of the detection of such singular point is to identify the existence, location and size of those singularities. Electrocardiogram (ECG) signal is used to analyze the cardiovascular activity in the human body. However the presence of noise due to several reasons limits the doctor's decision and prevents accurate identification of different pathologies. In this work we attempt to analyze the ECG signal with energy based approach and some heuristic methods to segment and identify different signatures inside the signal. ECG signal has been initially denoised by empirical wavelet shrinkage approach based on Steins Unbiased Risk Estimate (SURE). At the second stage, the ECG signal has been analyzed by Mallat approach based on modulus maximas and Lipschitz exponent computation. The results from both approaches has been discussed and important aspects has been highlighted. In order to evaluate the algorithm, the analysis has been done on MIT-BIH Arrhythmia database; a set of ECG data records sampled at a rate of 360 Hz with 11 bit resolution over a 10mv range. The results have been examined and approved by medical doctors.

On a 3-D singularity element for computation of combined mode stress intensities

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Generation of phase edge singularities by coplanar three-beam interference and their detection.

PubMed

Patorski, Krzysztof; Sluzewski, Lukasz; Trusiak, Maciej; Pokorski, Krzysztof

2017-02-06

In recent years singular optics has gained considerable attention in science and technology. Up to now optical vortices (phase point dislocations) have been of main interest. This paper presents the first general analysis of formation of phase edge singularities by coplanar three-beam interference. They can be generated, for example, by three-slit interference or self-imaging in the Fresnel diffraction field of a sinusoidal grating. We derive a general condition for the ratio of amplitudes of interfering beams resulting in phase edge dislocations, lateral separation of dislocations depends on this ratio as well. Analytically derived properties are corroborated by numerical and experimental studies. We develop a simple, robust, common path optical self-imaging configuration aided by a coherent tilted reference wave and spatial filtering. Finally, we propose an automatic fringe pattern analysis technique for detecting phase edge dislocations, based on the continuous wavelet transform. Presented studies open new possibilities for developing grating based sensing techniques for precision metrology of very small phase differences.

Resistive MHD Stability Analysis in Near Real-time

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen

2017-10-01

We discuss the feasibility of a near real-time calculation of the tokamak Δ' matrix, which summarizes MHD stability to resistive modes, such as tearing and interchange modes. As the operational phase of ITER approaches, solutions for active feedback tokamak stability control are needed. It has been previously demonstrated that an ideal MHD stability analysis is achievable on a sub- O (1 s) timescale, as is required to control phenomena comparable with the MHD-evolution timescale of ITER. In the present work, we broaden this result to incorporate the effects of resistive MHD modes. Such modes satisfy ideal MHD equations in regions outside narrow resistive layers that form at singular surfaces. We demonstrate that the use of asymptotic expansions at the singular surfaces, as well as the application of state transition matrices, enable a fast, parallelized solution to the singular outer layer boundary value problem, and thereby rapidly compute Δ'. Sponsored by US DOE under DE-SC0015878 and DE-FC02-04ER54698.

Embedding Dimension Selection for Adaptive Singular Spectrum Analysis of EEG Signal.

PubMed

Xu, Shanzhi; Hu, Hai; Ji, Linhong; Wang, Peng

2018-02-26

The recorded electroencephalography (EEG) signal is often contaminated with different kinds of artifacts and noise. Singular spectrum analysis (SSA) is a powerful tool for extracting the brain rhythm from a noisy EEG signal. By analyzing the frequency characteristics of the reconstructed component (RC) and the change rate in the trace of the Toeplitz matrix, it is demonstrated that the embedding dimension is related to the frequency bandwidth of each reconstructed component, in consistence with the component mixing in the singular value decomposition step. A method for selecting the embedding dimension is thereby proposed and verified by simulated EEG signal based on the Markov Process Amplitude (MPA) EEG Model. Real EEG signal is also collected from the experimental subjects under both eyes-open and eyes-closed conditions. The experimental results show that based on the embedding dimension selection method, the alpha rhythm can be extracted from the real EEG signal by the adaptive SSA, which can be effectively utilized to distinguish between the eyes-open and eyes-closed states.

Multiscale Analysis in the Compressible Rotating and Heat Conducting Fluids

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Maltese, David; Novotný, Antonín

2017-06-01

We consider the full Navier-Stokes-Fourier system under rotation in the singular regime of small Mach and Rossby, and large Reynolds and Péclet numbers, with ill prepared initial data on an infinite straight 3-D layer rotating with respect to the axis orthogonal to the layer. We perform the singular limit in the framework of weak solutions and identify the 2-D Euler-Boussinesq system as the target problem.

Singular-value demodulation of phase-shifted holograms.

PubMed

Lopes, Fernando; Atlan, Michael

2015-06-01

We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.

Comparison of two SVD-based color image compression schemes.

PubMed

Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli

2017-01-01

Color image compression is a commonly used process to represent image data as few bits as possible, which removes redundancy in the data while maintaining an appropriate level of quality for the user. Color image compression algorithms based on quaternion are very common in recent years. In this paper, we propose a color image compression scheme, based on the real SVD, named real compression scheme. First, we form a new real rectangular matrix C according to the red, green and blue components of the original color image and perform the real SVD for C. Then we select several largest singular values and the corresponding vectors in the left and right unitary matrices to compress the color image. We compare the real compression scheme with quaternion compression scheme by performing quaternion SVD using the real structure-preserving algorithm. We compare the two schemes in terms of operation amount, assignment number, operation speed, PSNR and CR. The experimental results show that with the same numbers of selected singular values, the real compression scheme offers higher CR, much less operation time, but a little bit smaller PSNR than the quaternion compression scheme. When these two schemes have the same CR, the real compression scheme shows more prominent advantages both on the operation time and PSNR.

Comparison of two SVD-based color image compression schemes

PubMed Central

Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli

2017-01-01

Color image compression is a commonly used process to represent image data as few bits as possible, which removes redundancy in the data while maintaining an appropriate level of quality for the user. Color image compression algorithms based on quaternion are very common in recent years. In this paper, we propose a color image compression scheme, based on the real SVD, named real compression scheme. First, we form a new real rectangular matrix C according to the red, green and blue components of the original color image and perform the real SVD for C. Then we select several largest singular values and the corresponding vectors in the left and right unitary matrices to compress the color image. We compare the real compression scheme with quaternion compression scheme by performing quaternion SVD using the real structure-preserving algorithm. We compare the two schemes in terms of operation amount, assignment number, operation speed, PSNR and CR. The experimental results show that with the same numbers of selected singular values, the real compression scheme offers higher CR, much less operation time, but a little bit smaller PSNR than the quaternion compression scheme. When these two schemes have the same CR, the real compression scheme shows more prominent advantages both on the operation time and PSNR. PMID:28257451

Optimal trajectory planning of free-floating space manipulator using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Fang, Jing; Yuan, Jianping

2018-03-01

The existence of the path dependent dynamic singularities limits the volume of available workspace of free-floating space robot and induces enormous joint velocities when such singularities are met. In order to overcome this demerit, this paper presents an optimal joint trajectory planning method using forward kinematics equations of free-floating space robot, while joint motion laws are delineated with application of the concept of reaction null-space. Bézier curve, in conjunction with the null-space column vectors, are applied to describe the joint trajectories. Considering the forward kinematics equations of the free-floating space robot, the trajectory planning issue is consequently transferred to an optimization issue while the control points to construct the Bézier curve are the design variables. A constrained differential evolution (DE) scheme with premature handling strategy is implemented to find the optimal solution of the design variables while specific objectives and imposed constraints are satisfied. Differ from traditional methods, we synthesize null-space and specialized curve to provide a novel viewpoint for trajectory planning of free-floating space robot. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a free-floating spacecraft and demonstrate the feasibility and effectiveness of the proposed method.

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

USGS Publications Warehouse

Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.

2011-01-01

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.

On the Convergence of Stresses in Fretting Fatigue

PubMed Central

Pereira, Kyvia; Bordas, Stephane; Tomar, Satyendra; Trobec, Roman; Depolli, Matjaz; Kosec, Gregor; Abdel Wahab, Magd

2016-01-01

Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy. PMID:28773760

Do sewn up singularities falsify the Palatini cosmology?

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander; Borowiec, Andrzej; Wojnar, Aneta

2016-10-01

We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R+γ R^2 in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the Ω _{γ } > 0 is favored by data only very small values of Ω _{γ } parameter are allowed if we require agreement with the Λ CDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of Ω _γ cannot be rejected. Therefore, observation data favor the universe without the ghost states (f'(hat{R})>0) and tachyons (f''(hat{R})>0).

Multiset singular value decomposition for joint analysis of multi-modal data: application to fingerprint analysis

NASA Astrophysics Data System (ADS)

Emge, Darren K.; Adalı, Tülay

2014-06-01

As the availability and use of imaging methodologies continues to increase, there is a fundamental need to jointly analyze data that is collected from multiple modalities. This analysis is further complicated when, the size or resolution of the images differ, implying that the observation lengths of each of modality can be highly varying. To address this expanding landscape, we introduce the multiset singular value decomposition (MSVD), which can perform a joint analysis on any number of modalities regardless of their individual observation lengths. Through simulations, the inter modal relationships across the different modalities which are revealed by the MSVD are shown. We apply the MSVD to forensic fingerprint analysis, showing that MSVD joint analysis successfully identifies relevant similarities for further analysis, significantly reducing the processing time required. This reduction, takes this technique from a laboratory method to a useful forensic tool with applications across the law enforcement and security regimes.

Finite-time singularities in the dynamics of hyperinflation in an economy.

PubMed

Szybisz, Martín A; Szybisz, Leszek

2009-08-01

The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t), changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time t(c). By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t) approximately (t(c)-t)(-alpha) (with alpha>0 ) and the other exhibits a logarithmic divergence, p(t) approximately ln[1/(t(c)-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.

The Semantics of Plurals: A Defense of Singularism

ERIC Educational Resources Information Center

Florio, Salvatore

2010-01-01

In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

Formation of turbulence around flow singularities

NASA Technical Reports Server (NTRS)

Zak, M.

1983-01-01

The formation of turbulence around singular points of a flow such as stagnation points, tangential jumps of velocity, are analyzed. It is proved that turbulence is inevitably generated by the rear stagnation point, but cannot be generated by the nose stagnation point of a streamlined body. Special attention is paid to an evolution of turbulence induced by a tangential jump of velocity. A qualitative analysis of a turbulent flow between two rotating concentric cylinders and around a streamlined cylinder is given.

Black holes in loop quantum gravity: the complete space-time.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2008-10-17

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Robustness analysis of multirate and periodically time varying systems

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1991-01-01

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1977-01-01

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Recent developments in rotary-wing aerodynamic theory

NASA Technical Reports Server (NTRS)

Johnson, W.

1986-01-01

Current progress in the computational analysis of rotary-wing flowfields is surveyed, and some typical results are presented in graphs. Topics examined include potential theory, rotating coordinate systems, lifting-surface theory (moving singularity, fixed wing, and rotary wing), panel methods (surface singularity representations, integral equations, and compressible flows), transonic theory (the small-disturbance equation), wake analysis (hovering rotor-wake models and transonic blade-vortex interaction), limitations on computational aerodynamics, and viscous-flow methods (dynamic-stall theories and lifting-line theory). It is suggested that the present algorithms and advanced computers make it possible to begin working toward the ultimate goal of turbulent Navier-Stokes calculations for an entire rotorcraft.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Emerging spectra of singular correlation matrices under small power-map deformations

NASA Astrophysics Data System (ADS)

Vinayak; Schäfer, Rudi; Seligman, Thomas H.

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Emerging spectra of singular correlation matrices under small power-map deformations.

PubMed

Vinayak; Schäfer, Rudi; Seligman, Thomas H

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Three-dimensional separation and reattachment

NASA Technical Reports Server (NTRS)

Peake, D. J.; Tobak, M.

1982-01-01

The separation of three dimensional turbulent boundary layers from the lee of flight vehicles at high angles of attack is investigated. The separation results in dominant, large scale, coiled vortex motions that pass along the body in the general direction of the free stream. In all cases of three dimensional flow separation and reattachment, the assumption of continuous vector fields of skin friction lines and external flow streamlines, coupled with simple laws of topology, provides a flow grammar whose elemental constituents are the singular points: the nodes, spiral nodes (foci), and saddles. The phenomenon of three dimensional separation may be construed as either a local or a global event, depending on whether the skin friction line that becomes a line of separation originates at a node or a saddle point.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

Self-consistent approach to many-body localization and subdiffusion

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Herbrych, J.

2017-07-01

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization. Results show a qualitative agreement with the numerically obtained dynamical structure factor in the whole range of frequencies and wave vectors, as well as across the transition to nonergodic behavior. The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity σ (ω ) ∝|ω| α , i.e., with vanishing dc limit σ0=0 and α <1 varying with disorder, while we get α >1 in the localized phase.

Three-dimensional interactions and vortical flows with emphasis on high speeds

NASA Technical Reports Server (NTRS)

Peake, D. J.; Tobak, M.

1980-01-01

Diverse kinds of three-dimensional regions of separation in laminar and turbulent boundary layers are discussed that exist on lifting aerodynamic configurations immersed in flows from subsonic to hypersonic speeds. In all cases of three dimensional flow separation, the assumption of continuous vector fields of skin-friction lines and external-flow streamlines, coupled with simple topology laws, provides a flow grammar whose elemental constituents are the singular points: nodes, foci, and saddles. Adopting these notions enables one to create sequences of plausible flow structures, to deduce mean flow characteristics, expose flow mechanisms, and to aid theory and experiment where lack of resolution in numerical calculations or wind tunnel observation causes imprecision in diagnosing the three dimensional flow features.

Differential Kinematics Of Contemporary Industrial Robots

NASA Astrophysics Data System (ADS)

Szkodny, T.

2014-08-01

The paper presents a simple method of avoiding singular configurations of contemporary industrial robot manipulators of such renowned companies as ABB, Fanuc, Mitsubishi, Adept, Kawasaki, COMAU and KUKA. To determine the singular configurations of these manipulators a global form of description of the end-effector kinematics was prepared, relative to the other links. On the basis of this description , the formula for the Jacobian was defined in the end-effector coordinates. Next, a closed form of the determinant of the Jacobian was derived. From the formula, singular configurations, where the determinant's value equals zero, were determined. Additionally, geometric interpretations of these configurations were given and they were illustrated. For the exemplary manipulator, small corrections of joint variables preventing the reduction of the Jacobian order were suggested. An analysis of positional errors, caused by these corrections, was presented

Integrated tools for control-system analysis

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Proffitt, Melissa S.; Clark, David R.

1989-01-01

The basic functions embedded within a user friendly software package (MATRIXx) are used to provide a high level systems approach to the analysis of linear control systems. Various control system analysis configurations are assembled automatically to minimize the amount of work by the user. Interactive decision making is incorporated via menu options and at selected points, such as in the plotting section, by inputting data. There are five evaluations such as the singular value robustness test, singular value loop transfer frequency response, Bode frequency response, steady-state covariance analysis, and closed-loop eigenvalues. Another section describes time response simulations. A time response for random white noise disturbance is available. The configurations and key equations used for each type of analysis, the restrictions that apply, the type of data required, and an example problem are described. One approach for integrating the design and analysis tools is also presented.

Naked singularity resolution in cylindrical collapse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurita, Yasunari; Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502; Nakao, Ken-ichi

In this paper, we study the gravitational collapse of null dust in cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the backreaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the nakedmore » singularity. In this case, although this naked singularity satisfies the strong curvature condition by Krolak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore, we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally, the singularity completely disappears and the flat spacetime remains.« less

Intangible pointlike tracers for liquid-crystal-based microsensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brasselet, Etienne; Juodkazis, Saulius

2010-12-15

We propose an optical detection technique for liquid-crystal-based sensors that is based on polarization-resolved tracking of optical singularities and does not rely on standard observation of light-intensity changes caused by modifications of the liquid crystal orientational ordering. It uses a natural two-dimensional network of polarization singularities embedded in the transverse cross section of a probe beam that passes through a liquid crystal sample, in our case, a nematic droplet held in laser tweezers. The identification and spatial evolution of such a topological fingerprint is retrieved from subwavelength polarization-resolved imaging, and the mechanical constraint exerted on the molecular ordering by themore » trapping beam itself is chosen as the control parameter. By restricting our analysis to one type of point singularity, C points, which correspond to location in space where the polarization azimuth is undefined, we show that polarization singularities appear as intangible pointlike tracers for liquid-crystal-based three-dimensional microsensors. The method has a superresolution potential and can be used to visualize changes at the nanoscale.« less

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.

PubMed

Pang, Xiaoyan; Gbur, Greg; Visser, Taco D

2015-12-28

It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated. This arrangement serves to clarify the relationships between the different singularity types, and provides a simple tool for further exploration.

Vibrations of Bladed Disk Assemblies

DTIC Science & Technology

1991-03-29

34, Contract Report to Gas Trubines, General Motors Corp., Indianapolis (31 pages). 3 Afolabi, D., 1982, "Some Vibration Characteristics of an Aeroengine ...10. SOUACIOFPUNOiNG NO. Bolling Air Force Base PROGRAM 0mo.0aC-r TASK "o mW Washington, D.C. 20332-6448 1 LFAANT NO. No. N. O Vibrations of Bladed Disk...identfy by loC* n u r) 011LO . 0.ou* sum G. Blade vibrations , singularity theory, singular perturbation analysis, mode localization iS. AST.OACT

Spectral analysis of a family of binary inflation rules

NASA Astrophysics Data System (ADS)

Baake, Michael; Grimm, Uwe; Mañibo, Neil

2018-01-01

The family of primitive binary substitutions defined by 1 \\mapsto 0 \\mapsto 0 1^m with m\\in N is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles (intervals) of natural length. Apart from the well-known Fibonacci inflation (m=1 ), the inflation rules either have integer inflation factors, but non-constant length, or are of non-Pisot type. We show that all of them have singular diffraction, either of pure point type or essentially singular continuous.

Application of reiteration of Hankel singular value decomposition in quality control

NASA Astrophysics Data System (ADS)

Staniszewski, Michał; Skorupa, Agnieszka; Boguszewicz, Łukasz; Michalczuk, Agnieszka; Wereszczyński, Kamil; Wicher, Magdalena; Konopka, Marek; Sokół, Maria; Polański, Andrzej

2017-07-01

Medical centres are obliged to store past medical records, including the results of quality assurance (QA) tests of the medical equipment, which is especially useful in checking reproducibility of medical devices and procedures. Analysis of multivariate time series is an important part of quality control of NMR data. In this work we proposean anomaly detection tool based on Reiteration of Hankel Singular Value Decomposition method. The presented method was compared with external software and authors obtained comparable results.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Workshop on Condition Based Maintenance Held in Atlantic Beach, North Carolina on November 15 - 17, 1993

DTIC Science & Technology

1993-11-17

pounds of Torque Over Three Minutes Continuous Operation IYMCO1A 14 DMAE Corporation C-130 Engine Gearbox January 19925 Stress Wave Analysis - I in’. I...FaUi.O The CBM needs associated with surface initiated failure mechanisms can be divided into I singular defects and low (h/a) operation. Singular defec-t...These include nicks, scratches, corrosion pits and dents caused by third’ body particles (hard or soft). These defects cause local stress risers

On important precursor of singular optics (tutorial)

NASA Astrophysics Data System (ADS)

Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.

2018-01-01

The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].

Principal Components Analysis Studies of Martian Clouds

NASA Astrophysics Data System (ADS)

Klassen, D. R.; Bell, J. F., III

2001-11-01

We present the principal components analysis (PCA) of absolutely calibrated multi-spectral images of Mars as a function of Martian season. The PCA technique is a mathematical rotation and translation of the data from a brightness/wavelength space to a vector space of principal ``traits'' that lie along the directions of maximal variance. The first of these traits, accounting for over 90% of the data variance, is overall brightness and represented by an average Mars spectrum. Interpretation of the remaining traits, which account for the remaining ~10% of the variance, is not always the same and depends upon what other components are in the scene and thus, varies with Martian season. For example, during seasons with large amounts of water ice in the scene, the second trait correlates with the ice and anti-corrlates with temperature. We will investigate the interpretation of the second, and successive important PCA traits. Although these PCA traits are orthogonal in their own vector space, it is unlikely that any one trait represents a singular, mineralogic, spectral end-member. It is more likely that there are many spectral endmembers that vary identically to within the noise level, that the PCA technique will not be able to distinguish them. Another possibility is that similar absorption features among spectral endmembers may be tied to one PCA trait, for example ''amount of 2 \\micron\\ absorption''. We thus attempt to extract spectral endmembers by matching linear combinations of the PCA traits to USGS, JHU, and JPL spectral libraries as aquired through the JPL Aster project. The recovered spectral endmembers are then linearly combined to model the multi-spectral image set. We present here the spectral abundance maps of the water ice/frost endmember which allow us to track Martian clouds and ground frosts. This work supported in part through NASA Planetary Astronomy Grant NAG5-6776. All data gathered at the NASA Infrared Telescope Facility in collaboration with the telescope operators and with thanks to the support staff and day crew.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Local performance optimization for a class of redundant eight-degree-of-freedom manipulators

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1994-01-01

Local performance optimization for joint limit avoidance and manipulability maximization (singularity avoidance) is obtained by using the Jacobian matrix pseudoinverse and by projecting the gradient of an objective function into the Jacobian null space. Real-time redundancy optimization control is achieved for an eight-joint redundant manipulator having a three-axis spherical shoulder, a single elbow joint, and a four-axis spherical wrist. Symbolic solutions are used for both full-Jacobian and wrist-partitioned pseudoinverses, partitioned null-space projection matrices, and all objective function gradients. A kinematic limitation of this class of manipulators and the limitation's effect on redundancy resolution are discussed. Results obtained with graphical simulation are presented to demonstrate the effectiveness of local redundant manipulator performance optimization. Actual hardware experiments performed to verify the simulated results are also discussed. A major result is that the partitioned solution is desirable because of low computation requirements. The partitioned solution is suboptimal compared with the full solution because translational and rotational terms are optimized separately; however, the results show that the difference is not significant. Singularity analysis reveals that no algorithmic singularities exist for the partitioned solution. The partitioned and full solutions share the same physical manipulator singular conditions. When compared with the full solution, the partitioned solution is shown to be ill-conditioned in smaller neighborhoods of the shared singularities.

Evolution of singularities in a partially coherent vortex beam.

PubMed

van Dijk, Thomas; Visser, Taco D

2009-04-01

We study the evolution of phase singularities and coherence singularities in a Laguerre-Gauss beam that is rendered partially coherent by letting it pass through a spatial light modulator. The original beam has an on-axis minumum of intensity--a phase singularity--that transforms into a maximum of the far-field intensity. In contrast, although the original beam has no coherence singularities, such singularities are found to develop as the beam propagates. This disappearance of one kind of singularity and the gradual appearance of another is illustrated with numerical examples.

The relationship between two fast/slow analysis techniques for bursting oscillations

PubMed Central

Teka, Wondimu; Tabak, Joël; Bertram, Richard

2012-01-01

Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. In this article, we investigate the relationships between the key structures of the two analysis techniques. We find that the z-curve and Hopf bifurcation of the two-fast/one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow. PMID:23278052

Deep learning for classification of islanding and grid disturbance based on multi-resolution singular spectrum entropy

NASA Astrophysics Data System (ADS)

Li, Tie; He, Xiaoyang; Tang, Junci; Zeng, Hui; Zhou, Chunying; Zhang, Nan; Liu, Hui; Lu, Zhuoxin; Kong, Xiangrui; Yan, Zheng

2018-02-01

Forasmuch as the distinguishment of islanding is easy to be interfered by grid disturbance, island detection device may make misjudgment thus causing the consequence of photovoltaic out of service. The detection device must provide with the ability to differ islanding from grid disturbance. In this paper, the concept of deep learning is introduced into classification of islanding and grid disturbance for the first time. A novel deep learning framework is proposed to detect and classify islanding or grid disturbance. The framework is a hybrid of wavelet transformation, multi-resolution singular spectrum entropy, and deep learning architecture. As a signal processing method after wavelet transformation, multi-resolution singular spectrum entropy combines multi-resolution analysis and spectrum analysis with entropy as output, from which we can extract the intrinsic different features between islanding and grid disturbance. With the features extracted, deep learning is utilized to classify islanding and grid disturbance. Simulation results indicate that the method can achieve its goal while being highly accurate, so the photovoltaic system mistakenly withdrawing from power grids can be avoided.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

A mesoscale connectome of the mouse brain

PubMed Central

Oh, Seung Wook; Harris, Julie A.; Ng, Lydia; Winslow, Brent; Cain, Nicholas; Mihalas, Stefan; Wang, Quanxin; Lau, Chris; Kuan, Leonard; Henry, Alex M.; Mortrud, Marty T.; Ouellette, Benjamin; Nguyen, Thuc Nghi; Sorensen, Staci A.; Slaughterbeck, Clifford R.; Wakeman, Wayne; Li, Yang; Feng, David; Ho, Anh; Nicholas, Eric; Hirokawa, Karla E.; Bohn, Phillip; Joines, Kevin M.; Peng, Hanchuan; Hawrylycz, Michael J.; Phillips, John W.; Hohmann, John G.; Wohnoutka, Paul; Gerfen, Charles R.; Koch, Christof; Bernard, Amy; Dang, Chinh; Jones, Allan R.; Zeng, Hongkui

2016-01-01

Comprehensive knowledge of the brain’s wiring diagram is fundamental for understanding how the nervous system processes information at both local and global scales. However, with the singular exception of the C. elegans microscale connectome, there are no complete connectivity data sets in other species. Here we report a brain-wide, cellular-level, mesoscale connectome for the mouse. The Allen Mouse Brain Connectivity Atlas uses enhanced green fluorescent protein (EGFP)-expressing adeno-associated viral vectors to trace axonal projections from defined regions and cell types, and high-throughput serial two-photon tomography to image the EGFP-labelled axons throughout the brain. This systematic and standardized approach allows spatial registration of individual experiments into a common three dimensional (3D) reference space, resulting in a whole-brain connectivity matrix. A computational model yields insights into connectional strength distribution, symmetry and other network properties. Virtual tractography illustrates 3D topography among interconnected regions. Cortico-thalamic pathway analysis demonstrates segregation and integration of parallel pathways. The Allen Mouse Brain Connectivity Atlas is a freely available, foundational resource for structural and functional investigations into the neural circuits that support behavioural and cognitive processes in health and disease. PMID:24695228

Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Huang, Xiangdi

2017-02-01

One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.

Bearing diagnostics: A method based on differential geometry

NASA Astrophysics Data System (ADS)

Tian, Ye; Wang, Zili; Lu, Chen; Wang, Zhipeng

2016-12-01

The structures around bearings are complex, and the working environment is variable. These conditions cause the collected vibration signals to become nonlinear, non-stationary, and chaotic characteristics that make noise reduction, feature extraction, fault diagnosis, and health assessment significantly challenging. Thus, a set of differential geometry-based methods with superiorities in nonlinear analysis is presented in this study. For noise reduction, the Local Projection method is modified by both selecting the neighborhood radius based on empirical mode decomposition and determining noise subspace constrained by neighborhood distribution information. For feature extraction, Hessian locally linear embedding is introduced to acquire manifold features from the manifold topological structures, and singular values of eigenmatrices as well as several specific frequency amplitudes in spectrograms are extracted subsequently to reduce the complexity of the manifold features. For fault diagnosis, information geometry-based support vector machine is applied to classify the fault states. For health assessment, the manifold distance is employed to represent the health information; the Gaussian mixture model is utilized to calculate the confidence values, which directly reflect the health status. Case studies on Lorenz signals and vibration datasets of bearings demonstrate the effectiveness of the proposed methods.

A multiple maximum scatter difference discriminant criterion for facial feature extraction.

PubMed

Song, Fengxi; Zhang, David; Mei, Dayong; Guo, Zhongwei

2007-12-01

Maximum scatter difference (MSD) discriminant criterion was a recently presented binary discriminant criterion for pattern classification that utilizes the generalized scatter difference rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing small-sample-size problems. MSD classifiers based on this criterion have been quite effective on face-recognition tasks, but as they are binary classifiers, they are not as efficient on large-scale classification tasks. To address the problem, this paper generalizes the classification-oriented binary criterion to its multiple counterpart--multiple MSD (MMSD) discriminant criterion for facial feature extraction. The MMSD feature-extraction method, which is based on this novel discriminant criterion, is a new subspace-based feature-extraction method. Unlike most other subspace-based feature-extraction methods, the MMSD computes its discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. The MMSD is theoretically elegant and easy to calculate. Extensive experimental studies conducted on the benchmark database, FERET, show that the MMSD out-performs state-of-the-art facial feature-extraction methods such as null space method, direct linear discriminant analysis (LDA), eigenface, Fisherface, and complete LDA.

Naked singularity, firewall, and Hawking radiation.

PubMed

Zhang, Hongsheng

2017-06-21

Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

On the Weyl curvature hypothesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoica, Ovidiu Cristinel, E-mail: holotronix@gmail.com

2013-11-15

The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein’s equation, which extends it and remains valid at an important class of singularities (including in particular the Schwarzschild, FLRW, and isotropic singularities). Here it is shown that if the Big-Bang singularity is from this class, it also satisfies the Weyl curvature hypothesis. As an application, we study a very general example of cosmologicalmore » models, which generalizes the FLRW model by dropping the isotropy and homogeneity constraints. This model also generalizes isotropic singularities, and a class of singularities occurring in Bianchi cosmologies. We show that the Big-Bang singularity of this model is of the type under consideration, and satisfies therefore the Weyl curvature hypothesis. -- Highlights: •The singularities we introduce are described by finite geometric/physical objects. •Our singularities have smooth Riemann and Weyl curvatures. •We show they satisfy Penrose’s Weyl curvature hypothesis (Weyl=0 at singularities). •Examples: FLRW, isotropic singularities, an extension of Schwarzschild’s metric. •Example: a large class of singularities which may be anisotropic and inhomogeneous.« less

Analysis of the cable equation with non-local and non-singular kernel fractional derivative

NASA Astrophysics Data System (ADS)

Karaagac, Berat

2018-02-01

Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.

Horizon quantum fuzziness for non-singular black holes

NASA Astrophysics Data System (ADS)

Giugno, Andrea; Giusti, Andrea; Helou, Alexis

2018-03-01

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

Low-energy effective worldsheet theory of a non-Abelian vortex in high-density QCD revisited: A regular gauge construction

NASA Astrophysics Data System (ADS)

Chatterjee, Chandrasekhar; Nitta, Muneto

2017-04-01

Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the C P2 model [1,2]. Here, we reconstruct the effective theory in a regular gauge without taking a singular gauge, confirming the previous results in the singular gauge. As a byproduct of our analysis, we find that non-Abelian vortices in high-density QCD do not suffer from any obstruction for the global definition of a symmetry breaking.

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

PubMed Central

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods. PMID:18567005

Theoretical analysis of linearized acoustics and aerodynamics of advanced supersonic propellers

NASA Technical Reports Server (NTRS)

Farassat, F.

1985-01-01

The derivation of a formula for prediction of the noise of supersonic propellers using time domain analysis is presented. This formula is a solution of the Ffowcs Williams-Hawkings equation and does not have the Doppler singularity of some other formulations. The result presented involves some surface integrals over the blade and line integrals over the leading and trailing edges. The blade geometry, motion and surface pressure are needed for noise calculation. To obtain the blade surface pressure, the observer is moved onto the blade surface and a linear singular integral equation is derived which can be solved numerically. Two examples of acoustic calculations using a computer program are currently under development.

SIGN SINGULARITY AND FLARES IN SOLAR ACTIVE REGION NOAA 11158

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sorriso-Valvo, L.; De Vita, G.; Kazachenko, M. D.

Solar Active Region NOAA 11158 has hosted a number of strong flares, including one X2.2 event. The complexity of current density and current helicity are studied through cancellation analysis of their sign-singular measure, which features power-law scaling. Spectral analysis is also performed, revealing the presence of two separate scaling ranges with different spectral index. The time evolution of parameters is discussed. Sudden changes of the cancellation exponents at the time of large flares and the presence of correlation with Extreme-Ultra-Violet and X-ray flux suggest that eruption of large flares can be linked to the small-scale properties of the current structures.

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

The geometry of singularities and the black hole information paradox

NASA Astrophysics Data System (ADS)

Stoica, O. C.

2015-07-01

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have nonsingular electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.

PubMed

Sochat, Vanessa V; Prybol, Cameron J; Kurtzer, Gregory M

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers

PubMed Central

Prybol, Cameron J.; Kurtzer, Gregory M.

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub’s primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers. PMID:29186161

Big bounce with finite-time singularity: The F(R) gravity description

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.

An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point in the context of F(R) modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce do not produce a scale-invariant spectrum and also the short wavelength modes after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result indicating that the singular bounce theory is unstable at the singularity point for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.

Multifractal and Singularity Maps of soil surface moisture distribution derived from 2D image analysis.

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Millán, Humberto; Martín-Sotoca, Juan Jose; Pérez Soto, Luis; Sanchez, Maria Elena; Tarquis, Ana Maria

2016-04-01

Soil moisture distribution usually presents extreme variation at multiple spatial scales. Image analysis could be a useful tool for investigating these spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to describe the local scaling of apparent soil moisture distribution and (ii) to define apparent soil moisture patterns from vertical planes of Vertisol pit images. Two soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. One was excavated in April/2011 and the other pit was established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. For more details see Cumbrera et al. (2012). Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, using the concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012). This method is based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. We have applied it to each soil image. The results show that, in spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used to study the dynamical change of soil moisture sampling in agreement with previous results (Millán et al., 2016). REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Cumbrera, R., Ana M. Tarquis, Gabriel Gascó, Humberto Millán (2012) Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images. Journal of Hydrology (452-453), 205-212. Martin Sotoca; J.J. Antonio Saa-Requejo, Juan Grau and Ana M. Tarquis (2016). Segmentation of singularity maps in the context of soil porosity. Geophysical Research Abstracts, 18, EGU2016-11402. Millán, H., Cumbrera, R. and Ana M. Tarquis (2016) Multifractal and Levy-stable statistics of soil surface moisture distribution derived from 2D image analysis. Applied Mathematical Modelling, 40(3), 2384-2395.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2007-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine's performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2007-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least-squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2005-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends upon knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined which accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Strong lensing probability in TeVeS (tensor-vector-scalar) theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Daming, E-mail: cdm@bao.ac.cn

2008-01-15

We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with {Omega}{sub b} = 0.04 and {Omega}{sub {Lambda}} = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We comparemore » our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function {mu}(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.« less

Singular Stokes-polarimetry as new technique for metrology and inspection of polarized speckle fields

NASA Astrophysics Data System (ADS)

Soskin, Marat S.; Denisenko, Vladimir G.; Egorov, Roman I.

2004-08-01

Polarimetry is effective technique for polarized light fields characterization. It was shown recently that most full "finger-print" of light fields with arbitrary complexity is network of polarization singularities: C points with circular polarization and L lines with variable azimuth. The new singular Stokes-polarimetry was elaborated for such measurements. It allows define azimuth, eccentricity and handedness of elliptical vibrations in each pixel of receiving CCD camera in the range of mega-pixels. It is based on precise measurement of full set of Stokes parameters by the help of high quality analyzers and quarter-wave plates with λ/500 preciseness and 4" adjustment. The matrices of obtained data are processed in PC by special programs to find positions of polarization singularities and other needed topological features. The developed SSP technique was proved successfully by measurements of topology of polarized speckle-fields produced by multimode "photonic-crystal" fibers, double side rubbed polymer films, biomedical samples. Each singularity is localized with preciseness up to +/- 1 pixel in comparison with 500 pixels dimensions of typical speckle. It was confirmed that network of topological features appeared in polarized light field after its interaction with specimen under inspection is exact individual "passport" for its characterization. Therefore, SSP can be used for smart materials characterization. The presented data show that SSP technique is promising for local analysis of properties and defects of thin films, liquid crystal cells, optical elements, biological samples, etc. It is able discover heterogeneities and defects, which define essentially merits of specimens under inspection and can"t be checked by usual polarimetry methods. The detected extra high sensitivity of polarization singularities position and network to any changes of samples position and deformation opens quite new possibilities for sensing of deformations and displacement of checked elements in the sub-micron range.

Physics of singularities in pressure-impulse theory

NASA Astrophysics Data System (ADS)

Krechetnikov, R.

2018-05-01

The classical solution in the pressure-impulse theory for the inviscid, incompressible, and zero-surface-tension water impact of a flat plate at zero dead-rise angle exhibits both singular-in-time initial fluid acceleration, ∂v /∂ t |t =0˜δ (t ) , and a near-plate-edge spatial singularity in the velocity distribution, v ˜r-1 /2 , where r is the distance from the plate edge. The latter velocity divergence also leads to the interface being stretched infinitely right after the impact, which is another nonphysical artifact. From the point of view of matched asymptotic analysis, this classical solution is a singular limit when three physical quantities achieve limiting values: sound speed c0→∞ , fluid kinematic viscosity ν →0 , and surface tension σ →0 . This leaves open a question on how to resolve these singularities mathematically by including the neglected physical effects—compressibility, viscosity, and surface tension—first one by one and then culminating in the local compressible viscous solution valid for t →0 and r →0 , demonstrating a nontrivial flow structure that changes with the degree of the bulk compressibility. In the course of this study, by starting with the general physically relevant formulation of compressible viscous flow, we clarify the parameter range(s) of validity of the key analytical solutions including classical ones (inviscid incompressible and compressible, etc.) and understand the solution structure, its intermediate asymptotics nature, characteristics influencing physical processes, and the role of potential and rotational flow components. In particular, it is pointed out that sufficiently close to the plate edge surface tension must be taken into account. Overall, the idea is to highlight the interesting physics behind the singularities in the pressure-impulse theory.

Multiscale Resilience of Complex Systems

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, I.; Schertzer, D. J. M.; Giangola-Murzyn, A.; Hoang Cong, T.

2014-12-01

We first argue the need for well defined resilience metrics to better evaluate the resilience of complex systems such as (peri-)urban flood management systems. We review both the successes and limitations of resilience metrics in the framework of dynamical systems and their generalization in the framework of the viability theory. We then point out that the most important step to achieve is to define resilience across scales instead of doing it at a given scale. Our preliminary, critical analysis of the series of attempts to define an operational resilience metrics led us to consider a scale invariant metrics based on the scale independent codimension of extreme singularities. Multifractal downscaling of climate scenarios can be considered as a first illustration. We focussed on a flood scenario evaluation method with the help of two singularities γ_s and γ_Max, corresponding respectively to an effective and a probable maximum singularity, that yield an innovative framework to address the issues of flood resilience systems in a scale independent manner. Indeed, the stationarity of the universal multifractal parameters would result into a rather stable value of probable maximum singularity γ_s. By fixing the limit of acceptability for a maximum flood water depth at a given scale, with a corresponding singularity, we effectively fix the threshold of the probable maximum singularity γ_s as a criterion of the flood resilience we accept. Then various scenarios of flood resilient measures could be simulated with the help of Multi-Hydro under upcoming climat scenarios. The scenarios that result in estimates of either γ_Max or γ_s below the pre-selected γ_s value will assure the effective flood resilience of the whole modeled system across scales. The research for this work was supported, in part, by the EU FP7 SMARTesT and INTERREG IVB RainGain projects.

Dynamic growth of mixed-mode shear cracks

USGS Publications Warehouse

Andrews, D.J.

1994-01-01

A pure mode II (in-plane) shear crack cannot propagate spontaneously at a speed between the Rayleigh and S-wave speeds, but a three-dimensional (3D) or two-dimensional (2D) mixed-mode shear crack can propagate in this range, being driven by the mode III (antiplane) component. Two different analytic solutions have been proposed for the mode II component in this case. The first is the solution valid for crack speed less than the Rayleigh speed. When applied above the Rayleigh speed, it predicts a negative stress intensity factor, which implies that energy is generated at the crack tip. Burridge proposed a second solution, which is continuous at the crack tip, but has a singularity in slip velocity at the Rayleigh wave. Spontaneous propagation of a mixed-mode rupture has been calculated with a slip-weakening friction law, in which the slip velocity vector is colinear with the total traction vector. Spontaneous trans-Rayleigh rupture speed has been found. The solution depends on the absolute stress level. The solution for the in-plane component appears to be a superposition of smeared-out versions of the two analytic solutions. The proportion of the first solution increases with increasing absolute stress. The amplitude of the negative in-plane traction pulse is less than the absolute final sliding traction, so that total in-plane traction does not reverse. The azimuth of the slip velocity vector varies rapidly between the onset of slip and the arrival of the Rayleigh wave. The variation is larger at smaller absolute stress.

Three-dimensional modelling and geothermal process simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burns, K.L.

1990-01-01

The subsurface geological model or 3-D GIS is constructed from three kinds of objects, which are a lithotope (in boundary representation), a number of fault systems, and volumetric textures (vector fields). The chief task of the model is to yield an estimate of the conductance tensors (fluid permeability and thermal conductivity) throughout an array of voxels. This is input as material properties to a FEHM numerical physical process model. The main task of the FEHM process model is to distinguish regions of convective from regions of conductive heat flow, and to estimate the fluid phase, pressure and flow paths. Themore » temperature, geochemical, and seismic data provide the physical constraints on the process. The conductance tensors in the Franciscan Complex are to be derived by the addition of two components. The isotropic component is a stochastic spatial variable due to disruption of lithologies in melange. The deviatoric component is deterministic, due to smoothness and continuity in the textural vector fields. This decomposition probably also applies to the engineering hydrogeological properties of shallow terrestrial fluvial systems. However there are differences in quantity. The isotropic component is much more variable in the Franciscan, to the point where volumetric averages are misleading, and it may be necessary to select that component from several, discrete possible states. The deviatoric component is interpolated using a textural vector field. The Franciscan field is much more complicated, and contains internal singularities. 27 refs., 10 figs.« less

Nested Krylov methods and preserving the orthogonality

NASA Technical Reports Server (NTRS)

Desturler, Eric; Fokkema, Diederik R.

1993-01-01

Recently the GMRESR inner-outer iteraction scheme for the solution of linear systems of equations was proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski and Saad (FGMRES). The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a new direction vector by approximately solving the residual equation. However, the optimality of the approximation over the space of outer search directions is ignored in the inner GMRES iteration. This leads to suboptimal corrections to the solution in the outer iteration, as components of the outer iteration directions may reenter in the inner iteration process. Therefore we propose to preserve the orthogonality relations of GCR in the inner GMRES iteration. This gives optimal corrections; however, it involves working with a singular, non-symmetric operator. We will discuss some important properties, and we will show by experiments that, in terms of matrix vector products, this modification (almost) always leads to better convergence. However, because we do more orthogonalizations, it does not always give an improved performance in CPU-time. Furthermore, we will discuss efficient implementations as well as the truncation possibilities of the outer GCR process. The experimental results indicate that for such methods it is advantageous to preserve the orthogonality in the inner iteration. Of course we can also use iteration schemes other than GMRES as the inner method; methods with short recurrences like GICGSTAB are of interest.

Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1982-01-01

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Performance Analysis of ICA in Sensor Array

PubMed Central

Cai, Xin; Wang, Xiang; Huang, Zhitao; Wang, Fenghua

2016-01-01

As the best-known scheme in the field of Blind Source Separation (BSS), Independent Component Analysis (ICA) has been intensively used in various domains, including biomedical and acoustics applications, cooperative or non-cooperative communication, etc. While sensor arrays are involved in most of the applications, the influence on the performance of ICA of practical factors therein has not been sufficiently investigated yet. In this manuscript, the issue is researched by taking the typical antenna array as an illustrative example. Factors taken into consideration include the environment noise level, the properties of the array and that of the radiators. We analyze the analytic relationship between the noise variance, the source variance, the condition number of the mixing matrix and the optimal signal to interference-plus-noise ratio, as well as the relationship between the singularity of the mixing matrix and practical factors concerned. The situations where the mixing process turns (nearly) singular have been paid special attention to, since such circumstances are critical in applications. Results and conclusions obtained should be instructive when applying ICA algorithms on mixtures from sensor arrays. Moreover, an effective countermeasure against the cases of singular mixtures has been proposed, on the basis of previous analysis. Experiments validating the theoretical conclusions as well as the effectiveness of the proposed scheme have been included. PMID:27164100

An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

NASA Technical Reports Server (NTRS)

Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

2007-01-01

Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO{sub 3} : Fe crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasil'ev, Vasilii I; Soskin, M S

2013-02-28

A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium - neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in amore » chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairs of singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing. (laser optics 2012)« less

Can accretion disk properties observationally distinguish black holes from naked singularities?

NASA Astrophysics Data System (ADS)

Kovács, Z.; Harko, T.

2010-12-01

Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. In the context of stationary and axially symmetrical geometries, a possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around axially-symmetric rotating naked singularities, obtained as solutions of the field equations in the Einstein-massless scalar field theory. A first major difference between rotating naked singularities and Kerr black holes is in the frame dragging effect, the angular velocity of a rotating naked singularity being inversely proportional to its spin parameter. Because of the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities. For specific values of the spin parameter and of the scalar charge, the energy flux from the disk around a rotating naked singularity can exceed by several orders of magnitude the flux from the disk of a Kerr black hole. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation by rotating naked singularities is always higher than the conversion efficiency for black holes, i.e., naked singularities provide a much more efficient mechanism for converting mass into radiation than black holes. Thus, these observational signatures may provide the necessary tools from clearly distinguishing rotating naked singularities from Kerr-type black holes.

Are Singularities Integral to General Theory of Relativity?

NASA Astrophysics Data System (ADS)

Krori, K.; Dutta, S.

2011-11-01

Since the 1960s the general relativists have been deeply obsessed with the possibilities of GTR singularities - blackhole as well as cosmological singularities. Senovilla, for the first time, followed by others, showed that there are cylindrically symmetric cosmological space-times which are free of singularities. On the other hand, Krori et al. have presently shown that spherically symmetric cosmological space-times - which later reduce to FRW space-times may also be free of singularities. Besides, Mitra has in the mean-time come forward with some realistic calculations which seem to rule out the possibility of a blackhole singularity. So whether singularities are integral to GTR seems to come under a shadow.

Maass Forms and Quantum Modular Forms

NASA Astrophysics Data System (ADS)

Rolen, Larry

This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his original definition.

Singular spectrum decomposition of Bouligand-Minkowski fractal descriptors: an application to the classification of texture Images

NASA Astrophysics Data System (ADS)

Florindo, João. Batista

2018-04-01

This work proposes the use of Singular Spectrum Analysis (SSA) for the classification of texture images, more specifically, to enhance the performance of the Bouligand-Minkowski fractal descriptors in this task. Fractal descriptors are known to be a powerful approach to model and particularly identify complex patterns in natural images. Nevertheless, the multiscale analysis involved in those descriptors makes them highly correlated. Although other attempts to address this point was proposed in the literature, none of them investigated the relation between the fractal correlation and the well-established analysis employed in time series. And SSA is one of the most powerful techniques for this purpose. The proposed method was employed for the classification of benchmark texture images and the results were compared with other state-of-the-art classifiers, confirming the potential of this analysis in image classification.

Direct Photon Production at Next-to–Next-to-Leading Order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campbell, John M.; Ellis, R. Keith; Williams, Ciaran

2017-05-01

We present the first calculation of direct photon production at next-to-next-to leading order (NNLO) accuracy in QCD. For this process, although the final state cuts mandate only the presence of a single electroweak boson, the underlying kinematics resembles that of a generic vector boson plus jet topology. In order to regulate the infrared singularities present at this order we use the $N$-jettiness slicing procedure, applied for the first time to a final state that at Born level includes colored partons but no required jet. We compare our predictions to ATLAS 8 TeV data and find that the inclusion of themore » NNLO terms in the perturbative expansion, supplemented by electroweak corrections, provides an excellent description of the data with greatly reduced theoretical uncertainties.« less

Note: Sound recovery from video using SVD-based information extraction

NASA Astrophysics Data System (ADS)

Zhang, Dashan; Guo, Jie; Lei, Xiujun; Zhu, Chang'an

2016-08-01

This note reports an efficient singular value decomposition (SVD)-based vibration extraction approach that recovers sound information in silent high-speed video. A high-speed camera of which frame rates are in the range of 2 kHz-10 kHz is applied to film the vibrating objects. Sub-images cut from video frames are transformed into column vectors and then reconstructed to a new matrix. The SVD of the new matrix produces orthonormal image bases (OIBs) and image projections onto specific OIB can be recovered as understandable acoustical signals. Standard frequencies of 256 Hz and 512 Hz tuning forks are extracted offline from their vibrating surfaces and a 3.35 s speech signal is recovered online from a piece of paper that is stimulated by sound waves within 1 min.

Automatic Seizure Detection in Rats Using Laplacian EEG and Verification with Human Seizure Signals

PubMed Central

Feltane, Amal; Boudreaux-Bartels, G. Faye; Besio, Walter

2012-01-01

Automated detection of seizures is still a challenging problem. This study presents an approach to detect seizure segments in Laplacian electroencephalography (tEEG) recorded from rats using the tripolar concentric ring electrode (TCRE) configuration. Three features, namely, median absolute deviation, approximate entropy, and maximum singular value were calculated and used as inputs into two different classifiers: support vector machines and adaptive boosting. The relative performance of the extracted features on TCRE tEEG was examined. Results are obtained with an overall accuracy between 84.81 and 96.51%. In addition to using TCRE tEEG data, the seizure detection algorithm was also applied to the recorded EEG signals from Andrzejak et al. database to show the efficiency of the proposed method for seizure detection. PMID:23073989

Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi-Pasta-Ulam lattices by the Generalized Alignment Index method

NASA Astrophysics Data System (ADS)

Skokos, C.; Bountis, T.; Antonopoulos, C.

2008-12-01

The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long-time behavior in the case of regular orbits lying on low-dimensional tori. The GALIk indices are applied to rapidly detect chaotic oscillations, identify low-dimensional tori of Fermi-Pasta-Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arroja, Frederico; Chen, Che-Yu; Chen, Pisin

In this work, we investigate O (4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, butmore » there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arroja, Frederico; Chen, Che -Yu; Chen, Pisin

In this study, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but theremore » is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

Imaging a non-singular rotating black hole at the center of the Galaxy

NASA Astrophysics Data System (ADS)

Lamy, F.; Gourgoulhon, E.; Paumard, T.; Vincent, F. H.

2018-06-01

We show that the rotating generalization of Hayward’s non-singular black hole previously studied in the literature is geodesically incomplete, and that its straightforward extension leads to a singular spacetime. We present another extension, which is devoid of any curvature singularity. The obtained metric depends on three parameters and, depending on their values, yields an event horizon or not. These two regimes, named respectively regular rotating Hayward black hole and naked rotating wormhole, are studied both numerically and analytically. In preparation for the upcoming results of the Event Horizon Telescope, the images of an accretion torus around Sgr A*, the supermassive object at the center of the Galaxy, are computed. These images contain, even in the absence of a horizon, a central faint region which bears a resemblance to the shadow of Kerr black holes and emphasizes the difficulty of claiming the existence of an event horizon from the analysis of strong-field images. The frequencies of the co- and contra-rotating orbits at the innermost stable circular orbit (ISCO) in this geometry are also computed, in the hope that quasi-periodic oscillations may permit to compare this model with Kerr’s black hole on observational grounds.

On SYM theory and all order bulk singularity structures of BPS strings in type II theory

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2018-06-01

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn-1 Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of t , s , (t + s + u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to , exploring all the entire correlation functions and all order α‧ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, and are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α‧ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α‧ contact terms of this S-matrix which carry momentum of RR in transverse directions.

On the dynamic singularities in the control of free-floating space manipulators

NASA Technical Reports Server (NTRS)

Papadopoulos, E.; Dubowsky, S.

1989-01-01

It is shown that free-floating space manipulator systems have configurations which are dynamically singular. At a dynamically singular position, the manipulator is unable to move its end effector in some direction. This problem appears in any free-floating space manipulator system that permits the vehicle to move in response to manipulator motion without correction from the vehicle's attitude control system. Dynamic singularities are functions of the dynamic properties of the system; their existence and locations cannot be predicted solely from the kinematic structure of the manipulator, unlike the singularities for fixed base manipulators. It is also shown that the location of these dynamic singularities in the workplace is dependent upon the path taken by the manipulator in reaching them. Dynamic singularities must be considered in the control, planning and design of free-floating space manipulator systems. A method for calculating these dynamic singularities is presented, and it is shown that the system parameters can be selected to reduce the effect of dynamic singularities on a system's performance.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

FREQ: A computational package for multivariable system loop-shaping procedures

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Armstrong, Ernest S.

1989-01-01

Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.

Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

USGS Publications Warehouse

Shaw, H.R.; Chouet, B.

1989-01-01

Fractal singularity analysis (FSA) is used to study a 22-yr record of deep seismic tremor (30-60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60 ?? 104 min; yearly average - 727 min yr-1; mean gradient = 24.2 min yr-1km-1). Partitioning of probabilities, Pi, in the phase space of normalized durations, xi, are expressed in terms of a function f(??), where ?? is a variable exponent of a length scale, l. Plots of f(??) vs. ?? are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by ?? values of about 0.4 and 1.9 at f = O; fmax ???1.0 for ?? ??? 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos. -Authors

Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis

NASA Astrophysics Data System (ADS)

Mantica, Giorgio; Perotti, Luca

2016-09-01

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.

Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.

PubMed

Nagarale, Ravindrakumar M; Patre, B M

2014-05-01

This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries.

PubMed

Brachet, M E; Bustamante, M D; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D

2013-01-01

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

Finite element techniques applied to cracks interacting with selected singularities

NASA Technical Reports Server (NTRS)

Conway, J. C.

1975-01-01

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

NASA Astrophysics Data System (ADS)

Luo, Yamei; Lü, Baida

2009-06-01

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.

Unidirectional spectral singularities.

PubMed

Ramezani, Hamidreza; Li, Hao-Kun; Wang, Yuan; Zhang, Xiang

2014-12-31

We propose a class of spectral singularities emerging from the coincidence of two independent singularities with highly directional responses. These spectral singularities result from resonance trapping induced by the interplay between parity-time symmetry and Fano resonances. At these singularities, while the system is reciprocal in terms of a finite transmission, a simultaneous infinite reflection from one side and zero reflection from the opposite side can be realized.

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1988-01-01

It has previously been shown that the no-slip boundary conditions leads to a singularity at a moving contact line and that this presumes some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition, the length of the slip region becomes a property of the fluid flow.

Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Kalantari, Mahdi; Yarmohammadi, Masoud; Hassani, Hossein; Silva, Emmanuel Sirimal

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the L1 norm-based version of Singular Spectrum Analysis (SSA), namely L1-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially L1-SSA can provide better imputation in comparison to other methods.

Text analysis devices, articles of manufacture, and text analysis methods

DOEpatents

Turner, Alan E; Hetzler, Elizabeth G; Nakamura, Grant C

2015-03-31

Text analysis devices, articles of manufacture, and text analysis methods are described according to some aspects. In one aspect, a text analysis device includes a display configured to depict visible images, and processing circuitry coupled with the display and wherein the processing circuitry is configured to access a first vector of a text item and which comprises a plurality of components, to access a second vector of the text item and which comprises a plurality of components, to weight the components of the first vector providing a plurality of weighted values, to weight the components of the second vector providing a plurality of weighted values, and to combine the weighted values of the first vector with the weighted values of the second vector to provide a third vector.

Tachyon field in loop quantum cosmology: An example of traversable singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Lifang; Zhu Jianyang

2009-06-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly,more » which is different from the classical big bang singularity. So this singularity is only a weak singularity.« less