Selecting appropriate singular values of transmission matrix to improve precision of incident wavefront retrieval

NASA Astrophysics Data System (ADS)

Fang, Longjie; Zhang, Xicheng; Zuo, Haoyi; Pang, Lin; Yang, Zuogang; Du, Jinglei

2018-06-01

A method of selecting appropriate singular values of the transmission matrix to improve the precision of incident wavefront retrieval in focusing light through scattering media is proposed. The optimal singular values selected by this method can reduce the degree of ill-conditionedness of the transmission matrix effectively, which indicates that the incident wavefront retrieved from the optimal set of singular values is more accurate than the incident wavefront retrieved from other sets of singular values. The validity of this method is verified by numerical simulation and actual measurements of the incident wavefront of coherent light through ground glass.

Classification of subsurface objects using singular values derived from signal frames

DOEpatents

Chambers, David H; Paglieroni, David W

2014-05-06

The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.

Singular spectrum and singular entropy used in signal processing of NC table

NASA Astrophysics Data System (ADS)

Wang, Linhong; He, Yiwen

2011-12-01

NC (numerical control) table is a complex dynamic system. The dynamic characteristics caused by backlash, friction and elastic deformation among each component are so complex that they have become the bottleneck of enhancing the positioning accuracy, tracking accuracy and dynamic behavior of NC table. This paper collects vibration acceleration signals from NC table, analyzes the signals with SVD (singular value decomposition) method, acquires the singular spectrum and calculates the singular entropy of the signals. The signal characteristics and their regulations of NC table are revealed via the characteristic quantities such as singular spectrum, singular entropy etc. The steep degrees of singular spectrums can be used to discriminate complex degrees of signals. The results show that the signals in direction of driving axes are the simplest and the signals in perpendicular direction are the most complex. The singular entropy values can be used to study the indetermination of signals. The results show that the signals of NC table are not simple signal nor white noise, the entropy values in direction of driving axe are lower, the entropy values increase along with the increment of driving speed and the entropy values at the abnormal working conditions such as resonance or creeping etc decrease obviously.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

Singular flow dynamics in three space dimensions driven by advection

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Schamel, H.

2002-03-01

The initial value problem of an ideal, compressible fluid is investigated in three space dimensions (3D). Starting from a situation where the inertia terms dominate over the force terms in Euler's equation we explore by means of the Lagrangian flow description the basic flow properties. Special attention is drawn to the appearance of singularities in the flow pattern at finite time. Classes of initial velocity profiles giving rise to collapses of density and vorticity are found. This paper, hence, furnishes evidence of focused singularities for coherent structures obeying the 3D Euler equation and applies to potential as well as vortex flows.

Applying Novel Time-Frequency Moments Singular Value Decomposition Method and Artificial Neural Networks for Ballistocardiography

NASA Astrophysics Data System (ADS)

Akhbardeh, Alireza; Junnila, Sakari; Koivuluoma, Mikko; Koivistoinen, Teemu; Värri, Alpo

2006-12-01

As we know, singular value decomposition (SVD) is designed for computing singular values (SVs) of a matrix. Then, if it is used for finding SVs of an [InlineEquation not available: see fulltext.]-by-1 or 1-by- [InlineEquation not available: see fulltext.] array with elements representing samples of a signal, it will return only one singular value that is not enough to express the whole signal. To overcome this problem, we designed a new kind of the feature extraction method which we call ''time-frequency moments singular value decomposition (TFM-SVD).'' In this new method, we use statistical features of time series as well as frequency series (Fourier transform of the signal). This information is then extracted into a certain matrix with a fixed structure and the SVs of that matrix are sought. This transform can be used as a preprocessing stage in pattern clustering methods. The results in using it indicate that the performance of a combined system including this transform and classifiers is comparable with the performance of using other feature extraction methods such as wavelet transforms. To evaluate TFM-SVD, we applied this new method and artificial neural networks (ANNs) for ballistocardiogram (BCG) data clustering to look for probable heart disease of six test subjects. BCG from the test subjects was recorded using a chair-like ballistocardiograph, developed in our project. This kind of device combined with automated recording and analysis would be suitable for use in many places, such as home, office, and so forth. The results show that the method has high performance and it is almost insensitive to BCG waveform latency or nonlinear disturbance.

An Efficient and Robust Singular Value Method for Star Pattern Recognition and Attitude Determination

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Kim, Hye-Young; Junkins, John L.

2003-01-01

A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value comparison is that a pairing process for individual measured and cataloged stars is not necessary, and the attitude estimation and pattern recognition process are not separated. An associated method for mission catalog design is introduced and simulation results are presented.

Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems. [stability margins for wing flutter suppression and drone lateral attitude control

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.

1982-01-01

A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.

Object detection with a multistatic array using singular value decomposition

DOEpatents

Hallquist, Aaron T.; Chambers, David H.

2014-07-01

A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across a surface and that travels down the surface. The detection system converts the return signals from a time domain to a frequency domain, resulting in frequency return signals. The detection system then performs a singular value decomposition for each frequency to identify singular values for each frequency. The detection system then detects the presence of a subsurface object based on a comparison of the identified singular values to expected singular values when no subsurface object is present.

A robust watermarking scheme using lifting wavelet transform and singular value decomposition

NASA Astrophysics Data System (ADS)

Bhardwaj, Anuj; Verma, Deval; Verma, Vivek Singh

2017-01-01

The present paper proposes a robust image watermarking scheme using lifting wavelet transform (LWT) and singular value decomposition (SVD). Second level LWT is applied on host/cover image to decompose into different subbands. SVD is used to obtain singular values of watermark image and then these singular values are updated with the singular values of LH2 subband. The algorithm is tested on a number of benchmark images and it is found that the present algorithm is robust against different geometric and image processing operations. A comparison of the proposed scheme is performed with other existing schemes and observed that the present scheme is better not only in terms of robustness but also in terms of imperceptibility.

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.

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.

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.

The Production of FRW Universe and Decay to Particles in Multiverse

NASA Astrophysics Data System (ADS)

Ghaffary, Tooraj

2017-09-01

In this study, first, it will be shown that as the Hubble parameter, " H", increases the production cross section for closed and flat Universes increases rapidly at smaller values of " H" and becomes constant for higher values of " H". However in the case of open Universe, the production cross section has been encountered a singularity. Before this singularity, as the H parameter increases, the cross section increases, for smaller H, ( H < 2.5), exhibits a turn-over at moderate values of H, (2.5 < H < 3.5), decreases for larger amount of H After that and for a special value of H, the cross section has been encountered with a singularity. Although the cross section cannot be defined at this singularity but before and after this point, it is certainly equal to zero. After this singularity, the cross section increases rapidly, when H increases. It is shown that if the production cross section of Universe happens before this singularity, it can't achieve to higher values of Hubble parameter after singularity. More over if the production cross section of Universe situates after the singularity, it won't get access to values of Hubble parameter less than the singularity. After that the thermal distribution for particles inside the FRW Universes are obtained. It is found that a large amount of particles are produced near apparent horizon due to their variety in their energy and their probabilities. Finally, comparing the particle production cross sections for flat, closed and open Universes, it is concluded that as the value of k increases, the cross section decreases.

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.

Contrasting eigenvalue and singular-value spectra for lasing and antilasing in a PT -symmetric periodic structure

NASA Astrophysics Data System (ADS)

Ge, Li; Feng, Liang

2017-01-01

It has been proposed and demonstrated that lasing and coherent perfect absorption (CPA or "antilasing") coexist in parity-time (PT ) symmetric photonic systems. In this work we show that the spectral signature of such a CPA laser displayed by the singular value spectrum of the scattering matrix (S ) can be orders of magnitude wider than that displayed by the eigenvalue spectrum of S . Since the former reflects how strongly light can be absorbed or amplified and the latter announces the spontaneous symmetry breaking of S , these contrasting spectral signatures indicate that near perfect absorption and extremely strong amplification can be achieved even in the PT -symmetric phase of S , which is known for and defined by its flux-conserving eigenstates. We also show that these contrasting spectral signatures are accompanied by strikingly different sensitivities to disorder and imperfection, suggesting that the eigenvalue spectrum is potentially suitable for sensing and the singular value spectrum for robust switching. A differential light amplifier may also be devised based on these two spectra.

Vibration Attenuation of the NASA Langley Evolutionary Structure Experiment Using H(infinity) and Structured Singular Value (mu) Robust Multivariable Control Techniques

NASA Technical Reports Server (NTRS)

Balas, Gary J.

1996-01-01

This final report summarizes the research results under NASA Contract NAG-1-1254 from May, 1991 - April, 1995. The main contribution of this research are in the areas of control of flexible structures, model validation, optimal control analysis and synthesis techniques, and use of shape memory alloys for structural damping.

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.

Singularity and Bohm criterion in hot positive ion species in the electronegative ion sources

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

Aslaninejad, Morteza; Yasserian, Kiomars

2016-05-15

The structure of the discharge for a magnetized electronegative ion source with two species of positive ions is investigated. The thermal motion of hot positive ions and the singularities involved with it are taken into account. By analytical solution of the neutral region, the location of the singular point and also the values of the plasma parameter such as electric potential and ion density at the singular point are obtained. A generalized Bohm criterion is recovered and discussed. In addition, for the non-neutral solution, the numerical method is used. In contrast with cold ion plasma, qualitative changes are observed. Themore » parameter space region within which oscillations in the density and potential can be observed has been scanned and discussed. The space charge behavior in the vicinity of edge of the ion sources has also been discussed in detail.« 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.

Boosting brain connectome classification accuracy in Alzheimer's disease using higher-order singular value decomposition

PubMed Central

Zhan, Liang; Liu, Yashu; Wang, Yalin; Zhou, Jiayu; Jahanshad, Neda; Ye, Jieping; Thompson, Paul M.

2015-01-01

Alzheimer's disease (AD) is a progressive brain disease. Accurate detection of AD and its prodromal stage, mild cognitive impairment (MCI), are crucial. There is also a growing interest in identifying brain imaging biomarkers that help to automatically differentiate stages of Alzheimer's disease. Here, we focused on brain structural networks computed from diffusion MRI and proposed a new feature extraction and classification framework based on higher order singular value decomposition and sparse logistic regression. In tests on publicly available data from the Alzheimer's Disease Neuroimaging Initiative, our proposed framework showed promise in detecting brain network differences that help in classifying different stages of Alzheimer's disease. PMID:26257601

Robust Fault Detection for Aircraft Using Mixed Structured Singular Value Theory and Fuzzy Logic

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G.

2000-01-01

The purpose of fault detection is to identify when a fault or failure has occurred in a system such as an aircraft or expendable launch vehicle. The faults may occur in sensors, actuators, structural components, etc. One of the primary approaches to model-based fault detection relies on analytical redundancy. That is the output of a computer-based model (actually a state estimator) is compared with the sensor measurements of the actual system to determine when a fault has occurred. Unfortunately, the state estimator is based on an idealized mathematical description of the underlying plant that is never totally accurate. As a result of these modeling errors, false alarms can occur. This research uses mixed structured singular value theory, a relatively recent and powerful robustness analysis tool, to develop robust estimators and demonstrates the use of these estimators in fault detection. To allow qualitative human experience to be effectively incorporated into the detection process fuzzy logic is used to predict the seriousness of the fault that has occurred.

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.

The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

NASA Technical Reports Server (NTRS)

Newsom, J. R.; Mukhopadhyay, V.

1983-01-01

A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two-input/two-output drone flight control system.

The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

NASA Technical Reports Server (NTRS)

Newsom, J. R.; Mukhopadhyay, V.

1983-01-01

A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system.

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.

Using Adolescent Fiction That Deals with Current Problems and Lifestyles to Explore Contemporary Values.

ERIC Educational Resources Information Center

Schwartz, Sheila

This paper argues that a value structure must be developed and taught in the schools. The values and principles contained in the Humanistic Manifesto II are examined in the context of current adolescent literature. Discussed are such books as "It's Not What You Expect" and "Mom, The Wolfman and Me" by Norma Klein; "First Person Singular" by Vida…

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.

Understanding Singular Vectors

ERIC Educational Resources Information Center

James, David; Botteron, Cynthia

2013-01-01

matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so…

Multivalued classical mechanics arising from singularity loops in complex time

NASA Astrophysics Data System (ADS)

Koch, Werner; Tannor, David J.

2018-02-01

Complex-valued classical trajectories in complex time encounter singular times at which the momentum diverges. A closed time contour around such a singular time may result in final values for q and p that differ from their initial values. In this work, we develop a calculus for determining the exponent and prefactor of the asymptotic time dependence of p from the singularities of the potential as the singularity time is approached. We identify this exponent with the number of singularity loops giving distinct solutions to Hamilton's equations of motion. The theory is illustrated for the Eckart, Coulomb, Morse, and quartic potentials. Collectively, these potentials illustrate a wide variety of situations: poles and essential singularities at finite and infinite coordinate values. We demonstrate quantitative agreement between analytical and numerical exponents and prefactors, as well as the connection between the exponent and the time circuit count. This work provides the theoretical underpinnings for the choice of time contours described in the studies of Doll et al. [J. Chem. Phys. 58(4), 1343-1351 (1973)] and Petersen and Kay [J. Chem. Phys. 141(5), 054114 (2014)]. It also has implications for wavepacket reconstruction from complex classical trajectories when multiple branches of trajectories are involved.

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.

2015-09-01

We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

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.

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.

Structural Limitations of Model Reference Adaptive Controllers

DTIC Science & Technology

1989-04-01

Global Uncertainty CkpVps)I4(s) kWVh(s) In [3) a design rule similar the one studied heme Dps(ms+Cs)V~)Ds = s (4) (ectly the samne when n-m--l) was...Ir represent the under the uncertainty indicated by ES and Eu. output of this structured singular value analysis, p: is an Defint 6: The Design

Entangled singularity patterns of photons in Ince-Gauss modes

NASA Astrophysics Data System (ADS)

Krenn, Mario; Fickler, Robert; Huber, Marcus; Lapkiewicz, Radek; Plick, William; Ramelow, Sven; Zeilinger, Anton

2013-01-01

Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify two-dimensional and three-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we nonlocally steer the singularity structure of its entangled partner, while the initial singularity structure of the photons is undefined. In addition we measure an Ince-Gauss specific quantum-correlation function with possible use in future quantum communication protocols.

Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value Decomposition (SVD)

DTIC Science & Technology

2017-09-27

ARL-TR-8161•SEP 2017 US Army Research Laboratory Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value...originator. ARL-TR-8161•SEP 2017 US Army Research Laboratory Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value...unlimited. October 2015–January 2016 US Army Research Laboratory ATTN: RDRL-CIH-C Aberdeen Proving Ground, MD 21005-5066 primary author’s email

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.

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.

The Cucker-Smale Equation: Singular Communication Weight, Measure-Valued Solutions and Weak-Atomic Uniqueness

NASA Astrophysics Data System (ADS)

Mucha, Piotr B.; Peszek, Jan

2018-01-01

The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency, e.g. to aggregate, flock or disperse. This paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space {C_{weak}(0,∞M)}. The solution is defined as a mean-field limit of the empirical distributions of particles, the dynamics of which is governed by the Cucker-Smale particle system. The studied communication weight is {ψ(s)=|s|^{-α}} with {α \\in (0,1/2)}. This range of singularity admits the sticking of characteristics/trajectories. The second result concerns the weak-atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form {m_i δ_{x_i} ⊗ δ_{v_i}}, preserves its atomic structure. Hence these coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.

A new approach for solving seismic tomography problems and assessing the uncertainty through the use of graph theory and direct methods

NASA Astrophysics Data System (ADS)

Bogiatzis, P.; Ishii, M.; Davis, T. A.

2016-12-01

Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. We show how combinatorics and graph theory can be used to analyze the structure of such problems, and to effectively decompose them into smaller ones that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. Furthermore, we show that a new sparse singular value decomposition method can be used to obtain the complete spectrum of the singular values. This procedure provides the means for more objective regularization and further dimensionality reduction of the problem. We apply this methodology to a moderate size, non-linear seismic tomography problem to image the structure of the crust and the upper mantle beneath Japan using local deep earthquakes recorded by the High Sensitivity Seismograph Network stations.

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.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

PubMed

Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

2008-07-01

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography

NASA Astrophysics Data System (ADS)

Chen, Huaiguang; Fu, Shujun; Wang, Hong; Lv, Hongli; Zhang, Caiming

2018-03-01

As a high-resolution imaging mode of biological tissues and materials, optical coherence tomography (OCT) is widely used in medical diagnosis and analysis. However, OCT images are often degraded by annoying speckle noise inherent in its imaging process. Employing the bilateral sparse representation an adaptive singular value shrinking method is proposed for its highly sparse approximation of image data. Adopting the generalized likelihood ratio as similarity criterion for block matching and an adaptive feature-oriented backward projection strategy, the proposed algorithm can restore better underlying layered structures and details of the OCT image with effective speckle attenuation. The experimental results demonstrate that the proposed algorithm achieves a state-of-the-art despeckling performance in terms of both quantitative measurement and visual interpretation.

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

A batch sliding window method for local singularity mapping and its application for geochemical anomaly identification

NASA Astrophysics Data System (ADS)

Xiao, Fan; Chen, Zhijun; Chen, Jianguo; Zhou, Yongzhang

2016-05-01

In this study, a novel batch sliding window (BSW) based singularity mapping approach was proposed. Compared to the traditional sliding window (SW) technique with disadvantages of the empirical predetermination of a fixed maximum window size and outliers sensitivity of least-squares (LS) linear regression method, the BSW based singularity mapping approach can automatically determine the optimal size of the largest window for each estimated position, and utilizes robust linear regression (RLR) which is insensitive to outlier values. In the case study, tin geochemical data in Gejiu, Yunnan, have been processed by BSW based singularity mapping approach. The results show that the BSW approach can improve the accuracy of the calculation of singularity exponent values due to the determination of the optimal maximum window size. The utilization of RLR method in the BSW approach can smoothen the distribution of singularity index values with few or even without much high fluctuate values looking like noise points that usually make a singularity map much roughly and discontinuously. Furthermore, the student's t-statistic diagram indicates a strong spatial correlation between high geochemical anomaly and known tin polymetallic deposits. The target areas within high tin geochemical anomaly could probably have much higher potential for the exploration of new tin polymetallic deposits than other areas, particularly for the areas that show strong tin geochemical anomalies whereas no tin polymetallic deposits have been found in them.

Scope insensitivity in helping decisions: Is it a matter of culture and values?

PubMed

Kogut, Tehila; Slovic, Paul; Västfjäll, Daniel

2015-12-01

The singularity effect of identifiable victims refers to people's greater willingness to help a single concrete victim compared with a group of victims experiencing the same need. We present 3 studies exploring values and cultural sources of this effect. In the first study, the singularity effect was found only among Western Israelis and not among Bedouin participants (a more collectivist group). In Study 2, individuals with higher collectivist values were more likely to contribute to a group of victims. Finally, the third study demonstrates a more causal relationship between collectivist values and the singularity effect by showing that enhancing people's collectivist values using a priming manipulation produces similar donations to single victims and groups. Moreover, participants' collectivist preferences mediated the interaction between the priming conditions and singularity of the recipient. Implications for several areas of psychology and ways to enhance caring for groups in need are discussed. (c) 2015 APA, all rights reserved).

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

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

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

Singularities of Three-Layered Complex-Valued Neural Networks With Split Activation Function.

PubMed

Kobayashi, Masaki

2018-05-01

There are three important concepts related to learning processes in neural networks: reducibility, nonminimality, and singularity. Although the definitions of these three concepts differ, they are equivalent in real-valued neural networks. This is also true of complex-valued neural networks (CVNNs) with hidden neurons not employing biases. The situation of CVNNs with hidden neurons employing biases, however, is very complicated. Exceptional reducibility was found, and it was shown that reducibility and nonminimality are not the same. Irreducibility consists of minimality and exceptional reducibility. The relationship between minimality and singularity has not yet been established. In this paper, we describe our surprising finding that minimality and singularity are independent. We also provide several examples based on exceptional reducibility.

Observation of Van Hove Singularities and Temperature Dependence of Electrical Characteristics in Suspended Carbon Nanotube Schottky Barrier Transistors

NASA Astrophysics Data System (ADS)

Zhang, Jian; Liu, Siyu; Nshimiyimana, Jean Pierre; Deng, Ya; Hu, Xiao; Chi, Xiannian; Wu, Pei; Liu, Jia; Chu, Weiguo; Sun, Lianfeng

2018-06-01

A Van Hove singularity (VHS) is a singularity in the phonon or electronic density of states of a crystalline solid. When the Fermi energy is close to the VHS, instabilities will occur, which can give rise to new phases of matter with desirable properties. However, the position of the VHS in the band structure cannot be changed in most materials. In this work, we demonstrate that the carrier densities required to approach the VHS are reached by gating in a suspended carbon nanotube Schottky barrier transistor. Critical saddle points were observed in regions of both positive and negative gate voltage, and the conductance flattened out when the gate voltage exceeded the critical value. These novel physical phenomena were evident when the temperature is below 100 K. Further, the temperature dependence of the electrical characteristics was also investigated in this type of Schottky barrier transistor.

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.

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

Stanley Corrsin Award Talk: The role of singularities in hydrodynamics

NASA Astrophysics Data System (ADS)

Eggers, Jens

2017-11-01

If a tap is opened slowly, a drop will form. The separation of the drop is described by a singularity of the Navier-Stokes equation with a free surface. Shock waves are singular solutions of the equations of ideal, compressible hydrodynamics. These examples show that singularities are characteristic for the tendency of the hydrodynamic equations to develop small scale features spontaneously, starting from smooth initial conditions. As a result, new structures are created, which form the building blocks of more complicated flows. The mathematical structure of singularities is self-similar, and their characteristics are fixed by universal properties. This will be illustrated by physical examples, as well as by applications to engineering problems such as printing, coating, or air entrainment. Finally, more recent developments will be discussed: the increasing complexity underlying the self-similar behavior of some singularities, and the spatial structure of shock waves.

Weighted low-rank sparse model via nuclear norm minimization for bearing fault detection

NASA Astrophysics Data System (ADS)

Du, Zhaohui; Chen, Xuefeng; Zhang, Han; Yang, Boyuan; Zhai, Zhi; Yan, Ruqiang

2017-07-01

It is a fundamental task in the machine fault diagnosis community to detect impulsive signatures generated by the localized faults of bearings. The main goal of this paper is to exploit the low-rank physical structure of periodic impulsive features and further establish a weighted low-rank sparse model for bearing fault detection. The proposed model mainly consists of three basic components: an adaptive partition window, a nuclear norm regularization and a weighted sequence. Firstly, due to the periodic repetition mechanism of impulsive feature, an adaptive partition window could be designed to transform the impulsive feature into a data matrix. The highlight of partition window is to accumulate all local feature information and align them. Then, all columns of the data matrix share similar waveforms and a core physical phenomenon arises, i.e., these singular values of the data matrix demonstrates a sparse distribution pattern. Therefore, a nuclear norm regularization is enforced to capture that sparse prior. However, the nuclear norm regularization treats all singular values equally and thus ignores one basic fact that larger singular values have more information volume of impulsive features and should be preserved as much as possible. Therefore, a weighted sequence with adaptively tuning weights inversely proportional to singular amplitude is adopted to guarantee the distribution consistence of large singular values. On the other hand, the proposed model is difficult to solve due to its non-convexity and thus a new algorithm is developed to search one satisfying stationary solution through alternatively implementing one proximal operator operation and least-square fitting. Moreover, the sensitivity analysis and selection principles of algorithmic parameters are comprehensively investigated through a set of numerical experiments, which shows that the proposed method is robust and only has a few adjustable parameters. Lastly, the proposed model is applied to the wind turbine (WT) bearing fault detection and its effectiveness is sufficiently verified. Compared with the current popular bearing fault diagnosis techniques, wavelet analysis and spectral kurtosis, our model achieves a higher diagnostic accuracy.

Combining local scaling and global methods to detect soil pore space

NASA Astrophysics Data System (ADS)

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

2017-04-01

The characterization of the spatial distribution of soil pore structures is essential to obtain different parameters that will influence in several models related to water flow and/or microbial growth processes. The first step in pore structure characterization is obtaining soil images that best approximate reality. Over the last decade, major technological advances in X-ray computed tomography (CT) have allowed for the investigation and reconstruction of natural porous media architectures at very fine scales. The subsequent step is delimiting the pore structure (pore space) from the CT soil images applying a thresholding. Many times we could find CT-scan images that show low contrast at the solid-void interface that difficult this step. Different delimitation methods can result in different spatial distributions of pores influencing the parameters used in the models. Recently, new local segmentation method using local greyscale value (GV) concentration variabilities, based on fractal concepts, has been presented. This method creates singularity maps to measure the GV concentration at each point. The C-A method was combined with the singularity map approach (Singularity-CA method) to define local thresholds that can be applied to binarize CT images. Comparing this method with classical methods, such as Otsu and Maximum Entropy, we observed that more pores can be detected mainly due to its ability to amplify anomalous concentrations. However, it delineated many small pores that were incorrect. In this work, we present an improve version of Singularity-CA method that avoid this problem basically combining it with the global classical methods. References Martín-Sotoca, J.J., A. Saa-Requejo, J.B. Grau, A.M. Tarquis. New segmentation method based on fractal properties using singularity maps. Geoderma, 287, 40-53, 2017. Martín-Sotoca, J.J, A. Saa-Requejo, J.B. Grau, A.M. Tarquis. Local 3D segmentation of soil pore space based on fractal properties using singularity maps. Geoderma, http://dx.doi.org/10.1016/j.geoderma.2016.11.029. Torre, Iván G., Juan C. Losada and A.M. Tarquis. Multiscaling properties of soil images. Biosystems Engineering, http://dx.doi.org/10.1016/j.biosystemseng.2016.11.006.

Constraint elimination in dynamical systems

NASA Technical Reports Server (NTRS)

Singh, R. P.; Likins, P. W.

1989-01-01

Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

A numerical method of detecting singularity

NASA Technical Reports Server (NTRS)

Laporte, M.; Vignes, J.

1978-01-01

A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D

NASA Astrophysics Data System (ADS)

Tyni, Teemu

2018-04-01

We consider a backscattering Born approximation for a perturbed biharmonic operator in three space dimensions. Previous results on this approach for biharmonic operator use the fact that the coefficients are real-valued to obtain the reconstruction of singularities in the coefficients. In this text we drop the assumption about real-valued coefficients and also establish the recovery of singularities for complex coefficients. The proof uses mapping properties of the Radon transform.

Planetary Gears Feature Extraction and Fault Diagnosis Method Based on VMD and CNN.

PubMed

Liu, Chang; Cheng, Gang; Chen, Xihui; Pang, Yusong

2018-05-11

Given local weak feature information, a novel feature extraction and fault diagnosis method for planetary gears based on variational mode decomposition (VMD), singular value decomposition (SVD), and convolutional neural network (CNN) is proposed. VMD was used to decompose the original vibration signal to mode components. The mode matrix was partitioned into a number of submatrices and local feature information contained in each submatrix was extracted as a singular value vector using SVD. The singular value vector matrix corresponding to the current fault state was constructed according to the location of each submatrix. Finally, by training a CNN using singular value vector matrices as inputs, planetary gear fault state identification and classification was achieved. The experimental results confirm that the proposed method can successfully extract local weak feature information and accurately identify different faults. The singular value vector matrices of different fault states have a distinct difference in element size and waveform. The VMD-based partition extraction method is better than ensemble empirical mode decomposition (EEMD), resulting in a higher CNN total recognition rate of 100% with fewer training times (14 times). Further analysis demonstrated that the method can also be applied to the degradation recognition of planetary gears. Thus, the proposed method is an effective feature extraction and fault diagnosis technique for planetary gears.

Planetary Gears Feature Extraction and Fault Diagnosis Method Based on VMD and CNN

PubMed Central

Cheng, Gang; Chen, Xihui

2018-01-01

Given local weak feature information, a novel feature extraction and fault diagnosis method for planetary gears based on variational mode decomposition (VMD), singular value decomposition (SVD), and convolutional neural network (CNN) is proposed. VMD was used to decompose the original vibration signal to mode components. The mode matrix was partitioned into a number of submatrices and local feature information contained in each submatrix was extracted as a singular value vector using SVD. The singular value vector matrix corresponding to the current fault state was constructed according to the location of each submatrix. Finally, by training a CNN using singular value vector matrices as inputs, planetary gear fault state identification and classification was achieved. The experimental results confirm that the proposed method can successfully extract local weak feature information and accurately identify different faults. The singular value vector matrices of different fault states have a distinct difference in element size and waveform. The VMD-based partition extraction method is better than ensemble empirical mode decomposition (EEMD), resulting in a higher CNN total recognition rate of 100% with fewer training times (14 times). Further analysis demonstrated that the method can also be applied to the degradation recognition of planetary gears. Thus, the proposed method is an effective feature extraction and fault diagnosis technique for planetary gears. PMID:29751671

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.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Design of control laws for flutter suppression based on the aerodynamic energy concept and comparisons with other design methods

NASA Technical Reports Server (NTRS)

Nissim, Eli

1990-01-01

The aerodynamic energy method is used to synthesize control laws for NASA's drone for aerodynamic and structural testing-aerodynamic research wing 1 (DAST-ARW1) mathematical model. The performance of these control laws in terms of closed-loop flutter dynamic pressure, control surface activity, and robustness is compared with other control laws that relate to the same model. A control law synthesis technique that makes use of the return difference singular values is developed. It is based on the aerodynamic energy approach and is shown to yield results that are superior to those results given in the literature and are based on optimal control theory. Nyquist plots are presented, together with a short discussion regarding the relative merits of the minimum singular value as a measure of robustness as compared with the more traditional measure involving phase and gain margins.

Design of control laws for flutter suppression based on the aerodynamic energy concept and comparisons with other design methods

NASA Technical Reports Server (NTRS)

Nissim, E.

1989-01-01

The aerodynamic energy method is used in this paper to synthesize control laws for NASA's Drone for Aerodynamic and Structural Testing-Aerodynamic Research Wing 1 (DAST-ARW1) mathematical model. The performance of these control laws in terms of closed-loop flutter dynamic pressure, control surface activity, and robustness is compared against other control laws that appear in the literature and relate to the same model. A control law synthesis technique that makes use of the return difference singular values is developed in this paper. it is based on the aerodynamic energy approach and is shown to yield results superior to those given in the literature and based on optimal control theory. Nyquist plots are presented together with a short discussion regarding the relative merits of the minimum singular value as a measure of robustness, compared with the more traditional measure of robustness involving phase and gain margins.

Low rank approximation methods for MR fingerprinting with large scale dictionaries.

PubMed

Yang, Mingrui; Ma, Dan; Jiang, Yun; Hamilton, Jesse; Seiberlich, Nicole; Griswold, Mark A; McGivney, Debra

2018-04-01

This work proposes new low rank approximation approaches with significant memory savings for large scale MR fingerprinting (MRF) problems. We introduce a compressed MRF with randomized singular value decomposition method to significantly reduce the memory requirement for calculating a low rank approximation of large sized MRF dictionaries. We further relax this requirement by exploiting the structures of MRF dictionaries in the randomized singular value decomposition space and fitting them to low-degree polynomials to generate high resolution MRF parameter maps. In vivo 1.5T and 3T brain scan data are used to validate the approaches. T 1 , T 2 , and off-resonance maps are in good agreement with that of the standard MRF approach. Moreover, the memory savings is up to 1000 times for the MRF-fast imaging with steady-state precession sequence and more than 15 times for the MRF-balanced, steady-state free precession sequence. The proposed compressed MRF with randomized singular value decomposition and dictionary fitting methods are memory efficient low rank approximation methods, which can benefit the usage of MRF in clinical settings. They also have great potentials in large scale MRF problems, such as problems considering multi-component MRF parameters or high resolution in the parameter space. Magn Reson Med 79:2392-2400, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Short time propagation of a singular wave function: Some surprising results

NASA Astrophysics Data System (ADS)

Marchewka, A.; Granot, E.; Schuss, Z.

2007-08-01

The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.

Three dimensional canonical singularity and five dimensional N = 1 SCFT

NASA Astrophysics Data System (ADS)

Xie, Dan; Yau, Shing-Tung

2017-06-01

We conjecture that every three dimensional canonical singularity defines a five dimensional N = 1 SCFT. Flavor symmetry can be found from singularity structure: non-abelian flavor symmetry is read from the singularity type over one dimensional singular locus. The dimension of Coulomb branch is given by the number of compact crepant divisors from a crepant resolution of singularity. The detailed structure of Coulomb branch is described as follows: a) a chamber of Coulomb branch is described by a crepant resolution, and this chamber is given by its Nef cone and the prepotential is computed from triple intersection numbers; b) Crepant resolution is not unique and different resolutions are related by flops; Nef cones from crepant resolutions form a fan which is claimed to be the full Coulomb branch.

Band structure of an electron in a kind of periodic potentials with singularities

NASA Astrophysics Data System (ADS)

Hai, Kuo; Yu, Ning; Jia, Jiangping

2018-06-01

Noninteracting electrons in some crystals may experience periodic potentials with singularities and the governing Schrödinger equation cannot be defined at the singular points. The band structure of a single electron in such a one-dimensional crystal has been calculated by using an equivalent integral form of the Schrödinger equation. Both the perturbed and exact solutions are constructed respectively for the cases of a general singular weak-periodic system and its an exactly solvable version, Kronig-Penney model. Any one of them leads to a special band structure of the energy-dependent parameter, which results in an effective correction to the previous energy-band structure and gives a new explanation for forming the band structure. The used method and obtained results could be a valuable aid in the study of energy bands in solid-state physics, and the new explanation may trigger investigation to different physical mechanism of electron band structures.

On the deep structure of the blowing-up of curve singularities

NASA Astrophysics Data System (ADS)

Elias, Juan

2001-09-01

Let C be a germ of curve singularity embedded in (kn, 0). It is well known that the blowing-up of C centred on its closed ring, Bl(C), is a finite union of curve singularities. If C is reduced we can iterate this process and, after a finite number of steps, we find only non-singular curves. This is the desingularization process. The main idea of this paper is to linearize the blowing-up of curve singularities Bl(C) [rightward arrow] C. We perform this by studying the structure of [script O]Bl(C)/[script O]C as W-module, where W is a discrete valuation ring contained in [script O]C. Since [script O]Bl(C)/[script O]C is a torsion W-module, its structure is determined by the invariant factors of [script O]C in [script O]Bl(C). The set of invariant factors is called in this paper as the set of micro-invariants of C (see Definition 1·2).In the first section we relate the micro-invariants of C to the Hilbert function of C (Proposition 1·3), and we show how to compute them from the Hilbert function of some quotient of [script O]C (see Proposition 1·4).The main result of this paper is Theorem 3·3 where we give upper bounds of the micro-invariants in terms of the regularity, multiplicity and embedding dimension. As a corollary we improve and we recover some results of [6]. These bounds can be established as a consequence of the study of the Hilbert function of a filtration of ideals g = {g[r,i+1]}i [gt-or-equal, slanted] 0 of the tangent cone of [script O]C (see Section 2). The main property of g is that the ideals g[r,i+1] have initial degree bigger than the Castelnuovo-Mumford regularity of the tangent cone of [script O]C.Section 4 is devoted to computation the micro-invariants of branches; we show how to compute them from the semigroup of values of C and Bl(C) (Proposition 4·3). The case of monomial curve singularities is especially studied; we end Section 4 with some explicit computations.In the last section we study some geometric properties of C that can be deduced from special values of the micro-invariants, and we specially study the relationship of the micro-invariants with the Hilbert function of [script O]Bl(C). We end the paper studying the natural equisingularity criteria that can be defined from the micro-invariants and its relationship with some of the known equisingularity criteria.

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.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

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

Zhou, Yao

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities. Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In thismore » thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation. Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands. We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.« less

Classical stability of sudden and big rip singularities

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

Barrow, John D.; Lip, Sean Z. W.

2009-08-15

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge-invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.

Dynamic soft variable structure control of singular systems

NASA Astrophysics Data System (ADS)

Liu, Yunlong; Zhang, Caihong; Gao, Cunchen

2012-08-01

The dynamic soft variable structure control (VSC) of singular systems is discussed in this paper. The definition of soft VSC and the design of its controller modes are given. The stability of singular systems with the dynamic soft VSC is proposed. The dynamic soft variable structure controller is designed, and the concrete algorithm on the dynamic soft VSC is given. The dynamic soft VSC of singular systems which was developed for the purpose of intentionally precluding chattering, achieving high regulation rates and shortening settling times enhanced the dynamic quality of the systems. It is illustrated the feasibility and validity of the proposed strategy by a simulation example, and an outlook on its auspicious further development is presented.

A robust indicator based on singular value decomposition for flaw feature detection from noisy ultrasonic signals

NASA Astrophysics Data System (ADS)

Cui, Ximing; Wang, Zhe; Kang, Yihua; Pu, Haiming; Deng, Zhiyang

2018-05-01

Singular value decomposition (SVD) has been proven to be an effective de-noising tool for flaw echo signal feature detection in ultrasonic non-destructive evaluation (NDE). However, the uncertainty in the arbitrary manner of the selection of an effective singular value weakens the robustness of this technique. Improper selection of effective singular values will lead to bad performance of SVD de-noising. What is more, the computational complexity of SVD is too large for it to be applied in real-time applications. In this paper, to eliminate the uncertainty in SVD de-noising, a novel flaw indicator, named the maximum singular value indicator (MSI), based on short-time SVD (STSVD), is proposed for flaw feature detection from a measured signal in ultrasonic NDE. In this technique, the measured signal is first truncated into overlapping short-time data segments to put feature information of a transient flaw echo signal in local field, and then the MSI can be obtained from the SVD of each short-time data segment. Research shows that this indicator can clearly indicate the location of ultrasonic flaw signals, and the computational complexity of this STSVD-based indicator is significantly reduced with the algorithm proposed in this paper. Both simulation and experiments show that this technique is very efficient for real-time application in flaw detection from noisy data.

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.

Polar and singular value decomposition of 3×3 magic squares

NASA Astrophysics Data System (ADS)

Trenkler, Götz; Schmidt, Karsten; Trenkler, Dietrich

2013-07-01

In this note, we find polar as well as singular value decompositions of a 3×3 magic square, i.e. a 3×3 matrix M with real elements where each row, column and diagonal adds up to the magic sum s of the magic square.

Simplex volume analysis for finding endmembers in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Li, Hsiao-Chi; Song, Meiping; Chang, Chein-I.

2015-05-01

Using maximal simplex volume as an optimal criterion for finding endmembers is a common approach and has been widely studied in the literature. Interestingly, very little work has been reported on how simplex volume is calculated. It turns out that the issue of calculating simplex volume is much more complicated and involved than what we may think. This paper investigates this issue from two different aspects, geometric structure and eigen-analysis. The geometric structure is derived from its simplex structure whose volume can be calculated by multiplying its base with its height. On the other hand, eigen-analysis takes advantage of the Cayley-Menger determinant to calculate the simplex volume. The major issue of this approach is that when the matrix is ill-rank where determinant is desired. To deal with this problem two methods are generally considered. One is to perform data dimensionality reduction to make the matrix to be of full rank. The drawback of this method is that the original volume has been shrunk and the found volume of a dimensionality-reduced simplex is not the real original simplex volume. Another is to use singular value decomposition (SVD) to find singular values for calculating simplex volume. The dilemma of this method is its instability in numerical calculations. This paper explores all of these three methods in simplex volume calculation. Experimental results show that geometric structure-based method yields the most reliable simplex volume.

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.

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

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

Kinetics of Structural Changes on GaSb(001) Singular and Vicinal Surfaces During the UHV Annealing

NASA Astrophysics Data System (ADS)

Vasev, A. V.; Putyato, M. A.; Preobrazhenskii, V. V.; Bakarov, A. K.; Toropov, A. I.

2018-05-01

The dynamics of processes of antimony desorption was investigated on the singular and vicinal GaSb(001) surface by RHEED method. The role of the terraces edges was determined during antimony evaporation in Langmuir desorption mode. It is shown that the structural transition (2x5) -> (1x3) is a complex of two transitions - order -> disorder and disorder -> order. The influence of the degree of surface miscut from the singular face on the dimension of the transition (2x5) -> DO was studied. The activation energies of structural transitions ex(2x5) -> (2x5), (2x5) -> DO and DO -> (1x3) on singular and vicinal faces GaSb(001) were determined.

Optical spectral singularities as threshold resonances

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

Mostafazadeh, Ali

2011-04-15

Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears whenever the gain coefficient coincides with its threshold value and other parameters of the system are selected properly. We explore a concrete realization of spectral singularities for a typical semiconductor gain medium and propose a method of constructing a tunable laser that operates at threshold gain.

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.

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.

Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure

NASA Astrophysics Data System (ADS)

Pestrenin, V. M.; Pestrenina, I. V.

2017-03-01

The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors' opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.

A novel fusion framework of visible light and infrared images based on singular value decomposition and adaptive DUAL-PCNN in NSST domain

NASA Astrophysics Data System (ADS)

Cheng, Boyang; Jin, Longxu; Li, Guoning

2018-06-01

Visible light and infrared images fusion has been a significant subject in imaging science. As a new contribution to this field, a novel fusion framework of visible light and infrared images based on adaptive dual-channel unit-linking pulse coupled neural networks with singular value decomposition (ADS-PCNN) in non-subsampled shearlet transform (NSST) domain is present in this paper. First, the source images are decomposed into multi-direction and multi-scale sub-images by NSST. Furthermore, an improved novel sum modified-Laplacian (INSML) of low-pass sub-image and an improved average gradient (IAVG) of high-pass sub-images are input to stimulate the ADS-PCNN, respectively. To address the large spectral difference between infrared and visible light and the occurrence of black artifacts in fused images, a local structure information operator (LSI), which comes from local area singular value decomposition in each source image, is regarded as the adaptive linking strength that enhances fusion accuracy. Compared with PCNN models in other studies, the proposed method simplifies certain peripheral parameters, and the time matrix is utilized to decide the iteration number adaptively. A series of images from diverse scenes are used for fusion experiments and the fusion results are evaluated subjectively and objectively. The results of the subjective and objective evaluation show that our algorithm exhibits superior fusion performance and is more effective than the existing typical fusion techniques.

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.

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

A copyright protection scheme for digital images based on shuffled singular value decomposition and visual cryptography.

PubMed

Devi, B Pushpa; Singh, Kh Manglem; Roy, Sudipta

2016-01-01

This paper proposes a new watermarking algorithm based on the shuffled singular value decomposition and the visual cryptography for copyright protection of digital images. It generates the ownership and identification shares of the image based on visual cryptography. It decomposes the image into low and high frequency sub-bands. The low frequency sub-band is further divided into blocks of same size after shuffling it and then the singular value decomposition is applied to each randomly selected block. Shares are generated by comparing one of the elements in the first column of the left orthogonal matrix with its corresponding element in the right orthogonal matrix of the singular value decomposition of the block of the low frequency sub-band. The experimental results show that the proposed scheme clearly verifies the copyright of the digital images, and is robust to withstand several image processing attacks. Comparison with the other related visual cryptography-based algorithms reveals that the proposed method gives better performance. The proposed method is especially resilient against the rotation attack.

A NEW GUI FOR GLOBAL ORBIT CORRECTION AT THE ALS USING MATLAB

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

Pachikara, J.; Portmann, G.

2007-01-01

Orbit correction is a vital procedure at particle accelerators around the world. The orbit correction routine currently used at the Advanced Light Source (ALS) is a bit cumbersome and a new Graphical User Interface (GUI) has been developed using MATLAB. The correction algorithm uses a singular value decomposition method for calculating the required corrector magnet changes for correcting the orbit. The application has been successfully tested at the ALS. The GUI display provided important information regarding the orbit including the orbit errors before and after correction, the amount of corrector magnet strength change, and the standard deviation of the orbitmore » error with respect to the number of singular values used. The use of more singular values resulted in better correction of the orbit error but at the expense of enormous corrector magnet strength changes. The results showed an inverse relationship between the peak-to-peak values of the orbit error and the number of singular values used. The GUI interface helps the ALS physicists and operators understand the specifi c behavior of the orbit. The application is convenient to use and is a substantial improvement over the previous orbit correction routine in terms of user friendliness and compactness.« less

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

The mechanics of delamination in fiber-reinforced composite materials. Part 1: Stress singularities and solution structure

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites.

Algorithm 971: An Implementation of a Randomized Algorithm for Principal Component Analysis

PubMed Central

LI, HUAMIN; LINDERMAN, GEORGE C.; SZLAM, ARTHUR; STANTON, KELLY P.; KLUGER, YUVAL; TYGERT, MARK

2017-01-01

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks’ MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces). PMID:28983138

Singularity and steering logic for control moment gyros on flexible space structures

NASA Astrophysics Data System (ADS)

Hu, Quan; Guo, Chuandong; Zhang, Jun

2017-08-01

Control moment gyros (CMGs) are a widely used device for generating control torques for spacecraft attitude control without expending propellant. Because of its effectiveness and cleanness, it has been considered to be mounted on a space structure for active vibration suppression. The resultant system is the so-called gyroelastic body. Since CMGs could exert both torque and modal force to the structure, it can also be used to simultaneously achieve attitude maneuver and vibration reduction of a flexible spacecraft. In this paper, we consider the singularity problem in such application of CMGs. The dynamics of an unconstrained gyroelastic body is established, from which the output equations of the CMGs are extracted. Then, torque singular state and modal force singular state are defined and visualized to demonstrate the singularity. Numerical examples of several typical CMGs configurations on a gyroelastic body are given. Finally, a steering law allowing output error is designed and applied to the vibration suppression of a plate with distributed CMGs.

Observation of van Hove Singularities in Twisted Silicene Multilayers.

PubMed

Li, Zhi; Zhuang, Jincheng; Chen, Lan; Ni, Zhenyi; Liu, Chen; Wang, Li; Xu, Xun; Wang, Jiaou; Pi, Xiaodong; Wang, Xiaolin; Du, Yi; Wu, Kehui; Dou, Shi Xue

2016-08-24

Interlayer interactions perturb the electronic structure of two-dimensional materials and lead to new physical phenomena, such as van Hove singularities and Hofstadter's butterfly pattern. Silicene, the recently discovered two-dimensional form of silicon, is quite unique, in that silicon atoms adopt competing sp(2) and sp(3) hybridization states leading to a low-buckled structure promising relatively strong interlayer interaction. In multilayer silicene, the stacking order provides an important yet rarely explored degree of freedom for tuning its electronic structures through manipulating interlayer coupling. Here, we report the emergence of van Hove singularities in the multilayer silicene created by an interlayer rotation. We demonstrate that even a large-angle rotation (>20°) between stacked silicene layers can generate a Moiré pattern and van Hove singularities due to the strong interlayer coupling in multilayer silicene. Our study suggests an intriguing method for expanding the tunability of the electronic structure for electronic applications in this two-dimensional material.

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity

NASA Astrophysics Data System (ADS)

Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek

2014-07-01

We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.

Wavefront reconstruction from non-modulated pyramid wavefront sensor data using a singular value type expansion

NASA Astrophysics Data System (ADS)

Hutterer, Victoria; Ramlau, Ronny

2018-03-01

The new generation of extremely large telescopes includes adaptive optics systems to correct for atmospheric blurring. In this paper, we present a new method of wavefront reconstruction from non-modulated pyramid wavefront sensor data. The approach is based on a simplified sensor model represented as the finite Hilbert transform of the incoming phase. Due to the non-compactness of the finite Hilbert transform operator the classical theory for singular systems is not applicable. Nevertheless, we can express the Moore-Penrose inverse as a singular value type expansion with weighted Chebychev polynomials.

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

A Gaussian-based rank approximation for subspace clustering

NASA Astrophysics Data System (ADS)

Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping

2018-04-01

Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.

Multirate sampled-data yaw-damper and modal suppression system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1990-01-01

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Using Singular Value Decomposition to Investigate Degraded Chinese Character Recognition: Evidence from Eye Movements during Reading

ERIC Educational Resources Information Center

Wang, Hsueh-Cheng; Schotter, Elizabeth R.; Angele, Bernhard; Yang, Jinmian; Simovici, Dan; Pomplun, Marc; Rayner, Keith

2013-01-01

Previous research indicates that removing initial strokes from Chinese characters makes them harder to read than removing final or internal ones. In the present study, we examined the contribution of important components to character configuration via singular value decomposition. The results indicated that when the least important segments, which…

A Survey of Singular Value Decomposition Methods and Performance Comparison of Some Available Serial Codes

NASA Technical Reports Server (NTRS)

Plassman, Gerald E.

2005-01-01

This contractor report describes a performance comparison of available alternative complete Singular Value Decomposition (SVD) methods and implementations which are suitable for incorporation into point spread function deconvolution algorithms. The report also presents a survey of alternative algorithms, including partial SVD's special case SVD's, and others developed for concurrent processing systems.

Extended space expectation values of position related operators for hydrogen-like quantum system evolutions

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

Kalay, Berfin; Demiralp, Metin

2014-10-06

The expectation value definitions over an extended space from the considered Hilbert space of the system under consideration is given in another paper of the second author in this symposium. There, in that paper, the conceptuality rather than specification is emphasized on. This work uses that conceptuality to investigate the time evolutions of the position related operators' expectation values not in its standard meaning but rather in a new version of the definition over not the original Hilbert space but in the space obtained by extensions via introducing the images of the given initial wave packet under the positive integermore » powers of the system Hamiltonian. These images may not be residing in the same space of the initial wave packet when certain singularities appear in the structure of the system Hamiltonian. This may break down the existence of the integrals in the definitions of the expectation values. The cure is the use of basis functions in the abovementioned extended space and the sandwiching of the target operator whose expectation value is under questioning by an appropriately chosen operator guaranteeing the existence of the relevant integrals. Work specifically focuses on the hydrogen-like quantum systems whose Hamiltonians contain a polar singularity at the origin.« less

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Rodina, Laurentiu; Trnka, Jaroslav

2018-06-01

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n -1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

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.

The accuracy comparison between ARFIMA and singular spectrum analysis for forecasting the sales volume of motorcycle in Indonesia

NASA Astrophysics Data System (ADS)

Sitohang, Yosep Oktavianus; Darmawan, Gumgum

2017-08-01

This research attempts to compare between two forecasting models in time series analysis for predicting the sales volume of motorcycle in Indonesia. The first forecasting model used in this paper is Autoregressive Fractionally Integrated Moving Average (ARFIMA). ARFIMA can handle non-stationary data and has a better performance than ARIMA in forecasting accuracy on long memory data. This is because the fractional difference parameter can explain correlation structure in data that has short memory, long memory, and even both structures simultaneously. The second forecasting model is Singular spectrum analysis (SSA). The advantage of the technique is that it is able to decompose time series data into the classic components i.e. trend, cyclical, seasonal and noise components. This makes the forecasting accuracy of this technique significantly better. Furthermore, SSA is a model-free technique, so it is likely to have a very wide range in its application. Selection of the best model is based on the value of the lowest MAPE. Based on the calculation, it is obtained the best model for ARFIMA is ARFIMA (3, d = 0, 63, 0) with MAPE value of 22.95 percent. For SSA with a window length of 53 and 4 group of reconstructed data, resulting MAPE value of 13.57 percent. Based on these results it is concluded that SSA produces better forecasting accuracy.

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.

Unattainable extended spacetime regions in conformal gravity

NASA Astrophysics Data System (ADS)

Chakrabarty, Hrishikesh; Benavides-Gallego, Carlos A.; Bambi, Cosimo; Modesto, Leonardo

2018-03-01

The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The γ-metric is instead a vacuum solution of Einstein's gravity. Both spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein's gravity.

The mechanics of delamination in fiber-reinforced composite materials. I - Stress singularities and solution structure

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be different from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites. Previously announced in STAR as N84-13221

Pseudoinverse Decoding Process in Delay-Encoded Synthetic Transmit Aperture Imaging.

PubMed

Gong, Ping; Kolios, Michael C; Xu, Yuan

2016-09-01

Recently, we proposed a new method to improve the signal-to-noise ratio of the prebeamformed radio-frequency data in synthetic transmit aperture (STA) imaging: the delay-encoded STA (DE-STA) imaging. In the decoding process of DE-STA, the equivalent STA data were obtained by directly inverting the coding matrix. This is usually regarded as an ill-posed problem, especially under high noise levels. Pseudoinverse (PI) is usually used instead for seeking a more stable inversion process. In this paper, we apply singular value decomposition to the coding matrix to conduct the PI. Our numerical studies demonstrate that the singular values of the coding matrix have a special distribution, i.e., all the values are the same except for the first and last ones. We compare the PI in two cases: complete PI (CPI), where all the singular values are kept, and truncated PI (TPI), where the last and smallest singular value is ignored. The PI (both CPI and TPI) DE-STA processes are tested against noise with both numerical simulations and experiments. The CPI and TPI can restore the signals stably, and the noise mainly affects the prebeamformed signals corresponding to the first transmit channel. The difference in the overall enveloped beamformed image qualities between the CPI and TPI is negligible. Thus, it demonstrates that DE-STA is a relatively stable encoding and decoding technique. Also, according to the special distribution of the singular values of the coding matrix, we propose a new efficient decoding formula that is based on the conjugate transpose of the coding matrix. We also compare the computational complexity of the direct inverse and the new formula.

Investigation of displacement, strain and stress in single step transversely isotropic elastic bonded joint

NASA Astrophysics Data System (ADS)

Apu, Md. Jakaria; Islam, Md. Shahidul

2016-07-01

Bi-material joint is often used in many advanced materials and structures. Determination of the bonding strength at the interface is very difficult because of the presence of the stress singularity. In this paper, the displacement and stress fields of a transversely isotropic bi-material joint around an interface edge are determined. Autodesk Simulation Mechanical 2015 is used to carry out the numerical computations. Stress and displacement fields demonstrate that the values near the edge of joint where the stress singularity occurs are larger than that at the inner portion. From the numerical results, it is suggested that de-bonding of the interface may occur at the interface edge of the joint due to the higher stress concentration at the free edge.

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.

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

NASA Technical Reports Server (NTRS)

Yakhot, A.; Staroselsky, I.; Orszag, S. A.

1994-01-01

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Analytically solvable model of an electronic Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Ngo Dinh, Stéphane; Bagrets, Dmitry A.; Mirlin, Alexander D.

2013-05-01

We consider a class of models of nonequilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities, determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities) and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed “lobe” structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.

Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error.

PubMed

Yin, X X; Ng, B W-H; Ramamohanarao, K; Baghai-Wadji, A; Abbott, D

2012-09-01

It has been shown that, magnetic resonance images (MRIs) with sparsity representation in a transformed domain, e.g. spatial finite-differences (FD), or discrete cosine transform (DCT), can be restored from undersampled k-space via applying current compressive sampling theory. The paper presents a model-based method for the restoration of MRIs. The reduced-order model, in which a full-system-response is projected onto a subspace of lower dimensionality, has been used to accelerate image reconstruction by reducing the size of the involved linear system. In this paper, the singular value threshold (SVT) technique is applied as a denoising scheme to reduce and select the model order of the inverse Fourier transform image, and to restore multi-slice breast MRIs that have been compressively sampled in k-space. The restored MRIs with SVT for denoising show reduced sampling errors compared to the direct MRI restoration methods via spatial FD, or DCT. Compressive sampling is a technique for finding sparse solutions to underdetermined linear systems. The sparsity that is implicit in MRIs is to explore the solution to MRI reconstruction after transformation from significantly undersampled k-space. The challenge, however, is that, since some incoherent artifacts result from the random undersampling, noise-like interference is added to the image with sparse representation. These recovery algorithms in the literature are not capable of fully removing the artifacts. It is necessary to introduce a denoising procedure to improve the quality of image recovery. This paper applies a singular value threshold algorithm to reduce the model order of image basis functions, which allows further improvement of the quality of image reconstruction with removal of noise artifacts. The principle of the denoising scheme is to reconstruct the sparse MRI matrices optimally with a lower rank via selecting smaller number of dominant singular values. The singular value threshold algorithm is performed by minimizing the nuclear norm of difference between the sampled image and the recovered image. It has been illustrated that this algorithm improves the ability of previous image reconstruction algorithms to remove noise artifacts while significantly improving the quality of MRI recovery.

Stochastic local operations and classical communication (SLOCC) and local unitary operations (LU) classifications of n qubits via ranks and singular values of the spin-flipping matrices

NASA Astrophysics Data System (ADS)

Li, Dafa

2018-06-01

We construct ℓ -spin-flipping matrices from the coefficient matrices of pure states of n qubits and show that the ℓ -spin-flipping matrices are congruent and unitary congruent whenever two pure states of n qubits are SLOCC and LU equivalent, respectively. The congruence implies the invariance of ranks of the ℓ -spin-flipping matrices under SLOCC and then permits a reduction of SLOCC classification of n qubits to calculation of ranks of the ℓ -spin-flipping matrices. The unitary congruence implies the invariance of singular values of the ℓ -spin-flipping matrices under LU and then permits a reduction of LU classification of n qubits to calculation of singular values of the ℓ -spin-flipping matrices. Furthermore, we show that the invariance of singular values of the ℓ -spin-flipping matrices Ω 1^{(n)} implies the invariance of the concurrence for even n qubits and the invariance of the n-tangle for odd n qubits. Thus, the concurrence and the n-tangle can be used for LU classification and computing the concurrence and the n-tangle only performs additions and multiplications of coefficients of states.

A novel image watermarking method based on singular value decomposition and digital holography

NASA Astrophysics Data System (ADS)

Cai, Zhishan

2016-10-01

According to the information optics theory, a novel watermarking method based on Fourier-transformed digital holography and singular value decomposition (SVD) is proposed in this paper. First of all, a watermark image is converted to a digital hologram using the Fourier transform. After that, the original image is divided into many non-overlapping blocks. All the blocks and the hologram are decomposed using SVD. The singular value components of the hologram are then embedded into the singular value components of each block using an addition principle. Finally, SVD inverse transformation is carried out on the blocks and hologram to generate the watermarked image. The watermark information embedded in each block is extracted at first when the watermark is extracted. After that, an averaging operation is carried out on the extracted information to generate the final watermark information. Finally, the algorithm is simulated. Furthermore, to test the encrypted image's resistance performance against attacks, various attack tests are carried out. The results show that the proposed algorithm has very good robustness against noise interference, image cut, compression, brightness stretching, etc. In particular, when the image is rotated by a large angle, the watermark information can still be extracted correctly.

Image compression using singular value decomposition

NASA Astrophysics Data System (ADS)

Swathi, H. R.; Sohini, Shah; Surbhi; Gopichand, G.

2017-11-01

We often need to transmit and store the images in many applications. Smaller the image, less is the cost associated with transmission and storage. So we often need to apply data compression techniques to reduce the storage space consumed by the image. One approach is to apply Singular Value Decomposition (SVD) on the image matrix. In this method, digital image is given to SVD. SVD refactors the given digital image into three matrices. Singular values are used to refactor the image and at the end of this process, image is represented with smaller set of values, hence reducing the storage space required by the image. Goal here is to achieve the image compression while preserving the important features which describe the original image. SVD can be adapted to any arbitrary, square, reversible and non-reversible matrix of m × n size. Compression ratio and Mean Square Error is used as performance metrics.

Reduced rank regression via adaptive nuclear norm penalization

PubMed Central

Chen, Kun; Dong, Hongbo; Chan, Kung-Sik

2014-01-01

Summary We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method has a global optimal solution obtained from an adaptively soft-thresholded singular value decomposition. The method is computationally efficient, and the resulting solution path is continuous. The rank consistency of and prediction/estimation performance bounds for the estimator are established for a high-dimensional asymptotic regime. Simulation studies and an application in genetics demonstrate its efficacy. PMID:25045172

A novel strategy for signal denoising using reweighted SVD and its applications to weak fault feature enhancement of rotating machinery

NASA Astrophysics Data System (ADS)

Zhao, Ming; Jia, Xiaodong

2017-09-01

Singular value decomposition (SVD), as an effective signal denoising tool, has been attracting considerable attention in recent years. The basic idea behind SVD denoising is to preserve the singular components (SCs) with significant singular values. However, it is shown that the singular values mainly reflect the energy of decomposed SCs, therefore traditional SVD denoising approaches are essentially energy-based, which tend to highlight the high-energy regular components in the measured signal, while ignoring the weak feature caused by early fault. To overcome this issue, a reweighted singular value decomposition (RSVD) strategy is proposed for signal denoising and weak feature enhancement. In this work, a novel information index called periodic modulation intensity is introduced to quantify the diagnostic information in a mechanical signal. With this index, the decomposed SCs can be evaluated and sorted according to their information levels, rather than energy. Based on that, a truncated linear weighting function is proposed to control the contribution of each SC in the reconstruction of the denoised signal. In this way, some weak but informative SCs could be highlighted effectively. The advantages of RSVD over traditional approaches are demonstrated by both simulated signals and real vibration/acoustic data from a two-stage gearbox as well as train bearings. The results demonstrate that the proposed method can successfully extract the weak fault feature even in the presence of heavy noise and ambient interferences.

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Hajkhalili, S.; Sheykhi, A.

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born-Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein-Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as r →∞. The maximum value of the electric field increases with increasing the nonlinear parameter β or decreasing the dilaton coupling α and is shifted to the singularity in the absence of either dilaton field (α = 0) or nonlinear gauge field (β →∞).

On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules

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

Myong, R. S., E-mail: myong@gnu.ac.kr

2014-05-15

The high Mach number shock structure singularity arising in moment equations of the Boltzmann equation was investigated. The source of the singularity is shown to be the unbalanced treatment between two high order kinematic and dissipation terms caused by the overreach of Maxwellian molecule assumption. In compressive gaseous flow, the high order stress-strain coupling term of quadratic nature will grow far faster than the strain term, resulting in an imbalance with the linear dissipation term and eventually a blow-up singularity in high thermal nonequilibrium. On the other hand, the singularity arising from unbalanced treatment does not occur in the casemore » of velocity shear and expansion flows, since the high order effects are cancelled under the constraint of the free-molecular asymptotic behavior. As an alternative method to achieve the balanced treatment, Eu's generalized hydrodynamics, consistent with the second law of thermodynamics, was revisited. After introducing the canonical distribution function in exponential form and applying the cumulant expansion to the explicit calculation of the dissipation term, a natural platform suitable for the balanced treatment was derived. The resulting constitutive equation with the nonlinear factor was then shown to be well-posed for all regimes, effectively removing the high Mach number shock structure singularity.« less

Singularity computations. [finite element methods for elastoplastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1978-01-01

Direct descriptions of the structure of a singularity would describe the radial and angular distributions of the field quantities as explicitly as practicable along with some measure of the intensity of the singularity. This paper discusses such an approach based on recent development of numerical methods for elastoplastic flow. Attention is restricted to problems where one variable or set of variables is finite at the origin of the singularity but a second set is not.

2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

PubMed

Kam, Chon-Fai; Liu, Ren-Bao

2017-08-29

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.

Observation of van Hove Singularities in Twisted Silicene Multilayers

PubMed Central

2016-01-01

Interlayer interactions perturb the electronic structure of two-dimensional materials and lead to new physical phenomena, such as van Hove singularities and Hofstadter’s butterfly pattern. Silicene, the recently discovered two-dimensional form of silicon, is quite unique, in that silicon atoms adopt competing sp2 and sp3 hybridization states leading to a low-buckled structure promising relatively strong interlayer interaction. In multilayer silicene, the stacking order provides an important yet rarely explored degree of freedom for tuning its electronic structures through manipulating interlayer coupling. Here, we report the emergence of van Hove singularities in the multilayer silicene created by an interlayer rotation. We demonstrate that even a large-angle rotation (>20°) between stacked silicene layers can generate a Moiré pattern and van Hove singularities due to the strong interlayer coupling in multilayer silicene. Our study suggests an intriguing method for expanding the tunability of the electronic structure for electronic applications in this two-dimensional material. PMID:27610412

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.

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

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.

The Singularity Mystery Associated with a Radially Continuous Maxwell Viscoelastic Structure

NASA Technical Reports Server (NTRS)

Fang, Ming; Hager, Bradford H.

1995-01-01

The singularity problem associated with a radially continuous Maxwell viscoclastic structure is investigated. A special tool called the isolation function is developed. Results calculated using the isolation function show that the discrete model assumption is no longer valid when the viscoelastic parameter becomes a continuous function of radius. Continuous variations in the upper mantle viscoelastic parameter are especially powerful in destroying the mode-like structures. The contribution to the load Love numbers of the singularities is sensitive to the convexity of the viscoelastic parameter models. The difference between the vertical response and the horizontal response found in layered viscoelastic parameter models remains with continuous models.

Robustness Analysis and Reliable Flight Regime Estimation of an Integrated Resilent Control System for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Belcastro, Christine

2008-01-01

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. As a part of the validation process, this paper describes an analysis method for determining a reliable flight regime in the flight envelope within which an integrated resilent control system can achieve the desired performance of tracking command signals and detecting additive faults in the presence of parameter uncertainty and unmodeled dynamics. To calculate a reliable flight regime, a structured singular value analysis method is applied to analyze the closed-loop system over the entire flight envelope. To use the structured singular value analysis method, a linear fractional transform (LFT) model of a transport aircraft longitudinal dynamics is developed over the flight envelope by using a preliminary LFT modeling software tool developed at the NASA Langley Research Center, which utilizes a matrix-based computational approach. The developed LFT model can capture original nonlinear dynamics over the flight envelope with the ! block which contains key varying parameters: angle of attack and velocity, and real parameter uncertainty: aerodynamic coefficient uncertainty and moment of inertia uncertainty. Using the developed LFT model and a formal robustness analysis method, a reliable flight regime is calculated for a transport aircraft closed-loop system.

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.

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.

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.

Spontaneous generation of singularities in paraxial optical fields.

PubMed

Aiello, Andrea

2016-04-01

In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrödinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

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.

Crystallographic parameters of compounds and solid solutions in binary systems Cu-Pt and Ga-Pt

NASA Astrophysics Data System (ADS)

Potekaev, Alexandr; Probova, Svetlana; Klopotov, Anatolii; Vlasov, Viktor; Markov, Tatiana; Klopotov, Vladimir

2015-10-01

The study establishes that the packing index in compounds of the system Cu-Pt is close to the value 0.74 against a slight deviation from the Zen law of atomic volumes. The compounds in the system Ga-Pt have the highest values of the packing index in the range of the equiatomic composition, which greatly exceed ψ for close-packed structures based on FCC and HCP lattices for compounds made of the same kind of atoms. A correlation between singular points on the phase diagram of the system Ga-Pt and high values of the packing index in compounds is established.

Analytic structure of the S-matrix for singular quantum mechanics

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

Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner

2015-06-15

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

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.

On computations of variance, covariance and correlation for interval data

NASA Astrophysics Data System (ADS)

Kishida, Masako

2017-02-01

In many practical situations, the data on which statistical analysis is to be performed is only known with interval uncertainty. Different combinations of values from the interval data usually lead to different values of variance, covariance, and correlation. Hence, it is desirable to compute the endpoints of possible values of these statistics. This problem is, however, NP-hard in general. This paper shows that the problem of computing the endpoints of possible values of these statistics can be rewritten as the problem of computing skewed structured singular values ν, for which there exist feasible (polynomial-time) algorithms that compute reasonably tight bounds in most practical cases. This allows one to find tight intervals of the aforementioned statistics for interval data.

Hypersonic vehicle control law development using H infinity and mu-synthesis

NASA Technical Reports Server (NTRS)

Gregory, Irene M.; Chowdhry, Rajiv S.; Mcminn, John D.; Shaughnessy, John D.

1992-01-01

Applicability and effectiveness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectiveness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Application of generalized singular value decomposition to ionospheric tomography

NASA Astrophysics Data System (ADS)

Bhuyan, K.; Singh, S.; Bhuyan, P.

2004-10-01

The electron density distribution of the low- and mid-latitude ionosphere has been investigated by the computerized tomography technique using a Generalized Singular Value Decomposition (GSVD) based algorithm. Model ionospheric total electron content (TEC) data obtained from the International Reference Ionosphere 2001 and slant relative TEC data measured at a chain of three stations receiving transit satellite transmissions in Alaska, USA are used in this analysis. The issue of optimum efficiency of the GSVD algorithm in the reconstruction of ionospheric structures is being addressed through simulation of the equatorial ionization anomaly (EIA), in addition to its application to investigate complicated ionospheric density irregularities. Results show that the Generalized Cross Validation approach to find the regularization parameter and the corresponding solution gives a very good reconstructed image of the low-latitude ionosphere and the EIA within it. Provided that some minimum norm is fulfilled, the GSVD solution is found to be least affected by considerations, such as pixel size and number of ray paths. The method has also been used to investigate the behaviour of the mid-latitude ionosphere under magnetically quiet and disturbed conditions.

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Experimental observation of the topological structure of exceptional points in an ultrathin hybridized metamaterial

NASA Astrophysics Data System (ADS)

Kang, Ming; Zhu, Weiren; Rukhlenko, Ivan D.

2017-12-01

The exceptional point (EP), which is one of the most important branch-type singularities exclusive to non-Hermitian systems, has been observed recently in various synthetic materials, giving rise to counterintuitive phenomena due to the nontrivial topology of the EP. Here, we present a direct experimental observation of the topological structure of the EPs via the angle-resolved transmission measurement of a hybridized metamaterial. Both eigenvalues and eigenvectors show branch-point singularities in the investigated biparametric space of frequency and incident angle. Importantly, the angle-resolved transmission coefficients provide all the information about the eigenvalues as well as the corresponding eigenvectors in the biparametric space, revealing the nontrivial topological structure of the EP, such as mode switching and the topological phase for a parameter loop encircling the EP. It is shown that the appearance of the EP in the scattering matrix is related directly to the perfect unidirectional transmission and the chirality of the EP corresponds to the maximum or minimum value of the asymmetric factor. Our investigation uncovers the capabilities of metamaterials for exploring the physics of EPs and their potential for having extreme optical properties, which provide potential applications in the spectral band ranging from microwaves to visible frequencies.

Assessing protein conformational sampling methods based on bivariate lag-distributions of backbone angles

PubMed Central

Maadooliat, Mehdi; Huang, Jianhua Z.

2013-01-01

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence–structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations. PMID:22926831

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.

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.

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)].

Optical character recognition with feature extraction and associative memory matrix

NASA Astrophysics Data System (ADS)

Sasaki, Osami; Shibahara, Akihito; Suzuki, Takamasa

1998-06-01

A method is proposed in which handwritten characters are recognized using feature extraction and an associative memory matrix. In feature extraction, simple processes such as shifting and superimposing patterns are executed. A memory matrix is generated with singular value decomposition and by modifying small singular values. The method is optically implemented with two liquid crystal displays. Experimental results for the recognition of 25 handwritten alphabet characters clearly shows the effectiveness of the method.

Incorporation of perceptually adaptive QIM with singular value decomposition for blind audio watermarking

NASA Astrophysics Data System (ADS)

Hu, Hwai-Tsu; Chou, Hsien-Hsin; Yu, Chu; Hsu, Ling-Yuan

2014-12-01

This paper presents a novel approach for blind audio watermarking. The proposed scheme utilizes the flexibility of discrete wavelet packet transformation (DWPT) to approximate the critical bands and adaptively determines suitable embedding strengths for carrying out quantization index modulation (QIM). The singular value decomposition (SVD) is employed to analyze the matrix formed by the DWPT coefficients and embed watermark bits by manipulating singular values subject to perceptual criteria. To achieve even better performance, two auxiliary enhancement measures are attached to the developed scheme. Performance evaluation and comparison are demonstrated with the presence of common digital signal processing attacks. Experimental results confirm that the combination of the DWPT, SVD, and adaptive QIM achieves imperceptible data hiding with satisfying robustness and payload capacity. Moreover, the inclusion of self-synchronization capability allows the developed watermarking system to withstand time-shifting and cropping attacks.

Cuckoo search algorithm based satellite image contrast and brightness enhancement using DWT-SVD.

PubMed

Bhandari, A K; Soni, V; Kumar, A; Singh, G K

2014-07-01

This paper presents a new contrast enhancement approach which is based on Cuckoo Search (CS) algorithm and DWT-SVD for quality improvement of the low contrast satellite images. The input image is decomposed into the four frequency subbands through Discrete Wavelet Transform (DWT), and CS algorithm used to optimize each subband of DWT and then obtains the singular value matrix of the low-low thresholded subband image and finally, it reconstructs the enhanced image by applying IDWT. The singular value matrix employed intensity information of the particular image, and any modification in the singular values changes the intensity of the given image. The experimental results show superiority of the proposed method performance in terms of PSNR, MSE, Mean and Standard Deviation over conventional and state-of-the-art techniques. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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

Art as a Singular Rule

ERIC Educational Resources Information Center

Avital, Doron

2007-01-01

This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…

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.

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Q{sub 2} evolution of parton distributions at small values of x: Effective scale for combined H1 and ZEUS data on the structure function F{sub 2}

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

Kotikov, A. V., E-mail: kotikov@theor.jinr.ru; Shaikhatdenov, B. G.

2015-06-15

An expression for the structure function F{sub 2} in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure functionmore » F{sub 2}.« less

Determining "small parameters" for quasi-steady state

NASA Astrophysics Data System (ADS)

Goeke, Alexandra; Walcher, Sebastian; Zerz, Eva

2015-08-01

For a parameter-dependent system of ordinary differential equations we present a systematic approach to the determination of parameter values near which singular perturbation scenarios (in the sense of Tikhonov and Fenichel) arise. We call these special values Tikhonov-Fenichel parameter values. The principal application we intend is to equations that describe chemical reactions, in the context of quasi-steady state (or partial equilibrium) settings. Such equations have rational (or even polynomial) right-hand side. We determine the structure of the set of Tikhonov-Fenichel parameter values as a semi-algebraic set, and present an algorithmic approach to their explicit determination, using Groebner bases. Examples and applications (which include the irreversible and reversible Michaelis-Menten systems) illustrate that the approach is rather easy to implement.

High-temperature superconductivity from fine-tuning of Fermi-surface singularities in iron oxypnictides.

PubMed

Charnukha, A; Evtushinsky, D V; Matt, C E; Xu, N; Shi, M; Büchner, B; Zhigadlo, N D; Batlogg, B; Borisenko, S V

2015-12-18

In the family of the iron-based superconductors, the REFeAsO-type compounds (with RE being a rare-earth metal) exhibit the highest bulk superconducting transition temperatures (Tc) up to 55 K and thus hold the key to the elusive pairing mechanism. Recently, it has been demonstrated that the intrinsic electronic structure of SmFe0.92Co0.08AsO (Tc = 18 K) is highly nontrivial and consists of multiple band-edge singularities in close proximity to the Fermi level. However, it remains unclear whether these singularities are generic to the REFeAsO-type materials and if so, whether their exact topology is responsible for the aforementioned record Tc. In this work, we use angle-resolved photoemission spectroscopy (ARPES) to investigate the inherent electronic structure of the NdFeAsO0.6F0.4 compound with a twice higher Tc = 38 K. We find a similarly singular Fermi surface and further demonstrate that the dramatic enhancement of superconductivity in this compound correlates closely with the fine-tuning of one of the band-edge singularities to within a fraction of the superconducting energy gap Δ below the Fermi level. Our results provide compelling evidence that the band-structure singularities near the Fermi level in the iron-based superconductors must be explicitly accounted for in any attempt to understand the mechanism of superconducting pairing in these materials.

High-temperature superconductivity from fine-tuning of Fermi-surface singularities in iron oxypnictides

NASA Astrophysics Data System (ADS)

Charnukha, A.; Evtushinsky, D. V.; Matt, C. E.; Xu, N.; Shi, M.; Büchner, B.; Zhigadlo, N. D.; Batlogg, B.; Borisenko, S. V.

2015-12-01

In the family of the iron-based superconductors, the REFeAsO-type compounds (with RE being a rare-earth metal) exhibit the highest bulk superconducting transition temperatures (Tc) up to 55 K and thus hold the key to the elusive pairing mechanism. Recently, it has been demonstrated that the intrinsic electronic structure of SmFe0.92Co0.08AsO (Tc = 18 K) is highly nontrivial and consists of multiple band-edge singularities in close proximity to the Fermi level. However, it remains unclear whether these singularities are generic to the REFeAsO-type materials and if so, whether their exact topology is responsible for the aforementioned record Tc. In this work, we use angle-resolved photoemission spectroscopy (ARPES) to investigate the inherent electronic structure of the NdFeAsO0.6F0.4 compound with a twice higher Tc = 38 K. We find a similarly singular Fermi surface and further demonstrate that the dramatic enhancement of superconductivity in this compound correlates closely with the fine-tuning of one of the band-edge singularities to within a fraction of the superconducting energy gap Δ below the Fermi level. Our results provide compelling evidence that the band-structure singularities near the Fermi level in the iron-based superconductors must be explicitly accounted for in any attempt to understand the mechanism of superconducting pairing in these materials.

Phases of unstable conifolds

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

Narayan, K.

2007-03-15

We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix Q=(n{sub 1}n{sub 2}-n{sub 3}-n{sub 4}), n{sub i}>0, iQ{sub i}{ne}0, initiated by Narayan [J. High Energy Phys. 03 (2006) 036]. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascadelike phase structure containing decays to lower order conifold-like singularities, including, in particular, the supersymmetric conifold and the Y{sup pq} spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometriesmore » include flips and flops.« less

Singularities of the quad curl problem

NASA Astrophysics Data System (ADS)

Nicaise, Serge

2018-04-01

We consider the quad curl problem in smooth and non smooth domains of the space. We first give an augmented variational formulation equivalent to the one from [25] if the datum is divergence free. We describe the singularities of the variational space which correspond to the ones of the Maxwell system with perfectly conducting boundary conditions. The edge and corner singularities of the solution of the corresponding boundary value problem with smooth data are also characterized. We finally obtain some regularity results of the variational solution.

Singular-value decomposition of a tomosynthesis system

PubMed Central

Burvall, Anna; Barrett, Harrison H.; Myers, Kyle J.; Dainty, Christopher

2010-01-01

Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object. The measurement component can be used as a reconstruction of the object, and can also be utilized in future observer studies of tomosynthesis image quality. PMID:20940966

Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1982.

DTIC Science & Technology

1982-12-01

established in the 1960s, when they first became a means for simplified computation of optimal trajectories. It was soon recognized that singular...null-space of P(ao). The asymptotic values of the invariant zeros and associated invariant-zero directions as € O are the values computed from the...49 ’ 49 7. WEAK COUPLING AND TIME SCALES The need for model simplification with a reduction (or distribution) of computational effort is

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Noniterative computation of infimum in H(infinity) optimisation for plants with invariant zeros on the j(omega)-axis

NASA Technical Reports Server (NTRS)

Chen, B. M.; Saber, A.

1993-01-01

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem is presented, as a continuation of our earlier work. Our problem formulation is general and we do not place any restrictions in the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j(omega) axis.

Review of LFTs, LMIs, and mu. [Linear Fractional Transformations, Linear Matrix Inequalities

NASA Technical Reports Server (NTRS)

Doyle, John; Packard, Andy; Zhou, Kemin

1991-01-01

The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu, and linear matrix inequalities (LMIs) in solving LFT problems. The authors first introduce the notation for LFTs and briefly discuss some of their properties. They then describe mu and its connections with LFTs. They focus on two standard notions of robust stability and performance, mu stability and performance and Q stability and performance, and their relationship is discussed. Comparisons with the L1 theory of robust performance with structured uncertainty are considered.

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

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.

Some Results on Proper Eigenvalues and Eigenvectors with Applications to Scaling.

ERIC Educational Resources Information Center

McDonald, Roderick P.; And Others

1979-01-01

Problems in avoiding the singularity problem in analyzing matrices for optimal scaling are addressed. Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. (Author/JKS)

Tailored vectorial light fields: flower, spider web and hybrid structures

NASA Astrophysics Data System (ADS)

Otte, Eileen; Alpmann, Christina; Denz, Cornelia

2017-04-01

We present the realization and analysis of tailored vector fields including polarization singularities. The fields are generated by a holographic method based on an advanced system including a spatial light modulator. We demonstrate our systems capabilities realizing specifically customized vector fields including stationary points of defined polarization in its transverse plane. Subsequently, vectorial flowers and spider webs as well as unique hybrid structures of these are introduced, and embedded singular points are characterized. These sophisticated light fields reveal attractive properties that pave the way to advanced application in e.g. optical micromanipulation. Beyond particle manipulation, they contribute essentially to actual questions in singular optics.

Generation of fractional acoustic vortex with a discrete Archimedean spiral structure plate

NASA Astrophysics Data System (ADS)

Jia, Yu-Rou; Wei, Qi; Wu, Da-Jian; Xu, Zheng; Liu, Xiao-Jun

2018-04-01

Artificial structure plates engraved with discrete Archimedean spiral slits have been well designed to achieve fractional acoustic vortices (FAVs). The phase and pressure field distributions of FAVs are investigated theoretically and demonstrated numerically. It is found that the phase singularities relating to the integer and fractional parts of the topological charge (TC) result in dark spots in the upper half of the pressure field profile and a low-intensity stripe in the lower half of the pressure field profile, respectively. The dynamic progress of the FAV is also discussed in detail as TC increases from 1 to 2. With increasing TC from 1 to 1.5, the splitting of the phase singularity leads to the deviation of the phase of the FAV from the integer case and hence a new phase singularity occurs. As TC m increases from 1.5 to 2, two phase singularities of the FAV approach together and finally merge as a new central phase singularity. We further perform an experiment based on the Schlieren method to demonstrate the generation of the FAV.

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).

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.

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

Singular temperature dependence of the equation of state of superconductors with spin–orbit interaction in the low-temperature region

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

Ovchinnikov, Yu. N., E-mail: ovc@itp.ac.ru

The equation of state is investigated for a thin superconducting film in a longitudinal magnetic field and with strong spin-orbit interaction at the critical point. As a first step, the state with the maximal value of the magnetic field for a given value of spin–orbit interaction at T = 0 is chosen. This state is investigated in the low-temperature region. The temperature contribution to the equation of state is weakly singular.

New inclusion sets for singular values.

PubMed

He, Jun; Liu, Yan-Min; Tian, Jun-Kang; Ren, Ze-Rong

2017-01-01

In this paper, for a given matrix [Formula: see text], in terms of [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the Geršgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984) and the Brauer-type sets (Li in Comput. Math. Appl. 37:9-15, 1999). A numerical experiment shows the efficiency of our new results.

Tests of conformal field theory at the Yang-Lee singularity

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

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

Evidence of van Hove singularities in ordered grain boundaries of graphene.

PubMed

Ma, Chuanxu; Sun, Haifeng; Zhao, Yeliang; Li, Bin; Li, Qunxiang; Zhao, Aidi; Wang, Xiaoping; Luo, Yi; Yang, Jinlong; Wang, Bing; Hou, J G

2014-06-06

It has long been under debate whether the electron transport performance of graphene could be enhanced by the possible occurrence of van Hove singularities in grain boundaries. Here, we provide direct experimental evidence to confirm the existence of van Hove singularity states close to the Fermi energy in certain ordered grain boundaries using scanning tunneling microscopy. The intrinsic atomic and electronic structures of two ordered grain boundaries, one with alternative pentagon and heptagon rings and the other with alternative pentagon pair and octagon rings, are determined. It is firmly verified that the carrier concentration and, thus, the conductance around ordered grain boundaries can be significantly enhanced by the van Hove singularity states. This finding strongly suggests that a graphene nanoribbon with a properly embedded ordered grain boundary can be a promising structure to improve the performance of graphene-based electronic devices.

Tailoring Eigenmodes at Spectral Singularities in Graphene-based PT Systems.

PubMed

Zhang, Weixuan; Wu, Tong; Zhang, Xiangdong

2017-09-12

The spectral singularity existing in PT-synthetic plasmonic system has been widely investigated. Only lasing-mode can be excited resulting from the passive characteristic of metallic materials. Here, we investigated the spectral singularity in the hybrid structure composed of the photoexcited graphene and one-dimensional PT-diffractive grating. In this system, both lasing- and absorption-modes can be excited with the surface conductivity of photoexcited graphene being loss and gain, respectively. Remarkably, the spectral singularity will disappear with the optically pumped graphene to be lossless. In particular, we find that spectral singularities can exhibit symmetry-modes, when the loss and gain of the grating is unbalanced. Meanwhile, by tuning the loss (gain) of graphene and non-PT diffraction grating, lasing- and absorption-modes can also be excited. We hope that tunable optical modes at spectral singularities can have some applications in designing novel surface-enhanced spectroscopies and plasmon lasers.

Progress in multirate digital control system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1991-01-01

A new methodology for multirate sampled-data control design based on a new generalized control law structure, two new parameter-optimization-based control law synthesis methods, and a new singular-value-based robustness analysis method are described. The control law structure can represent multirate sampled-data control laws of arbitrary structure and dynamic order, with arbitrarily prescribed sampling rates for all sensors and update rates for all processor states and actuators. The two control law synthesis methods employ numerical optimization to determine values for the control law parameters. The robustness analysis method is based on the multivariable Nyquist criterion applied to the loop transfer function for the sampling period equal to the period of repetition of the system's complete sampling/update schedule. The complete methodology is demonstrated by application to the design of a combination yaw damper and modal suppression system for a commercial aircraft.

Observational constraints on finite scale factor singularities

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

Denkiewicz, Tomasz, E-mail: atomekd@wmf.univ.szczecin.pl

2012-07-01

We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter R, baryon acoustic oscillations (BAO) A, and from the type Ia supernovae. We show that observations allow existence of such singularities in the 2 × 10{sup 9} years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is anmore » allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.« less

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Influence of local meshing size on stress intensity factor of orthopedic lag screw

NASA Astrophysics Data System (ADS)

Husain, M. N.; Daud, R.; Basaruddin, K. S.; Mat, F.; Bajuri, M. Y.; Arifin, A. K.

2017-09-01

Linear elastic fracture mechanics (LEFM) concept is generally used to study the influence of crack on the performance of structures. In order to study the LEFM concept on damaged structure, the usage of finite element analysis software is implemented to do the simulation of the structure. Mesh generation is one of the most crucial procedures in finite element method. For the structure that crack or damaged, it is very important to determine the accurate local meshing size at the crack tip of the crack itself in order to get the accurate value of stress intensity factor, KI. Pre crack will be introduced to the lag screw based on the von mises' stress result that had been performed in previous research. This paper shows the influence of local mesh arrangement on numerical value of the stress intensity factor, KI obtained by the displacement method. This study aims to simulate the effect of local meshing which is the singularity region on stress intensity factor, KI to the critical point of failure in screw. Five different set of wedges meshing size are introduced during the simulation of finite element analysis. The number of wedges used to simulate this research is 8, 10, 14, 16 and 20. There are three set of numerical equations used to validate the results which are brown and srawley, gross and brown and Tada equation. The result obtained from the finite element software (ANSYS APDL) has a positive agreement with the numerical analysis which is Brown and Srawley compared to other numerical formula. Radius of first row size of 0.014 and singularity element with 14 numbers of wedges is proved to be the best local meshing for this study.

Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with δ-potential

NASA Astrophysics Data System (ADS)

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga

2018-03-01

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.

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.

Yang-Lee zeros, Julia sets, and their singularity spectra

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

Hu, B.; Lin, B.

1989-05-01

We have studied the global scaling properties of the Julia sets of the Yang-Lee zeros of the s-state Potts model on the diamond hierarchical lattice. The singularity spectrum f(..cap alpha..) and the generalized dimension D/sub q/ are calculated for different s values. General observations are made on their variations.

Structure of polarization singularities of a light beam at triple frequency generated in isotropic medium by singularly polarized beam.

PubMed

Grigoriev, K S; Ryzhikov, P S; Cherepetskaya, E B; Makarov, V A

2017-10-16

The components of electric field of the third harmonic beam, generated in isotropic medium with cubic nonlinearity by a monochromatic light beam carrying polarization singularity of an arbitrary type, are found analytically. The relation between C-points characteristics in the fundamental and signal beams are determined, as well as the impact of the phase mismatch on the shape of the C-lines.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

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

Singular behavior of jet substructure observables

DOE PAGES

Larkoski, Andrew J.; Moult, Ian

2016-01-20

Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, N-subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limits in which two-prong structure is resolved or unresolved. Dependingmore » on the choice of subjet axes, we demonstrate that at fixed order, N-subjettiness can manifest myriad behaviors in the unresolved region: smooth tails, end-point singularities, or singularities in the physical region. The energy correlation functions, by contrast, only have non-singular perturbative tails extending to the end point. We discuss the effect of hadronization on the various observables with Monte Carlo simulation and demonstrate that the modeling of these effects with non-perturbative shape functions is highly dependent on the N-subjettiness axes definitions. Lastly, our study illustrates those regions of phase space that must be controlled for high-precision jet substructure calculations, and emphasizes how such calculations can be facilitated by designing substructure observables with simple singular structures.« less

Robust penalty method for structural synthesis

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1983-01-01

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

Constructing Current Singularity in a 3D Line-tied Plasma

DOE PAGES

Zhou, Yao; Huang, Yi-Min; Qin, Hong; ...

2017-12-27

We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finitemore » amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. Finally, with the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.« less

Time Hierarchies and Model Reduction in Canonical Non-linear Models

PubMed Central

Löwe, Hannes; Kremling, Andreas; Marin-Sanguino, Alberto

2016-01-01

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems. PMID:27708665

The predictive power of singular value decomposition entropy for stock market dynamics

NASA Astrophysics Data System (ADS)

Caraiani, Petre

2014-01-01

We use a correlation-based approach to analyze financial data from the US stock market, both daily and monthly observations from the Dow Jones. We compute the entropy based on the singular value decomposition of the correlation matrix for the components of the Dow Jones Industrial Index. Based on a moving window, we derive time varying measures of entropy for both daily and monthly data. We find that the entropy has a predictive ability with respect to stock market dynamics as indicated by the Granger causality tests.

Collisional evolution - an analytical study for the non steady-state mass distribution.

NASA Astrophysics Data System (ADS)

Vieira Martins, R.

1999-05-01

To study the collisional evolution of asteroidal groups one can use an analytical solution for the self-similar collision cascades. This solution is suitable to study the steady-state mass distribution of the collisional fragmentation. However, out of the steady-state conditions, this solution is not satisfactory for some values of the collisional parameters. In fact, for some values for the exponent of the mass distribution power law of an asteroidal group and its relation to the exponent of the function which describes "how rocks break" the author arrives at singular points for the equation which describes the collisional evolution. These singularities appear since some approximations are usually made in the laborious evaluation of many integrals that appear in the analytical calculations. They concern the cutoff for the smallest and the largest bodies. These singularities set some restrictions to the study of the analytical solution for the collisional equation. To overcome these singularities the author performed an algebraic computation considering the smallest and the largest bodies and he obtained the analytical expressions for the integrals that describe the collisional evolution without restriction on the parameters. However, the new distribution is more sensitive to the values of the collisional parameters. In particular the steady-state solution for the differential mass distribution has exponents slightly different from 11/6 for the usual parameters in the asteroid belt. The sensitivity of this distribution with respect to the parameters is analyzed for the usual values in the asteroidal groups. With an expression for the mass distribution without singularities, one can evaluate also its time evolution. The author arrives at an analytical expression given by a power series of terms constituted by a small parameter multiplied by the mass to an exponent, which depends on the initial power law distribution. This expression is a formal solution for the equation which describes the collisional evolution.

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

Fracture and fatigue analysis of functionally graded and homogeneous materials using singular integral equation approach

NASA Astrophysics Data System (ADS)

Zhao, Huaqing

There are two major objectives of this thesis work. One is to study theoretically the fracture and fatigue behavior of both homogeneous and functionally graded materials, with or without crack bridging. The other is to further develop the singular integral equation approach in solving mixed boundary value problems. The newly developed functionally graded materials (FGMs) have attracted considerable research interests as candidate materials for structural applications ranging from aerospace to automobile to manufacturing. From the mechanics viewpoint, the unique feature of FGMs is that their resistance to deformation, fracture and damage varies spatially. In order to guide the microstructure selection and the design and performance assessment of components made of functionally graded materials, in this thesis work, a series of theoretical studies has been carried out on the mode I stress intensity factors and crack opening displacements for FGMs with different combinations of geometry and material under various loading conditions, including: (1) a functionally graded layer under uniform strain, far field pure bending and far field axial loading, (2) a functionally graded coating on an infinite substrate under uniform strain, and (3) a functionally graded coating on a finite substrate under uniform strain, far field pure bending and far field axial loading. In solving crack problems in homogeneous and non-homogeneous materials, a very powerful singular integral equation (SEE) method has been developed since 1960s by Erdogan and associates to solve mixed boundary value problems. However, some of the kernel functions developed earlier are incomplete and possibly erroneous. In this thesis work, mode I fracture problems in a homogeneous strip are reformulated and accurate singular Cauchy type kernels are derived. Very good convergence rates and consistency with standard data are achieved. Other kernel functions are subsequently developed for mode I fracture in functionally graded materials. This work provides a solid foundation for further applications of the singular integral equation approach to fracture and fatigue problems in advanced composites. The concept of crack bridging is a unifying theory for fracture at various length scales, from atomic cleavage to rupture of concrete structures. However, most of the previous studies are limited to small scale bridging analyses although large scale bridging conditions prevail in engineering materials. In this work, a large scale bridging analysis is included within the framework of singular integral equation approach. This allows us to study fracture, fatigue and toughening mechanisms in advanced materials with crack bridging. As an example, the fatigue crack growth of grain bridging ceramics is studied. With the advent of composite materials technology, more complex material microstructures are being introduced, and more mechanics issues such as inhomogeneity and nonlinearity come into play. Improved mathematical and numerical tools need to be developed to allow theoretical modeling of these materials. This thesis work is an attempt to meet these challenges by making contributions to both micromechanics modeling and applied mathematics. It sets the stage for further investigations of a wide range of problems in the deformation and fracture of advanced engineering materials.

Non-singular Brans-Dicke collapse in deformed phase space

NASA Astrophysics Data System (ADS)

Rasouli, S. M. M.; Ziaie, A. H.; Jalalzadeh, S.; Moniz, P. V.

2016-12-01

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

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.

Fully stable cosmological solutions with a non-singular classical bounce

DOE PAGES

Ijjas, Anna; Steinhardt, Paul J.

2016-11-28

Recently, we showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. One drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L 4 Galileon interaction.more » In using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.« less

Collapse of a self-similar cylindrical scalar field with non-minimal coupling II: strong cosmic censorship

NASA Astrophysics Data System (ADS)

Condron, Eoin; Nolan, Brien C.

2014-08-01

We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We extend the work of Condron and Nolan (2014 Class. Quantum Grav. 31 015015), which determined the global structure of all solutions with a regular axis in the causal past of the singularity. We identified a class of solutions that evolves through the past null cone of the singularity. We give the global structure of these solutions and show that the singularity is censored in all cases.

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.

Tangled nonlinear driven chain reactions of all optical singularities

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Soskin, M. S.

2012-03-01

Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

Characteristic classes, singular embeddings, and intersection homology.

PubMed

Cappell, S E; Shaneson, J L

1987-06-01

This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Bossel, H. H.

1972-01-01

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

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

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.

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices.

PubMed

Hooper, I R; Philbin, T G

2013-12-30

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co-ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an "invisible disc" and "multipole" lenses.

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%.

MIB Galerkin method for elliptic interface problems.

PubMed

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-12-15

Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the designed second order convergence of the MIB Galerkin method in the L ∞ and L 2 errors. Some of the best results are obtained in the present work when the interface is C 1 or Lipschitz continuous and the solution is C 2 continuous.

Electronic structure and the van Hove singularity scenario in high-T(sub c)H(g)Ba2CuO(4+delta) superconductors

NASA Technical Reports Server (NTRS)

Agrawal, Bal K.; Agrawal, Savitri

1995-01-01

The electronic structure and the hole concentrations in the high Tc superconductor HgBa2CuO(4+delta) (delta = O, 1) has been investigated by employing a first principles full potential self-consistent LMTO method with the local density functional theory. The scalar relativistic effects have been considered. The hole concentrations of the Cu-d and O-p(x,y) orbitals are seen to be larger for the HgBaCuO5 system than those of the HgBaCuO4 solid. However, the van Hove singularity (vHs) induced Cu-d and O-p peak which is seen to lie comparatively away and above the Fermi level in the delta = 1 system shifts towards the Fermi level in the delta = 0 system. Thus, the superconducting behavior appears to originate from the occurrence of the vHs peak at the Fermi level. The Fermi surface nesting area in the delta = 0 compound is seen to be larger than in the delta = 1 compound. The calculation reveals that the increase in pressure on the crystal enhances the hole concentrations but without showing any optimum value, On the other hand, the vHs peak approaches to-wards the Fermi level with pressure and crosses the Fermi surface near V/Vo approximately equals 0.625 (V and Vo are the crystal volumes at high and normal pressures, respectively). Our calculated value of the bulk modulus equal to 0.626 Mbar predicts the occurrence of this crossover at about 24 GPa which is in complete agreement with the experimental value. At this pressure the compound has maximum nesting area and self-doped behavior.

Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization

NASA Astrophysics Data System (ADS)

Jia, Zhongxiao; Yang, Yanfei

2018-05-01

In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: subject to , where L is a regularization matrix. Our algorithms are inspired by the modified truncated singular value decomposition (MTSVD) method, which suits only for small to medium scale problems, and randomized SVD (RSVD) algorithms that generate good low rank approximations to A. We use rank-k truncated randomized SVD (TRSVD) approximations to A by truncating the rank- RSVD approximations to A, where q is an oversampling parameter. The resulting algorithms are called modified TRSVD (MTRSVD) methods. At every step, we use the LSQR algorithm to solve the resulting inner least squares problem, which is proved to become better conditioned as k increases so that LSQR converges faster. We present sharp bounds for the approximation accuracy of the RSVDs and TRSVDs for severely, moderately and mildly ill-posed problems, and substantially improve a known basic bound for TRSVD approximations. We prove how to choose the stopping tolerance for LSQR in order to guarantee that the computed and exact best regularized solutions have the same accuracy. Numerical experiments illustrate that the best regularized solutions by MTRSVD are as accurate as the ones by the truncated generalized singular value decomposition (TGSVD) algorithm, and at least as accurate as those by some existing truncated randomized generalized singular value decomposition (TRGSVD) algorithms. This work was supported in part by the National Science Foundation of China (Nos. 11771249 and 11371219).

Radar Imaging of Spheres in 3D using MUSIC

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

Chambers, D H; Berryman, J G

2003-01-21

We have shown that multiple spheres can be imaged by linear and planar EM arrays using only one component of polarization. The imaging approach involves calculating the SVD of the scattering response matrix, selecting a subset of singular values that represents noise, and evaluating the MUSIC functional. The noise threshold applied to the spectrum of singular values for optimal performance is typically around 1%. The resulting signal subspace includes more than one singular value per sphere. The presence of reflections from the ground improves height localization, even for a linear array parallel to the ground. However, the interference between directmore » and reflected energy modulates the field, creating periodic nulls that can obscure targets in typical images. These nulls are largely eliminated by normalizing the MUSIC functional with the broadside beam pattern of the array. The resulting images show excellent localization for 1 and 2 spheres. The performance for the 3 sphere configurations are complicated by shadowing effects and the greater range of the 3rd sphere in case 2. Two of the three spheres are easily located by MUSIC but the third is difficult to distinguish from other local maxima of the complex imaging functional. Improvement is seen when the linear array is replace with a planar array, which increases the effective aperture height. Further analysis of the singular values and their relationship to modes of scattering from the spheres, as well as better ways to exploit polarization, should improve performance. Work along these lines is currently being pursued by the authors.« less

Structural acoustic control of plates with variable boundary conditions: design methodology.

PubMed

Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L

2007-07-01

A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties.

Cosmology with an interacting van der Waals fluid

NASA Astrophysics Data System (ADS)

Elizalde, E.; Khurshudyan, M.

A model for the late-time accelerated expansion of the Universe is considered where a van der Waals fluid interacting with matter plays the role of dark energy. The transition towards this phase in the cosmic evolution history is discussed in detail and, moreover, a complete classification of the future finite-time singularities is obtained for six different possible forms of the nongravitational interaction between dark energy (the van der Waals fluid) and dark matter. This study shows, in particular, that a Universe with a noninteracting three-parameter van der Waals fluid can evolve into a Universe characterized by a type IV (generalized sudden) singularity. On the other hand, for certain values of the parameters, exit from the accelerated expanding phase is possible in the near future, what means that the expansion of the Universe in the future could become decelerated - to our knowledge, this interesting situation is not commonplace in the literature. On the other hand, our study shows that space can be divided into different regions. For some of them, in particular, the nongravitational interactions Q = 3Hbρde, Q = 3Hbρdm and Q = 3Hb(ρde + ρde) may completely suppress future finite-time singularity formation, for sufficiently high values of b. On the other hand, for some other regions of the parameter space, the mentioned interactions would not affect the singularity type, namely the type IV singularity generated in the case of the noninteracting model would be preserved. A similar conclusion has been archived for the cases of Q = 3bHρdeρdm/(ρde + ρdm), Q = 3bHρdm2/(ρ de + ρdm) and Q = 3bHρde2/(ρ de + ρdm) nongravitational interactions, with only one difference: the Q = 3bHρdm2/(ρ de + ρdm) interaction will change the type IV singularity of the noninteracting model into a type II (the sudden) singularity.

Hilbert's Hotel in polarization singularities.

PubMed

Wang, Yangyundou; Gbur, Greg

2017-12-15

We demonstrate theoretically how the creation of polarization singularities by the evolution of a fractional nonuniform polarization optical element involves the peculiar mathematics of countably infinite sets in the form of "Hilbert's Hotel." Two distinct topological processes can be observed, depending on the structure of the fractional optical element.

A circumferential crack in a cylindrical shell under tension.

NASA Technical Reports Server (NTRS)

Duncan-Fama, M. E.; Sanders, J. L., Jr.

1972-01-01

A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.

Robust Control of Multivariable and Large Scale Systems.

DTIC Science & Technology

1988-03-23

D, and let A E [0, 1]. We need to show that h ((1 - A)D1 + AD2 ) < (1 - A)h(D 1 ) + Ah(D 2) Define f:R-+R by f(t) := h((1 - t)D 1 + tD 2 ) = ebt...SVD -S M = 3UV * + U2E2 V2 *. (13.11) In this setting, / is any singular value of M, not necessarily &(M), but none of the singular values in E 2 should...a)f (x) -afr(y)] and let A be the largest value in [0, 1] that achieves #3. Obviously, since /3 > 0, A E (0, 1). Define tD := (1 - A)x + Ay. Hence f

Bianchi I cosmology in the presence of a causally regularized viscous fluid

NASA Astrophysics Data System (ADS)

Montani, Giovanni; Venanzi, Marta

2017-07-01

We analyze the dynamics of a Bianchi I cosmology in the presence of a viscous fluid, causally regularized according to the Lichnerowicz approach. We show how the effect induced by shear viscosity is still able to produce a matter creation phenomenon, meaning that also in the regularized theory we address, the Universe is emerging from a singularity with a vanishing energy density value. We discuss the structure of the singularity in the isotropic limit, when bulk viscosity is the only retained contribution. We see that, as far as viscosity is not a dominant effect, the dynamics of the isotropic Universe possesses the usual non-viscous power-law behaviour but in correspondence to an effective equation of state, depending on the bulk viscosity coefficient. Finally, we show that, in the limit of a strong non-thermodynamical equilibrium of the Universe mimicked by a dominant contribution of the effective viscous pressure, a power-law inflation behaviour of the Universe appears, the cosmological horizons are removed and a significant amount of entropy is produced.

Application of higher order SVD to vibration-based system identification and damage detection

NASA Astrophysics Data System (ADS)

Chao, Shu-Hsien; Loh, Chin-Hsiung; Weng, Jian-Huang

2012-04-01

Singular value decomposition (SVD) is a powerful linear algebra tool. It is widely used in many different signal processing methods, such principal component analysis (PCA), singular spectrum analysis (SSA), frequency domain decomposition (FDD), subspace identification and stochastic subspace identification method ( SI and SSI ). In each case, the data is arranged appropriately in matrix form and SVD is used to extract the feature of the data set. In this study three different algorithms on signal processing and system identification are proposed: SSA, SSI-COV and SSI-DATA. Based on the extracted subspace and null-space from SVD of data matrix, damage detection algorithms can be developed. The proposed algorithm is used to process the shaking table test data of the 6-story steel frame. Features contained in the vibration data are extracted by the proposed method. Damage detection can then be investigated from the test data of the frame structure through subspace-based and nullspace-based damage indices.

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.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

Non-Cooperative Target Recognition by Means of Singular Value Decomposition Applied to Radar High Resolution Range Profiles †

PubMed Central

López-Rodríguez, Patricia; Escot-Bocanegra, David; Fernández-Recio, Raúl; Bravo, Ignacio

2015-01-01

Radar high resolution range profiles are widely used among the target recognition community for the detection and identification of flying targets. In this paper, singular value decomposition is applied to extract the relevant information and to model each aircraft as a subspace. The identification algorithm is based on angle between subspaces and takes place in a transformed domain. In order to have a wide database of radar signatures and evaluate the performance, simulated range profiles are used as the recognition database while the test samples comprise data of actual range profiles collected in a measurement campaign. Thanks to the modeling of aircraft as subspaces only the valuable information of each target is used in the recognition process. Thus, one of the main advantages of using singular value decomposition, is that it helps to overcome the notable dissimilarities found in the shape and signal-to-noise ratio between actual and simulated profiles due to their difference in nature. Despite these differences, the recognition rates obtained with the algorithm are quite promising. PMID:25551484

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.

Multifractal surrogate-data generation algorithm that preserves pointwise Hölder regularity structure, with initial applications to turbulence

NASA Astrophysics Data System (ADS)

Keylock, C. J.

2017-03-01

An algorithm is described that can generate random variants of a time series while preserving the probability distribution of original values and the pointwise Hölder regularity. Thus, it preserves the multifractal properties of the data. Our algorithm is similar in principle to well-known algorithms based on the preservation of the Fourier amplitude spectrum and original values of a time series. However, it is underpinned by a dual-tree complex wavelet transform rather than a Fourier transform. Our method, which we term the iterated amplitude adjusted wavelet transform can be used to generate bootstrapped versions of multifractal data, and because it preserves the pointwise Hölder regularity but not the local Hölder regularity, it can be used to test hypotheses concerning the presence of oscillating singularities in a time series, an important feature of turbulence and econophysics data. Because the locations of the data values are randomized with respect to the multifractal structure, hypotheses about their mutual coupling can be tested, which is important for the velocity-intermittency structure of turbulence and self-regulating processes.

Using linear algebra for protein structural comparison and classification

PubMed Central

2009-01-01

In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in. PMID:21637532

Using linear algebra for protein structural comparison and classification.

PubMed

Gomide, Janaína; Melo-Minardi, Raquel; Dos Santos, Marcos Augusto; Neshich, Goran; Meira, Wagner; Lopes, Júlio César; Santoro, Marcelo

2009-07-01

In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in.

Singular Atom Optics with Spinor BECs

NASA Astrophysics Data System (ADS)

Schultz, Justin T.; Hansen, Azure; Bigelow, Nicholas P.

2015-05-01

We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.

Correlation between topological structure and its properties in dynamic singular vector fields.

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 10³  s order.

Signal evaluations using singular value decomposition for Thomson scattering diagnostics.

PubMed

Tojo, H; Yamada, I; Yasuhara, R; Yatsuka, E; Funaba, H; Hatae, T; Hayashi, H; Itami, K

2014-11-01

This paper provides a novel method for evaluating signal intensities in incoherent Thomson scattering diagnostics. A double-pass Thomson scattering system, where a laser passes through the plasma twice, generates two scattering pulses from the plasma. Evaluations of the signal intensities in the spectrometer are sometimes difficult due to noise and stray light. We apply the singular value decomposition method to Thomson scattering data with strong noise components. Results show that the average accuracy of the measured electron temperature (Te) is superior to that of temperature obtained using a low-pass filter (<20 MHz) or without any filters.

Signal evaluations using singular value decomposition for Thomson scattering diagnostics

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

Tojo, H., E-mail: tojo.hiroshi@jaea.go.jp; Yatsuka, E.; Hatae, T.

2014-11-15

This paper provides a novel method for evaluating signal intensities in incoherent Thomson scattering diagnostics. A double-pass Thomson scattering system, where a laser passes through the plasma twice, generates two scattering pulses from the plasma. Evaluations of the signal intensities in the spectrometer are sometimes difficult due to noise and stray light. We apply the singular value decomposition method to Thomson scattering data with strong noise components. Results show that the average accuracy of the measured electron temperature (T{sub e}) is superior to that of temperature obtained using a low-pass filter (<20 MHz) or without any filters.

Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage.

PubMed

Aggarwal, Priya; Shrivastava, Parth; Kabra, Tanay; Gupta, Anubha

2017-03-01

This paper presents a new accelerated fMRI reconstruction method, namely, OptShrink LR + S method that reconstructs undersampled fMRI data using a linear combination of low-rank and sparse components. The low-rank component has been estimated using non-convex optimal singular value shrinkage algorithm, while the sparse component has been estimated using convex l 1 minimization. The performance of the proposed method is compared with the existing state-of-the-art algorithms on real fMRI dataset. The proposed OptShrink LR + S method yields good qualitative and quantitative results.

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.

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

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.

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.

Integrated flight/propulsion control - Subsystem specifications for performance

NASA Technical Reports Server (NTRS)

Neighbors, W. K.; Rock, Stephen M.

1993-01-01

A procedure is presented for calculating multiple subsystem specifications given a number of performance requirements on the integrated system. This procedure applies to problems where the control design must be performed in a partitioned manner. It is based on a structured singular value analysis, and generates specifications as magnitude bounds on subsystem uncertainties. The performance requirements should be provided in the form of bounds on transfer functions of the integrated system. This form allows the expression of model following, command tracking, and disturbance rejection requirements. The procedure is demonstrated on a STOVL aircraft design.

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.

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.

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.

Timelike naked singularity

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

Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo

We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularitymore » formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture.« less

Non-singular Brans–Dicke collapse in deformed phase space

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

Rasouli, S.M.M., E-mail: mrasouli@ubi.pt; Centro de Matemática e Aplicações; Physics Group, Qazvin Branch, Islamic Azad University, Qazvin

2016-12-15

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theorymore » is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.« less

Electronics and Algorithms for HOM Based Beam Diagnostics

NASA Astrophysics Data System (ADS)

Frisch, Josef; Baboi, Nicoleta; Eddy, Nathan; Nagaitsev, Sergei; Hensler, Olaf; McCormick, Douglas; May, Justin; Molloy, Stephen; Napoly, Olivier; Paparella, Rita; Petrosyan, Lyudvig; Ross, Marc; Simon, Claire; Smith, Tonee

2006-11-01

The signals from the Higher Order Mode (HOM) ports on superconducting cavities can be used as beam position monitors and to do survey structure alignment. A HOM-based diagnostic system has been installed to instrument both couplers on each of the 40 cryogenic accelerating structures in the DESY TTF2 Linac. The electronics uses a single stage down conversion from the 1.7 GHz HOM spectral line to a 20MHz IF which has been digitized. The electronics is based on low cost surface mount components suitable for large scale production. The analysis of the HOM data is based on Singular Value Decomposition. The response of the OM modes is calibrated using conventional BPMs.

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

NASA Technical Reports Server (NTRS)

Hogan, Robert C.; Cuzzi, Jeffrey N.; Dobrovolskis, Anthony R.; DeVincenzi, Donald (Technical Monitor)

1998-01-01

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

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

Haro, Jaume de, E-mail: jaime.haro@upc.edu

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent waymore » to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.« less

Antiferromagnetic order in the Hubbard model on the Penrose lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Tsunetsugu, Hirokazu

2017-12-01

We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion U →+0 , the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing U , they continuously evolve to those of the corresponding spin model in the U =∞ limit. In both limits of U , local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.

Relativistic model for anisotropic strange stars

NASA Astrophysics Data System (ADS)

Deb, Debabrata; Chowdhury, Sourav Roy; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2017-12-01

In this article, we attempt to find a singularity free solution of Einstein's field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002) , which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses below the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant Bg.

Inferring Gene Regulatory Networks by Singular Value Decomposition and Gravitation Field Algorithm

PubMed Central

Zheng, Ming; Wu, Jia-nan; Huang, Yan-xin; Liu, Gui-xia; Zhou, You; Zhou, Chun-guang

2012-01-01

Reconstruction of gene regulatory networks (GRNs) is of utmost interest and has become a challenge computational problem in system biology. However, every existing inference algorithm from gene expression profiles has its own advantages and disadvantages. In particular, the effectiveness and efficiency of every previous algorithm is not high enough. In this work, we proposed a novel inference algorithm from gene expression data based on differential equation model. In this algorithm, two methods were included for inferring GRNs. Before reconstructing GRNs, singular value decomposition method was used to decompose gene expression data, determine the algorithm solution space, and get all candidate solutions of GRNs. In these generated family of candidate solutions, gravitation field algorithm was modified to infer GRNs, used to optimize the criteria of differential equation model, and search the best network structure result. The proposed algorithm is validated on both the simulated scale-free network and real benchmark gene regulatory network in networks database. Both the Bayesian method and the traditional differential equation model were also used to infer GRNs, and the results were used to compare with the proposed algorithm in our work. And genetic algorithm and simulated annealing were also used to evaluate gravitation field algorithm. The cross-validation results confirmed the effectiveness of our algorithm, which outperforms significantly other previous algorithms. PMID:23226565

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

A comparative study of multivariable robustness analysis methods as applied to integrated flight and propulsion control

NASA Technical Reports Server (NTRS)

Schierman, John D.; Lovell, T. A.; Schmidt, David K.

1993-01-01

Three multivariable robustness analysis methods are compared and contrasted. The focus of the analysis is on system stability and performance robustness to uncertainty in the coupling dynamics between two interacting subsystems. Of particular interest is interacting airframe and engine subsystems, and an example airframe/engine vehicle configuration is utilized in the demonstration of these approaches. The singular value (SV) and structured singular value (SSV) analysis methods are compared to a method especially well suited for analysis of robustness to uncertainties in subsystem interactions. This approach is referred to here as the interacting subsystem (IS) analysis method. This method has been used previously to analyze airframe/engine systems, emphasizing the study of stability robustness. However, performance robustness is also investigated here, and a new measure of allowable uncertainty for acceptable performance robustness is introduced. The IS methodology does not require plant uncertainty models to measure the robustness of the system, and is shown to yield valuable information regarding the effects of subsystem interactions. In contrast, the SV and SSV methods allow for the evaluation of the robustness of the system to particular models of uncertainty, and do not directly indicate how the airframe (engine) subsystem interacts with the engine (airframe) subsystem.

Holographic entanglement entropy in Suzuki-Trotter decomposition of spin systems.

PubMed

Matsueda, Hiroaki

2012-03-01

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of "holographic" entanglement entropy. At T(c), the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Furthermore, the spectrum, which is a set of logarithms of the singular values, also seems to be a holographic entanglement spectrum. We find multiple gaps in the spectrum, and in contrast to the topological phases, the low-lying levels below the gap represent spontaneous symmetry breaking. These contrasts are strong evidence of the dual nature of the holography. Based on these observations, we discuss the amount of information contained in one snapshot.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Singular dynamics of a q-difference Painlevé equation in its initial-value space

NASA Astrophysics Data System (ADS)

Joshi, N.; Lobb, S. B.

2016-01-01

We construct the initial-value space of a q-discrete first Painlevé equation explicitly and describe the behaviours of its solutions w(n) in this space as n\\to ∞ , with particular attention paid to neighbourhoods of exceptional lines and irreducible components of the anti-canonical divisor. These results show that trajectories starting in domains bounded away from the origin in initial value space are repelled away from such singular lines. However, the dynamical behaviours in neighbourhoods containing the origin are complicated by the merger of two simple base points at the origin in the limit. We show that these lead to a saddle-point-type behaviour in a punctured neighbourhood of the origin.

Spectral and entropic characterizations of Wigner functions: applications to model vibrational systems.

PubMed

Luzanov, A V

2008-09-07

The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK(+) (for coordinate variables) and K(+)K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

Shock Dynamics for particle-laden thin film

NASA Astrophysics Data System (ADS)

Wang, Li; Bertozzi, Andrea

2013-11-01

We study the shock dynamics for a recently proposed system of conservation laws (Murisic et al. [J. Fluid Mech. 2013]) describing gravity-driven thin film flow of a suspension of particles down an incline. When the particle concentration is above a critical value, singular shock solutions can occur. We analyze the Hugoniot topology associated with the Riemann problem for this system, describing in detail how the transition from a double shock to a singular shock happen. We also derive the singular shock speed based on a key observation that the particles pilling up at the maximum packing fraction near the contact line. These results are further applied to constant volume case to generate a rarefaction-singular shock solution. The particle/fluid front are shown to move linearly to the leading order with time to the one-third power as predicted by the Huppert solution for clear fluid.

Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities.

PubMed

Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge

2017-03-31

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the rôle of quantum mechanics as a cosmic censor in nature.

Correlation matching method for high-precision position detection of optical vortex using Shack-Hartmann wavefront sensor.

PubMed

Huang, Chenxi; Huang, Hongxin; Toyoda, Haruyoshi; Inoue, Takashi; Liu, Huafeng

2012-11-19

We propose a new method for realizing high-spatial-resolution detection of singularity points in optical vortex beams. The method uses a Shack-Hartmann wavefront sensor (SHWS) to record a Hartmanngram. A map of evaluation values related to phase slope is then calculated from the Hartmanngram. The position of an optical vortex is determined by comparing the map with reference maps that are calculated from numerically created spiral phases having various positions. Optical experiments were carried out to verify the method. We displayed various spiral phase distribution patterns on a phase-only spatial light modulator and measured the resulting singularity point using the proposed method. The results showed good linearity in detecting the position of singularity points. The RMS error of the measured position of the singularity point was approximately 0.056, in units normalized to the lens size of the lenslet array used in the SHWS.

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.

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

Perturbation analysis of the limit cycle of the free van der Pol equation

NASA Technical Reports Server (NTRS)

Dadfar, M. B.; Geer, J.; Anderson, C. M.

1983-01-01

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Symmetry breaking and singularity structure in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.

2012-08-01

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data.

PubMed

Luo, Jianhua; Mou, Zhiying; Qin, Binjie; Li, Wanqing; Ogunbona, Philip; Robini, Marc C; Zhu, Yuemin

2018-07-01

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.

Architecture of chaotic attractors for flows in the absence of any singular point

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

Letellier, Christophe; Malasoma, Jean-Marc

2016-06-15

Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 × 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in themore » neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.« less

Spectral Properties of Dirac Billiards at the van Hove Singularities.

PubMed

Dietz, B; Klaus, T; Miski-Oglu, M; Richter, A; Wunderle, M; Bouazza, C

2016-01-15

We study distributions of the ratios of level spacings of rectangular and Africa-shaped superconducting microwave resonators containing circular scatterers on a triangular grid, so-called Dirac billiards (DBs). The high-precision measurements allowed the determination of, respectively, all 1651 and 1823 eigenfrequencies in the first two bands. The resonance densities are similar to that of graphene. They exhibit two sharp peaks at the van Hove singularities which separate the band structure into regions with a linear and a quadratic dispersion relation, respectively. In the vicinity of the van Hove singularities we observe rapid changes in, e.g., the wave function structure. Accordingly, we question whether the spectral properties are there still determined by the shapes of the DBs. The commonly used statistical measures are no longer applicable; however, we demonstrate in this Letter that the ratio distributions provide suitable measures.

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

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

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

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.

The singularity structure of scale-invariant rank-2 Coulomb branches

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Asymptotics of action variables near semi-toric singularities

NASA Astrophysics Data System (ADS)

Wacheux, Christophe

2015-12-01

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behavior and the multi-valuedness of the Action integrals is given by a complex logarithm. This extends a previous result by San Vũ Ngọc to any dimension. We also calculate the monodromy matrix for these systems.

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.

Reaction trajectory revealed by a joint analysis of protein data bank.

PubMed

Ren, Zhong

2013-01-01

Structural motions along a reaction pathway hold the secret about how a biological macromolecule functions. If each static structure were considered as a snapshot of the protein molecule in action, a large collection of structures would constitute a multidimensional conformational space of an enormous size. Here I present a joint analysis of hundreds of known structures of human hemoglobin in the Protein Data Bank. By applying singular value decomposition to distance matrices of these structures, I demonstrate that this large collection of structural snapshots, derived under a wide range of experimental conditions, arrange orderly along a reaction pathway. The structural motions along this extensive trajectory, including several helical transformations, arrive at a reverse engineered mechanism of the cooperative machinery (Ren, companion article), and shed light on pathological properties of the abnormal homotetrameric hemoglobins from α-thalassemia. This method of meta-analysis provides a general approach to structural dynamics based on static protein structures in this post genomics era.

Reaction Trajectory Revealed by a Joint Analysis of Protein Data Bank

PubMed Central

Ren, Zhong

2013-01-01

Structural motions along a reaction pathway hold the secret about how a biological macromolecule functions. If each static structure were considered as a snapshot of the protein molecule in action, a large collection of structures would constitute a multidimensional conformational space of an enormous size. Here I present a joint analysis of hundreds of known structures of human hemoglobin in the Protein Data Bank. By applying singular value decomposition to distance matrices of these structures, I demonstrate that this large collection of structural snapshots, derived under a wide range of experimental conditions, arrange orderly along a reaction pathway. The structural motions along this extensive trajectory, including several helical transformations, arrive at a reverse engineered mechanism of the cooperative machinery (Ren, companion article), and shed light on pathological properties of the abnormal homotetrameric hemoglobins from α-thalassemia. This method of meta-analysis provides a general approach to structural dynamics based on static protein structures in this post genomics era. PMID:24244274

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).

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 numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

NASA Astrophysics Data System (ADS)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

Controllability of switched singular mix-valued logical control networks with constraints

NASA Astrophysics Data System (ADS)

Deng, Lei; Gong, Mengmeng; Zhu, Peiyong

2018-03-01

The present paper investigates the controllability problem of switched singular mix-valued logical control networks (SSMLCNs) with constraints on states and controls. First, using the semi-tenser product (STP) of matrices, the SSMLCN is expressed in an algebraic form, based on which a necessary and sufficient condition is given for the uniqueness of solution of SSMLCNs. Second, a necessary and sufficient criteria is derived for the controllability of constrained SSMLCNs, by converting a constrained SSMLCN into a parallel constrained switched mix-valued logical control network. Third, an algorithm is presented to design a proper switching sequence and a control scheme which force a state to a reachable state. Finally, a numerical example is given to demonstrate the efficiency of the results obtained in this paper.

An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Cooper, J. E.; Wright, J. R.

1987-01-01

A modification to the Eigensystem Realization Algorithm (ERA) for modal parameter identification is presented in this paper. The ERA minimum order realization approach using singular value decomposition is combined with the philosophy of the Correlation Fit method in state space form such that response data correlations rather than actual response values are used for modal parameter identification. This new method, the ERA using data correlations (ERA/DC), reduces bias errors due to noise corruption significantly without the need for model overspecification. This method is tested using simulated five-degree-of-freedom system responses corrupted by measurement noise. It is found for this case that, when model overspecification is permitted and a minimum order solution obtained via singular value truncation, the results from the two methods are of similar quality.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study.

PubMed

Singh, R R P; Young, A P

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Singular structures on liquid rims

NASA Astrophysics Data System (ADS)

Mayer, Hans C.; Krechetnikov, Rouslan

2014-03-01

This experimental note is concerned with a new effect we discovered in the course of studying water hammering phenomena. Namely, the ejecta originating from the solid plate impact on a water surface brings about a liquid rim at its edge with the fluid flowing towards the rim center and forming a singular structure resembling a "pancake." Here, we present the experimental observations and a qualitative physical explanation for the effect, which proves to be fundamental to the situation when the size and speed of the impacting body are such that the capillary effects become important.

3D topology of orientation columns in visual cortex revealed by functional optical coherence tomography.

PubMed

Nakamichi, Yu; Kalatsky, Valery A; Watanabe, Hideyuki; Sato, Takayuki; Rajagopalan, Uma Maheswari; Tanifuji, Manabu

2018-04-01

Orientation tuning is a canonical neuronal response property of six-layer visual cortex that is encoded in pinwheel structures with center orientation singularities. Optical imaging of intrinsic signals enables us to map these surface two-dimensional (2D) structures, whereas lack of appropriate techniques has not allowed us to visualize depth structures of orientation coding. In the present study, we performed functional optical coherence tomography (fOCT), a technique capable of acquiring a 3D map of the intrinsic signals, to study the topology of orientation coding inside the cat visual cortex. With this technique, for the first time, we visualized columnar assemblies in orientation coding that had been predicted from electrophysiological recordings. In addition, we found that the columnar structures were largely distorted around pinwheel centers: center singularities were not rigid straight lines running perpendicularly to the cortical surface but formed twisted string-like structures inside the cortex that turned and extended horizontally through the cortex. Looping singularities were observed with their respective termini accessing the same cortical surface via clockwise and counterclockwise orientation pinwheels. These results suggest that a 3D topology of orientation coding cannot be fully anticipated from 2D surface measurements. Moreover, the findings demonstrate the utility of fOCT as an in vivo mesoscale imaging method for mapping functional response properties of cortex in the depth axis. NEW & NOTEWORTHY We used functional optical coherence tomography (fOCT) to visualize three-dimensional structure of the orientation columns with millimeter range and micrometer spatial resolution. We validated vertically elongated columnar structure in iso-orientation domains. The columnar structure was distorted around pinwheel centers. An orientation singularity formed a string with tortuous trajectories inside the cortex and connected clockwise and counterclockwise pinwheel centers in the surface orientation map. The results were confirmed by comparisons with conventional optical imaging and electrophysiological recordings.

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.

On the nature of control algorithms for free-floating space manipulators

NASA Technical Reports Server (NTRS)

Papadopoulos, Evangelos; Dubowsky, Steven

1991-01-01

It is suggested that nearly any control algorithm that can be used for fixed-based manipulators also can be employed in the control of free-floating space manipulator systems, with the additional conditions of estimating or measuring a spacecraft's orientation and of avoiding dynamic singularities. This result is based on the structural similarities between the kinematic and dynamic equations for the same manipulator but with a fixed base. Barycenters are used to formulate the kinematic and dynamic equations of free-floating space manipulators. A control algorithm for a space manipulator system is designed to demonstrate the value of the analysis.

Fermi-edge singularity and the functional renormalization group

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

A spin-liquid with pinch-line singularities on the pyrochlore lattice.

PubMed

Benton, Owen; Jaubert, L D C; Yan, Han; Shannon, Nic

2016-05-26

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.

A spin-liquid with pinch-line singularities on the pyrochlore lattice

PubMed Central

Benton, Owen; Jaubert, L.D.C.; Yan, Han; Shannon, Nic

2016-01-01

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7. PMID:27225400

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

NASA Astrophysics Data System (ADS)

Kiselev, Alexei D.; Chigrinov, Vladimir G.

2014-10-01

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature.

PubMed

Bisquert, Juan; Henn, François; Giuntini, Jean-Charles

2005-03-01

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.

Current singularities at quasi-separatrix layers and three-dimensional magnetic nulls

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

Craig, I. J. D.; Effenberger, Frederic, E-mail: feffen@waikato.ac.nz

2014-11-10

The open problem of how singular current structures form in line-tied, three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional relaxation method is employed to model the field evolution toward the final near-singular state. Our starting point is an exact force-free solution of the governing magnetohydrodynamic equations that is sufficiently general to allow for topological features like magnetic nulls to be inside or outside the computational domain, depending on a simple set of parameters. Quasi-separatrix layers (QSLs) are present in these structures and, together with the magnetic nulls, they significantly influence the accumulation of current. It is shown that perturbations affectingmore » the lateral boundaries of the configuration lead not only to collapse around the magnetic null but also to significant QSL currents. Our results show that once a magnetic null is present, the developing currents are always attracted to that specific location and show a much stronger scaling with resolution than the currents that form along the QSL. In particular, the null-point scalings can be consistent with models of 'fast' reconnection. The QSL currents also appear to be unbounded but give rise to weaker singularities, independent of the perturbation amplitude.« less

Stable and unstable singularities in the unforced Hele-Shaw cell

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

Almgren, R.; Bertozzi, A.; Brenner, M.P.

We study singularity formation in the lubrication model for the unforced Hele-Shaw system, describing the breaking in two of a fluid droplet confined between two narrowly spaced glass plates. By varying the initial data, we exhibit four different scenarios: (1) the droplet breaks in finite time, with two pinch points moving toward each other and merging at the singular time; (2) the droplet breaks in finite time, with two asymmetric pinch points propagating away from each other; (3) the droplet breaks in finite time, with a single symmetric pinch point; or (4) the droplet relaxes to a stable equilibrium shapemore » without a finite time breakup. Each of the three singular scenarios has a self-similar structure with different scaling laws; the first scenario has not been observed before in other Hele-Shaw studies. We demonstrate instabilities of the second and third scenarios, in which the solution changes its behavior at a thickness that can be arbitrarily small depending on the initial condition. These transitions can be identified by examining the structure of the solution in the intermediate scaling region. {copyright} {ital 1996 American Institute of Physics.}« less

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.

Use of principle velocity patterns in the analysis of structural acoustic optimization.

PubMed

Johnson, Wayne M; Cunefare, Kenneth A

2007-02-01

This work presents an application of principle velocity patterns in the analysis of the structural acoustic design optimization of an eight ply composite cylindrical shell. The approach consists of performing structural acoustic optimizations of a composite cylindrical shell subject to external harmonic monopole excitation. The ply angles are used as the design variables in the optimization. The results of the ply angle design variable formulation are interpreted using the singular value decomposition of the interior acoustic potential energy. The decomposition of the acoustic potential energy provides surface velocity patterns associated with lower levels of interior noise. These surface velocity patterns are shown to correspond to those from the structural acoustic optimization results. Thus, it is demonstrated that the capacity to design multi-ply composite cylinders for quiet interiors is determined by how well the cylinder be can designed to exhibit particular surface velocity patterns associated with lower noise levels.

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.

Non-Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics

NASA Astrophysics Data System (ADS)

Korsunsky, Alexander M.

2010-03-01

One of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two-dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two-dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non-singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Composite operators in the hopping parameter expansion in the free quark model

NASA Astrophysics Data System (ADS)

Kunszt, Z.

1983-11-01

I have calculated hopping parameter series of meson and baryon propagators up to O(K32) in the Wilson formulation of the free quark model. The position of branch point singularities has been found with the help of Padé approximants. The values of the position of the singularities in K agreed with the exact values within 1-2% in case of mesons and 4-5% in case of baryons. It is argued that in QCD at the cross-over region the systematic errors of the method must be even smaller. Part of this work has been done while the author was visiting the Rutherford and Appleton Laboratories, UK.

Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

NASA Astrophysics Data System (ADS)

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

2016-01-01

Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

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

Through Wall Radar Classification of Human Micro-Doppler Using Singular Value Decomposition Analysis

PubMed Central

Ritchie, Matthew; Ash, Matthew; Chen, Qingchao; Chetty, Kevin

2016-01-01

The ability to detect the presence as well as classify the activities of individuals behind visually obscuring structures is of significant benefit to police, security and emergency services in many situations. This paper presents the analysis from a series of experimental results generated using a through-the-wall (TTW) Frequency Modulated Continuous Wave (FMCW) C-Band radar system named Soprano. The objective of this analysis was to classify whether an individual was carrying an item in both hands or not using micro-Doppler information from a FMCW sensor. The radar was deployed at a standoff distance, of approximately 0.5 m, outside a residential building and used to detect multiple people walking within a room. Through the application of digital filtering, it was shown that significant suppression of the primary wall reflection is possible, significantly enhancing the target signal to clutter ratio. Singular Value Decomposition (SVD) signal processing techniques were then applied to the micro-Doppler signatures from different individuals. Features from the SVD information have been used to classify whether the person was carrying an item or walking free handed. Excellent performance of the classifier was achieved in this challenging scenario with accuracies up to 94%, suggesting that future through wall radar sensors may have the ability to reliably recognize many different types of activities in TTW scenarios using these techniques. PMID:27589760

Through Wall Radar Classification of Human Micro-Doppler Using Singular Value Decomposition Analysis.

PubMed

Ritchie, Matthew; Ash, Matthew; Chen, Qingchao; Chetty, Kevin

2016-08-31

The ability to detect the presence as well as classify the activities of individuals behind visually obscuring structures is of significant benefit to police, security and emergency services in many situations. This paper presents the analysis from a series of experimental results generated using a through-the-wall (TTW) Frequency Modulated Continuous Wave (FMCW) C-Band radar system named Soprano. The objective of this analysis was to classify whether an individual was carrying an item in both hands or not using micro-Doppler information from a FMCW sensor. The radar was deployed at a standoff distance, of approximately 0.5 m, outside a residential building and used to detect multiple people walking within a room. Through the application of digital filtering, it was shown that significant suppression of the primary wall reflection is possible, significantly enhancing the target signal to clutter ratio. Singular Value Decomposition (SVD) signal processing techniques were then applied to the micro-Doppler signatures from different individuals. Features from the SVD information have been used to classify whether the person was carrying an item or walking free handed. Excellent performance of the classifier was achieved in this challenging scenario with accuracies up to 94%, suggesting that future through wall radar sensors may have the ability to reliably recognize many different types of activities in TTW scenarios using these techniques.

A singularity free approach to post glacial rebound calculations

NASA Technical Reports Server (NTRS)

Fang, Ming; Hager, Bradford H.

1994-01-01

Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

The scattering variety

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Matti, Cyril; Sun, Chuang

2014-10-01

The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective geometries which we call Scattering Varieties by analyzing such properties as Hilbert series, Euler characteristic and singularities. Interestingly, we find structures such as affine Calabi-Yau threefolds as well as singular K3 and Fano varieties.

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

NASA Astrophysics Data System (ADS)

Meng, Xin-You; Wu, Yu-Qian

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

Spherically Symmetric Gravitational Collapse of a Dust Cloud in Third-Order Lovelock Gravity

NASA Astrophysics Data System (ADS)

Zhou, Kang; Yang, Zhan-Ying; Zou, De-Cheng; Yue, Rui-Hong

We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB-type spacetime in third-order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions which separately corresponding to hyperbolic, parabolic and elliptic. Notice that the contribution of high-order curvature corrections have a profound influence on the nature of the singularity, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the presence of high order Lovelock terms leads to the formation of massive, naked and timelike singularities in the 7D spacetime, which is disallowed in general relativity. Moveover, we point out that the naked singularities in the 7D case may be gravitational weak therefore may not be a serious threat to the cosmic censorship hypothesis, while the naked singularities in the D ≥ 8 inhomogeneous collapse violate the cosmic censorship hypothesis seriously.

Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces

NASA Astrophysics Data System (ADS)

Guenneau, Sébastien; Ramakrishna, S. Anantha

2009-06-01

Newly discovered metamaterials have opened new vistas for better control of light via negative refraction, whereby light refracts in the "wrong" manner. These are dielectric and metallic composite materials structured at subwavelength lengthscales. Their building blocks consist of local resonators such as conducting thin bars and split rings driving the material parameters such as the dielectric permittivity and magnetic permeability to negative (complex) values. Combined together, these structural elements can bring about a (complex valued) negative effective refractive index for the Snell-Descartes law and result in negative refraction of radiation. Negative refractive index materials can support a host of surface plasmon states for both polarizations of light. This makes possible unique effects such as imaging with subwavelength image resolution through the Pendry-Veselago slab lens. Other geometries have also been investigated, such as cylindrical or spherical lenses that enable a magnification of images with subwavelength resolution. Superlenses of three-fold (equilateral triangle), four-fold (square) and six-fold (hexagonal) geometry allow for multiple images, respectively two, three, and five. Generalization to rectangular and triangular checkerboards consisting of alternating cells of positive and negative refractive index represents a very singular situation in which the density of modes diverges at the corners, with an infinity of images. Sine-cosecant anisotropic heterogeneous square and triangular checkerboards can be respectively mapped onto three-dimensional cubic and icosahedral corner lenses consisting of alternating positive and negative refractive regions. All such systems with corners between negative and positive refractive media display very singular behavior with the local density of states becoming infinitely large at the corner, in the limit of no dissipation. We investigate all of these, using the unifying viewpoint of transformation optics. To cite this article: S. Guenneau, S.A. Ramakrishna, C. R. Physique 10 (2009).

Future singularities and teleparallelism in loop quantum cosmology

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

Bamba, Kazuharu; Haro, Jaume de; Odintsov, Sergei D., E-mail: bamba@kmi.nagoya-u.ac.jp, E-mail: jaime.haro@upc.edu, E-mail: odintsov@ieec.uab.es

2013-02-01

We demonstrate how holonomy corrections in loop quantum cosmology (LQC) prevent the Big Rip singularity by introducing a quadratic modification in terms of the energy density ρ in the Friedmann equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) space-time in a consistent and useful way. In addition, we investigate whether other kind of singularities like Type II,III and IV singularities survive or are avoided in LQC when the universe is filled by a barotropic fluid with the state equation P = −ρ−f(ρ), where P is the pressure and f(ρ) a function of ρ. It is shown that the Little Rip cosmology does notmore » happen in LQC. Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom universe approaches the de Sitter one asymptotically, is established, and the corresponding example is presented. It is interesting that the disintegration of bound structures in the Pseudo-Rip cosmology in LQC always takes more time than that in Einstein cosmology. Our investigation on future singularities is generalized to that in modified teleparallel gravity, where LQC and Brane Cosmology in the Randall-Sundrum scenario are the best examples. It is remarkable that F(T) gravity may lead to all the kinds of future singularities including Little Rip.« less

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.

Identification and modification of dominant noise sources in diesel engines

NASA Astrophysics Data System (ADS)

Hayward, Michael D.

Determination of dominant noise sources in diesel engines is an integral step in the creation of quiet engines, but is a process which can involve an extensive series of expensive, time-consuming fired and motored tests. The goal of this research is to determine dominant noise source characteristics of a diesel engine in the near and far-fields with data from fewer tests than is currently required. Pre-conditioning and use of numerically robust methods to solve a set of cross-spectral density equations results in accurate calculation of the transfer paths between the near- and far-field measurement points. Application of singular value decomposition to an input cross-spectral matrix determines the spectral characteristics of a set of independent virtual sources, that, when scaled and added, result in the input cross spectral matrix. Each virtual source power spectral density is a singular value resulting from the decomposition performed over a range of frequencies. The complex relationship between virtual and physical sources is estimated through determination of virtual source contributions to each input measurement power spectral density. The method is made more user-friendly through use of a percentage contribution color plotting technique, where different normalizations can be used to help determine the presence of sources and the strengths of their contributions. Convolution of input measurements with the estimated path impulse responses results in a set of far-field components, to which the same singular value contribution plotting technique can be applied, thus allowing dominant noise source characteristics in the far-field to also be examined. Application of the methods presented results in determination of the spectral characteristics of dominant noise sources both in the near- and far-fields from one fired test, which significantly reduces the need for extensive fired and motored testing. Finally, it is shown that the far-field noise time history of a physically altered engine can be simulated through modification of singular values and recalculation of transfer paths between input and output measurements of previously recorded data.

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

Analysis and modelling of septic shock microarray data using Singular Value Decomposition.

PubMed

Allanki, Srinivas; Dixit, Madhulika; Thangaraj, Paul; Sinha, Nandan Kumar

2017-06-01

Being a high throughput technique, enormous amounts of microarray data has been generated and there arises a need for more efficient techniques of analysis, in terms of speed and accuracy. Finding the differentially expressed genes based on just fold change and p-value might not extract all the vital biological signals that occur at a lower gene expression level. Besides this, numerous mathematical models have been generated to predict the clinical outcome from microarray data, while very few, if not none, aim at predicting the vital genes that are important in a disease progression. Such models help a basic researcher narrow down and concentrate on a promising set of genes which leads to the discovery of gene-based therapies. In this article, as a first objective, we have used the lesser known and used Singular Value Decomposition (SVD) technique to build a microarray data analysis tool that works with gene expression patterns and intrinsic structure of the data in an unsupervised manner. We have re-analysed a microarray data over the clinical course of Septic shock from Cazalis et al. (2014) and have shown that our proposed analysis provides additional information compared to the conventional method. As a second objective, we developed a novel mathematical model that predicts a set of vital genes in the disease progression that works by generating samples in the continuum between health and disease, using a simple normal-distribution-based random number generator. We also verify that most of the predicted genes are indeed related to septic shock. Copyright © 2017 Elsevier Inc. All rights reserved.

Theoretical analysis of metamaterial-gold auxiliary grating sensing structure for surface plasmon resonance sensing application based on polarization control method

NASA Astrophysics Data System (ADS)

Sun, Yi; Cai, Haoyuan; Wang, Xiaoping

2017-12-01

A metamaterial-gold multilayer sensing structure designed using the particle swarm optimization (PSO) algorithm with an auxiliary grating is proposed for using in a surface plasmon resonance (SPR) sensor system based on the polarization control method. After numerical calculations and simulation analysis, it was found that the metamaterial sensing structure significantly improves the sensitivity of the SPR signal with intensity singularity. The metamaterial sensing structure also increases the penetration depth of evanescent wave, making it possible to detect low-molecular-weight biomolecules and larger cells such as bacteria. The auxiliary grating structure was designed to identify the refractive index of the sensing region on both sides of intensity singularity. The stability of recognition and the electric field intensity of the visible light band were also studied.

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

Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images.

PubMed

Vadnjal, Ana Laura; Etchepareborda, Pablo; Federico, Alejandro; Kaufmann, Guillermo H

2013-03-20

We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object. The performance of this method is evaluated using simulated speckle patterns and experimental data. The proposed approach is compared with the optical vortex metrology and digital image correlation methods in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed.

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

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.

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.

Recent Results on Singularity Strengths

NASA Astrophysics Data System (ADS)

Nolan, Brien

2002-12-01

In this contribution, we review some recent results on strengths of singularities. In a space-time (M,g), let γ[τ0, 0) → M be an incomplete, inextendible causal geodesic, affinely parametrised by τ, tangent ěc k. Let Jτ1 :=set of Jacobi fields along γ, orthogonal to γ and vanishing at time τ1 ≥ τ0 i.e. ěc ξ ∈ J{τ 1 } iff D2ξa = -Rbcdakbkdξc, gabξakb = 0, and ěc ξ (τ 1 ) = 0. Vτ1(τ) := volume element defined by full set of independent elements of Jτ1 (2-dim for null geodesies, 3-dim for time-like); Vτ1 := ∥Vτ1∥. Definition (Tipler 1977): γ terminates in a gravitationally strong singularity if for all 0 > τ1 ≥ τ0, lim infτ→0- Vτ1(τ) = 0. γ... gravitationally weak ... lim infτ→0- Vτ1(τ) > 0. The interpretation is that at a strong singularity, an extended body, e.g. a gravitational wave detector, is crushed to zero volume by the singularity. Tipler's definition does not take account of the possibility that (i) V → ∞ or (ii) V → finite, non-zero value, but with infinite stretching/crushing in orthogonal directions ('spaghettifying singularity'). Extended definition (Nolan 1999): strong if either V → 0,∞ or if for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> 0. Otherwise weak. (Ori 2000): singularity is 'deformationally strong' if either (i) it is Tipler-strong or (ii) for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> ∞ . Otherwise, deformationally weak...

Calculation of potential flow past non-lifting bodies at angle of attack using axial and surface singularity methods. M.S. Thesis. Contractor Report, 1 Jan. 1981 - 31 Aug. 1982

NASA Technical Reports Server (NTRS)

Shu, J. Y.

1983-01-01

Two different singularity methods have been utilized to calculate the potential flow past a three dimensional non-lifting body. Two separate FORTRAN computer programs have been developed to implement these theoretical models, which will in the future allow inclusion of the fuselage effect in a pair of existing subcritical wing design computer programs. The first method uses higher order axial singularity distributions to model axisymmetric bodies of revolution in an either axial or inclined uniform potential flow. Use of inset of the singularity line away from the body for blunt noses, and cosine-type element distributions have been applied to obtain the optimal results. Excellent agreement to five significant figures with the exact solution pressure coefficient value has been found for a series of ellipsoids at different angles of attack. Solutions obtained for other axisymmetric bodies compare well with available experimental data. The second method utilizes distributions of singularities on the body surface, in the form of a discrete vortex lattice. This program is capable of modeling arbitrary three dimensional non-lifting bodies. Much effort has been devoted to finding the optimal method of calculating the tangential velocity on the body surface, extending techniques previously developed by other workers.

Loop Quantum Cosmology.

PubMed

Bojowald, Martin

2008-01-01

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.

Using chaotic forcing to detect damage in a structure

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure. ?? 2005 American Institute of Physics.

Using chaotic forcing to detect damage in a structure.

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure.

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.

A technique for plasma velocity-space cross-correlation

NASA Astrophysics Data System (ADS)

Mattingly, Sean; Skiff, Fred

2018-05-01

An advance in experimental plasma diagnostics is presented and used to make the first measurement of a plasma velocity-space cross-correlation matrix. The velocity space correlation function can detect collective fluctuations of plasmas through a localized measurement. An empirical decomposition, singular value decomposition, is applied to this Hermitian matrix in order to obtain the plasma fluctuation eigenmode structure on the ion distribution function. A basic theory is introduced and compared to the modes obtained by the experiment. A full characterization of these modes is left for future work, but an outline of this endeavor is provided. Finally, the requirements for this experimental technique in other plasma regimes are discussed.

An Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction

NASA Technical Reports Server (NTRS)

Juang, J. N.; Pappa, R. S.

1985-01-01

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

A μ analysis-based, controller-synthesis framework for robust bioinspired visual navigation in less-structured environments.

PubMed

Keshavan, J; Gremillion, G; Escobar-Alvarez, H; Humbert, J S

2014-06-01

Safe, autonomous navigation by aerial microsystems in less-structured environments is a difficult challenge to overcome with current technology. This paper presents a novel visual-navigation approach that combines bioinspired wide-field processing of optic flow information with control-theoretic tools for synthesis of closed loop systems, resulting in robustness and performance guarantees. Structured singular value analysis is used to synthesize a dynamic controller that provides good tracking performance in uncertain environments without resorting to explicit pose estimation or extraction of a detailed environmental depth map. Experimental results with a quadrotor demonstrate the vehicle's robust obstacle-avoidance behaviour in a straight line corridor, an S-shaped corridor and a corridor with obstacles distributed in the vehicle's path. The computational efficiency and simplicity of the current approach offers a promising alternative to satisfying the payload, power and bandwidth constraints imposed by aerial microsystems.

Electronic Structures of Purple Bronze KMo6O17 Studied by X-Ray Photoemission Spectra

NASA Astrophysics Data System (ADS)

Qin, Xiaokui; Wei, Junyin; Shi, Jing; Tian, Mingliang; Chen, Hong; Tian, Decheng

X-ray photoemission spectroscopy study has been performed for the purple bronze KMo6O17. The structures of conduction band and valence band are analogous to the results of ultraviolet photoemission spectra and are also consistent with the model of Travaglini et al., but the gap between conduction and valence band is insignificant. The shape of asymmetric and broadening line of O-1s is due to unresolved contributions from the many inequivalent oxygen sites in this crystal structure. Mo 3d core-level spectrum reveals that there are two kinds of valence states of Molybdenum (Mo+5 and Mo+6). The calculated average valence state is about +5.6, which is consistent with the expectation value from the composition of this material. The tail of Mo-3d spectrum toward higher binding energy is the consequence of the excitation of electron-hole pairs with singularity index of 0.21.

String modular phases in Calabi-Yau families

NASA Astrophysics Data System (ADS)

Kadir, Shabnam; Lynker, Monika; Schimmrigk, Rolf

2011-12-01

We investigate the structure of singular Calabi-Yau varieties in moduli spaces that contain a Brieskorn-Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the L-series for singular fibers for several families. We find that the resulting motivic L-functions agree with the L-series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic L-functions are identical in several cases to L-series derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi-Yau varieties of different dimensions.

Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials

NASA Astrophysics Data System (ADS)

Zhu, Weiwei; Ding, Ya-qiong; Ren, Jie; Sun, Yong; Li, Yunhui; Jiang, Haitao; Chen, Hong

2018-05-01

The Zak phase, which refers to Berry's phase picked up by a particle moving across the Brillouin zone, characterizes the topological properties of Bloch bands in a one-dimensional periodic system. Here the Zak phase in dimerized one-dimensional locally resonant metamaterials is investigated. It is found that there are some singular points in the bulk band across which the Bloch states contribute π to the Zak phase, whereas in the rest of the band the contribution is nearly zero. These singular points associated with zero reflection are caused by two different mechanisms: the dimerization-independent antiresonance of each branch and the dimerization-dependent destructive interference in multiple backscattering. The structure undergoes a topological phase-transition point in the band structure where the band inverts, and the Zak phase, which is determined by the numbers of singular points in the bulk band, changes following a shift in dimerization parameter. Finally, the interface state between two dimerized metamaterial structures with different topological properties in the first band gap is demonstrated experimentally. The quasi-one-dimensional configuration of the system allows one to explore topology-inspired new methods and applications on the subwavelength scale.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field.

PubMed

Carmelo, J M P; Sacramento, P D; Machado, J D P; Campbell, D K

2015-10-14

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

NASA Astrophysics Data System (ADS)

Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.

2015-10-01

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Tumor or abnormality identification from magnetic resonance images using statistical region fusion based segmentation.

PubMed

Subudhi, Badri Narayan; Thangaraj, Veerakumar; Sankaralingam, Esakkirajan; Ghosh, Ashish

2016-11-01

In this article, a statistical fusion based segmentation technique is proposed to identify different abnormality in magnetic resonance images (MRI). The proposed scheme follows seed selection, region growing-merging and fusion of multiple image segments. In this process initially, an image is divided into a number of blocks and for each block we compute the phase component of the Fourier transform. The phase component of each block reflects the gray level variation among the block but contains a large correlation among them. Hence a singular value decomposition (SVD) technique is adhered to generate a singular value of each block. Then a thresholding procedure is applied on these singular values to identify edgy and smooth regions and some seed points are selected for segmentation. By considering each seed point we perform a binary segmentation of the complete MRI and hence with all seed points we get an equal number of binary images. A parcel based statistical fusion process is used to fuse all the binary images into multiple segments. Effectiveness of the proposed scheme is tested on identifying different abnormalities: prostatic carcinoma detection, tuberculous granulomas identification and intracranial neoplasm or brain tumor detection. The proposed technique is established by comparing its results against seven state-of-the-art techniques with six performance evaluation measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Light focusing through a multiple scattering medium: ab initio computer simulation

NASA Astrophysics Data System (ADS)

Danko, Oleksandr; Danko, Volodymyr; Kovalenko, Andrey

2018-01-01

The present study considers ab initio computer simulation of the light focusing through a complex scattering medium. The focusing is performed by shaping the incident light beam in order to obtain a small focused spot on the opposite side of the scattering layer. MSTM software (Auburn University) is used to simulate the propagation of an arbitrary monochromatic Gaussian beam and obtain 2D distribution of the optical field in the selected plane of the investigated volume. Based on the set of incident and scattered fields, the pair of right and left eigen bases and corresponding singular values were calculated. The pair of right and left eigen modes together with the corresponding singular value constitute the transmittance eigen channel of the disordered media. Thus, the scattering process is described in three steps: 1) initial field decomposition in the right eigen basis; 2) scaling of decomposition coefficients for the corresponding singular values; 3) assembling of the scattered field as the composition of the weighted left eigen modes. Basis fields are represented as a linear combination of the original Gaussian beams and scattered fields. It was demonstrated that 60 independent control channels provide focusing the light into a spot with the minimal radius of approximately 0.4 μm at half maximum. The intensity enhancement in the focal plane was equal to 68 that coincided with theoretical prediction.

Characterization of cancer and normal tissue fluorescence through wavelet transform and singular value decomposition

NASA Astrophysics Data System (ADS)

Gharekhan, Anita H.; Biswal, Nrusingh C.; Gupta, Sharad; Pradhan, Asima; Sureshkumar, M. B.; Panigrahi, Prasanta K.

2008-02-01

The statistical and characteristic features of the polarized fluorescence spectra from cancer, normal and benign human breast tissues are studied through wavelet transform and singular value decomposition. The discrete wavelets enabled one to isolate high and low frequency spectral fluctuations, which revealed substantial randomization in the cancerous tissues, not present in the normal cases. In particular, the fluctuations fitted well with a Gaussian distribution for the cancerous tissues in the perpendicular component. One finds non-Gaussian behavior for normal and benign tissues' spectral variations. The study of the difference of intensities in parallel and perpendicular channels, which is free from the diffusive component, revealed weak fluorescence activity in the 630nm domain, for the cancerous tissues. This may be ascribable to porphyrin emission. The role of both scatterers and fluorophores in the observed minor intensity peak for the cancer case is experimentally confirmed through tissue-phantom experiments. Continuous Morlet wavelet also highlighted this domain for the cancerous tissue fluorescence spectra. Correlation in the spectral fluctuation is further studied in different tissue types through singular value decomposition. Apart from identifying different domains of spectral activity for diseased and non-diseased tissues, we found random matrix support for the spectral fluctuations. The small eigenvalues of the perpendicular polarized fluorescence spectra of cancerous tissues fitted remarkably well with random matrix prediction for Gaussian random variables, confirming our observations about spectral fluctuations in the wavelet domain.

Lateral control system design for VTOL landing on a DD963 in high sea states. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bodson, M.

1982-01-01

The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.

Non-negative infrared patch-image model: Robust target-background separation via partial sum minimization of singular values

NASA Astrophysics Data System (ADS)

Dai, Yimian; Wu, Yiquan; Song, Yu; Guo, Jun

2017-03-01

To further enhance the small targets and suppress the heavy clutters simultaneously, a robust non-negative infrared patch-image model via partial sum minimization of singular values is proposed. First, the intrinsic reason behind the undesirable performance of the state-of-the-art infrared patch-image (IPI) model when facing extremely complex backgrounds is analyzed. We point out that it lies in the mismatching of IPI model's implicit assumption of a large number of observations with the reality of deficient observations of strong edges. To fix this problem, instead of the nuclear norm, we adopt the partial sum of singular values to constrain the low-rank background patch-image, which could provide a more accurate background estimation and almost eliminate all the salient residuals in the decomposed target image. In addition, considering the fact that the infrared small target is always brighter than its adjacent background, we propose an additional non-negative constraint to the sparse target patch-image, which could not only wipe off more undesirable components ulteriorly but also accelerate the convergence rate. Finally, an algorithm based on inexact augmented Lagrange multiplier method is developed to solve the proposed model. A large number of experiments are conducted demonstrating that the proposed model has a significant improvement over the other nine competitive methods in terms of both clutter suppressing performance and convergence rate.

Vafa-Witten theorem and Lee-Yang singularities

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

Aguado, M.; Asorey, M.

2009-12-15

We prove the analyticity of the finite volume QCD partition function for complex values of the {theta}-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at {theta}=0 and has an important consequence: the absence of a first order phase transition at {theta}=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, andmore » existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP{sup N} sigma model.« less

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Energy management of three-dimensional minimum-time intercept. [for aircraft flight optimization

NASA Technical Reports Server (NTRS)

Kelley, H. J.; Cliff, E. M.; Visser, H. G.

1985-01-01

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Strong gravitational lensing by a Konoplya-Zhidenko rotating non-Kerr compact object

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

Wang, Shangyun; Chen, Songbai; Jing, Jiliang, E-mail: shangyun_wang@163.com, E-mail: csb3752@hunnu.edu.cn, E-mail: jljing@hunnu.edu.cn

Konoplya and Zhidenko have proposed recently a rotating non-Kerr black hole metric beyond General Relativity and make an estimate for the possible deviations from the Kerr solution with the data of GW 150914. We here study the strong gravitational lensing in such a rotating non-Kerr spacetime with an extra deformation parameter. We find that the condition of existence of horizons is not inconsistent with that of the marginally circular photon orbit. Moreover, the deflection angle of the light ray near the weakly naked singularity covered by the marginally circular orbit diverges logarithmically in the strong-field limit. In the case ofmore » the completely naked singularity, the deflection angle near the singularity tends to a certain finite value, whose sign depends on the rotation parameter and the deformation parameter. These properties of strong gravitational lensing are different from those in the Johannsen-Psaltis rotating non-Kerr spacetime and in the Janis-Newman-Winicour spacetime. Modeling the supermassive central object of the Milk Way Galaxy as a Konoplya-Zhidenko rotating non-Kerr compact object, we estimated the numerical values of observables for the strong gravitational lensing including the time delay between two relativistic images.« less

Interior sound field control using generalized singular value decomposition in the frequency domain.

PubMed

Pasco, Yann; Gauthier, Philippe-Aubert; Berry, Alain; Moreau, Stéphane

2017-01-01

The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.

Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect

PubMed Central

Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang

2014-01-01

The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved. PMID:24784778

Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect.

PubMed

Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang

2014-05-02

The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.

Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect

NASA Astrophysics Data System (ADS)

Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang

2014-05-01

The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.

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.

A fingerprint classification algorithm based on combination of local and global information

NASA Astrophysics Data System (ADS)

Liu, Chongjin; Fu, Xiang; Bian, Junjie; Feng, Jufu

2011-12-01

Fingerprint recognition is one of the most important technologies in biometric identification and has been wildly applied in commercial and forensic areas. Fingerprint classification, as the fundamental procedure in fingerprint recognition, can sharply decrease the quantity for fingerprint matching and improve the efficiency of fingerprint recognition. Most fingerprint classification algorithms are based on the number and position of singular points. Because the singular points detecting method only considers the local information commonly, the classification algorithms are sensitive to noise. In this paper, we propose a novel fingerprint classification algorithm combining the local and global information of fingerprint. Firstly we use local information to detect singular points and measure their quality considering orientation structure and image texture in adjacent areas. Furthermore the global orientation model is adopted to measure the reliability of singular points group. Finally the local quality and global reliability is weighted to classify fingerprint. Experiments demonstrate the accuracy and effectivity of our algorithm especially for the poor quality fingerprint images.

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1982-01-01

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

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.

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.

The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram

NASA Astrophysics Data System (ADS)

Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.

2016-09-01

The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).

Polymer-Fourier quantization of the scalar field revisited

NASA Astrophysics Data System (ADS)

Garcia-Chung, Angel; Vergara, J. David

2016-10-01

The polymer quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such polymer quantization is the subgroup SDiff(ℝ4) which is a subgroup of Diff(ℝ4) formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the canonical commutation relations, nonunitary equivalent to the standard Fock representation. We also compared the Poincaré invariant Fock vacuum with the polymer Fourier vacuum.

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

Callias, C.J.

It has been known for a long time that the spectrum of the Sturm-Liouville operator {minus}{partial_derivative}{sub x}{sup 2}+ v(x) on a finite interval does not uniquely determine the potential v(x). In fact there are infinite-dimensional isospectral classes of potentials [PT]. Highly singular problems have been addressed as well, notably the question of the isospectral classes of the harmonic oscillator on the real line [McK-T], and, more recently, of the singular Sturm-Liouville operator {minus}{partial_derivative}{sub x}{sup 2} + {ell}({ell}+1)/x{sup 2} + v(x) on [0,1][GR]. In this paper we examine the question of whether the structure of isolated singularities in the potential ismore » spectrally determined. As an example of the fruits of our efforts we were able to prove the following result for the Dirichlet problem: Suppose that v(x) {epsilon} C{sup {infinity}}([-1,1]/(0)) is real-valued and v{sup (k)}(1) for all k. Suppose that xv(x) is infinitely differentiable at x = 0 from the right and from the left and lim{sub x}{r_arrow}0+ (d/{sub dx}){sup K}xv(x) = (-1){sup k+1}lim{sub x{r_arrow}0}-(d/dx){sup k}xv(x), so that v(x) {approximately} {Sigma}{sub k}{sup {infinity}}=-1{sup vk}{center_dot}{vert_bar}x{vert_bar}{sup k} as x {r_arrow} 0, for some constants v{sub k}. Suppose that v{sub {minus}1}{ne}0. Then the spectrum of the Sturm-Liousville operator with periodic boundary conditions at {plus_minus}1 and Dirichlet conditions at x = 0 uniquely determines the sequence of asymptotic coefficients v{sub {minus}1}, v{sub 0}, v{sub 1},...Potentials with the 1/x singularity arise in the wave equation for a vibrating rod of variable cross-section, when the cross-sectional area of the rod vanishes quadratically (as a function of the distance from the end of the rod) at one point. The main reason why we look at this problem is as a model that will give us an idea of what can be expected when one attempts to get information about singularities from the spectrum.« less

Coulomb wave functions in momentum space

DOE PAGES

Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; ...

2015-10-15

We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10 -1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.« less

Singular values behaviour optimization in the diagnosis of feed misalignments in radioastronomical reflectors

NASA Astrophysics Data System (ADS)

Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore; Schipani, Pietro

2016-07-01

The communication presents an innovative method for the diagnosis of reflector antennas in radio astronomical applications. The approach is based on the optimization of the number and the distribution of the far field sampling points exploited to retrieve the antenna status in terms of feed misalignments, this to drastically reduce the time length of the measurement process and minimize the effects of variable environmental conditions and simplifying the tracking process of the source. The feed misplacement is modeled in terms of an aberration function of the aperture field. The relationship between the unknowns and the far field pattern samples is linearized thanks to a Principal Component Analysis. The number and the position of the field samples are then determined by optimizing the Singular Values behaviour of the relevant operator.

Singular value decomposition for collaborative filtering on a GPU

NASA Astrophysics Data System (ADS)

Kato, Kimikazu; Hosino, Tikara

2010-06-01

A collaborative filtering predicts customers' unknown preferences from known preferences. In a computation of the collaborative filtering, a singular value decomposition (SVD) is needed to reduce the size of a large scale matrix so that the burden for the next phase computation will be decreased. In this application, SVD means a roughly approximated factorization of a given matrix into smaller sized matrices. Webb (a.k.a. Simon Funk) showed an effective algorithm to compute SVD toward a solution of an open competition called "Netflix Prize". The algorithm utilizes an iterative method so that the error of approximation improves in each step of the iteration. We give a GPU version of Webb's algorithm. Our algorithm is implemented in the CUDA and it is shown to be efficient by an experiment.

Boosting Classification Accuracy of Diffusion MRI Derived Brain Networks for the Subtypes of Mild Cognitive Impairment Using Higher Order Singular Value Decomposition

PubMed Central

Zhan, L.; Liu, Y.; Zhou, J.; Ye, J.; Thompson, P.M.

2015-01-01

Mild cognitive impairment (MCI) is an intermediate stage between normal aging and Alzheimer's disease (AD), and around 10-15% of people with MCI develop AD each year. More recently, MCI has been further subdivided into early and late stages, and there is interest in identifying sensitive brain imaging biomarkers that help to differentiate stages of MCI. Here, we focused on anatomical brain networks computed from diffusion MRI and proposed a new feature extraction and classification framework based on higher order singular value decomposition and sparse logistic regression. In tests on publicly available data from the Alzheimer's Disease Neuroimaging Initiative, our proposed framework showed promise in detecting brain network differences that help in classifying early versus late MCI. PMID:26413202

Singular value decomposition for the truncated Hilbert transform

NASA Astrophysics Data System (ADS)

Katsevich, A.

2010-11-01

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

Comninou contact zones for a crack parallel to an interface

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

Joseph, P.F.; Gadi, K.S.; Erdogen, F.

One of the interesting features in studying the state of stress in elastic solids near singular points, is the so called complex singularity that gives rise to an apparent local oscillatory behavior in the stress and displacement fields. The region in which this occurs is very small, much smaller than any plastic zone would be, and therefore the oscillations can be ignored in practical applications. Nevertheless, it is a matter of interesting theoretical investigation. The Comninou model of a small contact zone near the crack tip appears to correct for this anomaly within the framework of the linear theory. Thismore » model seems to make sense out of a {open_quotes}solution{close_quotes} that violates the boundary conditions. Erdogan and Joseph, showed (to themselves anyway) that the Comninou model actually has a physical basis. They considered a crack parallel to an interface where the order of the singularity is always real. With great care in solving the singular integral equations, it was shown that as the crack approaches the interface, a pinching effect is observed at the crack tip. This pinching effect proves that in the limit as the crack approaches the interface, the correct way to handle the problem is to consider crack surface contact. In this way, the issue of {open_quotes}oscillations{close_quotes} is never encountered for the interface crack problem. In the present study, the value of h/a that corresponds to crack closure (zero value of the stress intensity factor) will be determined for a given material pair for tensile loading. An asymptotic numerical method for the solution of singular integral equations making use of is used to obtain this result. Results for the crack opening displacement near the tip of the crack and the behavior of the stress intensity factor for cracks very close to the interface are presented. Among other interesting issues to be discussed, this solution shows that the semi-infinite crack parallel to an interface is closed.« less

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.

Towards realistic string vacua from branes at singularities

NASA Astrophysics Data System (ADS)

Conlon, Joseph P.; Maharana, Anshuman; Quevedo, Fernando

2009-05-01

We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dPn) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singularity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also describe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

NASA Astrophysics Data System (ADS)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

The nature of spherical collapse and a study of black hole dynamics

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh

Gravitational waves and singularities are two of the most significant predictions of General Relativity. Binary systems are the most promising sources of gravitational waves that are expected to be detected with the current ground-based and upcoming space-based gravitational wave detectors. During the merger of binary compact objects, an important stage is the plunge. A small part of the gravitational waveform, it marks the end of early inspiral and determines the quasinormal ringing (QNR) of the final product of the merger. It is also the part of the waveform where most of the gravitational energy is released. But, unlike early inspiral and late ringdown, it is poorly understood in terms of phenomenology. This thesis introduces a novel approach combining the Fourier domain Green's function in the particle perturbation approximation and a simple model to understand this crucial stage. The resulting understanding is successful in explaining QNR for a Schwarzschild black hole and opens a new approach to understanding binary inspiral. It holds the promise of a much improved understanding, and improved efficiency in making astrophysical estimates of gravitational wave source strength. Singularities are known to be the ultimate fate of all massive stars undergoing gravitational collapse. The cosmic censorship hypothesis predicts that all these singularities are generically covered by event horizons, i.e., all collapsing stars, if they result in a singularity, end up as black holes. Although several theoretical examples of non-hidden (naked) singularities have been found, the question of the genericity of naked singularities is far from settled. This thesis presents a study of the causal structure of spherically symmetric models of dust collapse and its perturbations to investigate the genericity of naked singularities.

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

NASA Technical Reports Server (NTRS)

Baker, Gregory; Siegel, Michael; Tanveer, Saleh

1995-01-01

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small round-off errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out.

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.

Collisional evolution - an analytical study for the nonsteady-state mass distribution

NASA Astrophysics Data System (ADS)

Martins, R. Vieira

1999-05-01

To study the collisional evolution of asteroidal groups we can use an analytical solutionfor the self-similar collision cascades. This solution is suitable to study the steady-state massdistribution of the collisional fragmentation. However, out of the steady-state conditions, thissolution is not satisfactory for some values of the collisional parameters. In fact, for some valuesfor the exponent of the mass distribution power law of an asteroidal group and its relation to theexponent of the function which describes how rocks break we arrive at singular points for theequation which describes the collisional evolution. These singularities appear since someapproximations are usually made in the laborious evaluation of many integrals that appear in theanalytical calculations. They concern the cutoff for the smallest and the largest bodies. Thesesingularities set some restrictions to the study of the analytical solution for the collisionalequation. To overcome these singularities we performed an algebraic computationconsidering the smallest and the largest bodies and we obtained the analytical expressions for theintegrals that describe the collisional evolution without restriction on the parameters. However,the new distribution is more sensitive to the values of the collisional parameters. In particular thesteady-state solution for the differential mass distribution has exponents slightly different from11⧸6 for the usual parameters in the Asteroid Belt. The sensitivity of this distribution with respectto the parameters is analyzed for the usual values in the asteroidal groups. With anexpression for the mass distribution without singularities, we can evaluate also its time evolution.We arrive at an analytical expression given by a power series of terms constituted by a smallparameter multiplied by the mass to an exponent, which depends on the initial power lawdistribution. This expression is a formal solution for the equation which describes the collisionalevolution. Furthermore, the first-order term for this solution is the time rate of the distribution atthe initial time. In particular the solution shows the fundamental importance played by theexponent of the power law initial condition in the evolution of the system.

Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Ramazanoğlu, Fethi M.

2015-12-01

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

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

Pulse reflectometry as an acoustical inverse problem: Regularization of the bore reconstruction

NASA Astrophysics Data System (ADS)

Forbes, Barbara J.; Sharp, David B.; Kemp, Jonathan A.

2002-11-01

The theoretical basis of acoustic pulse reflectometry, a noninvasive method for the reconstruction of an acoustical duct from the reflections measured in response to an input pulse, is reviewed in terms of the inversion of the central Fredholm equation. It is known that this is an ill-posed problem in the context of finite-bandwidth experimental signals. Recent work by the authors has proposed the truncated singular value decomposition (TSVD) in the regularization of the transient input impulse response, a non-measurable quantity from which the spatial bore reconstruction is derived. In the present paper we further emphasize the relevance of the singular system framework to reflectometry applications, examining for the first time the transient bases of the system. In particular, by varying the truncation point for increasing condition numbers of the system matrix, it is found that the effects of out-of-bandwidth singular functions on the bore reconstruction can be systematically studied.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Leading singularities and off-shell conformal integrals

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

Drummond, James; Duhr, Claude; Eden, Burkhard

2013-08-29

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certainmore » limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.« less

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

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« 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

Initial-boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system

NASA Astrophysics Data System (ADS)

Fei, Mingwen; Han, Daozhi; Wang, Xiaoming

2017-01-01

In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

Continuous analogues of matrix factorizations

PubMed Central

Townsend, Alex; Trefethen, Lloyd N.

2015-01-01

Analogues of singular value decomposition (SVD), QR, LU and Cholesky factorizations are presented for problems in which the usual discrete matrix is replaced by a ‘quasimatrix’, continuous in one dimension, or a ‘cmatrix’, continuous in both dimensions. Two challenges arise: the generalization of the notions of triangular structure and row and column pivoting to continuous variables (required in all cases except the SVD, and far from obvious), and the convergence of the infinite series that define the cmatrix factorizations. Our generalizations of triangularity and pivoting are based on a new notion of a ‘triangular quasimatrix’. Concerning convergence of the series, we prove theorems asserting convergence provided the functions involved are sufficiently smooth. PMID:25568618

A Worst-Case Approach for On-Line Flutter Prediction

NASA Technical Reports Server (NTRS)

Lind, Rick C.; Brenner, Martin J.

1998-01-01

Worst-case flutter margins may be computed for a linear model with respect to a set of uncertainty operators using the structured singular value. This paper considers an on-line implementation to compute these robust margins in a flight test program. Uncertainty descriptions are updated at test points to account for unmodeled time-varying dynamics of the airplane by ensuring the robust model is not invalidated by measured flight data. Robust margins computed with respect to this uncertainty remain conservative to the changing dynamics throughout the flight. A simulation clearly demonstrates this method can improve the efficiency of flight testing by accurately predicting the flutter margin to improve safety while reducing the necessary flight time.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Pleasure, Change and Values in Doctoral Pedagogy

ERIC Educational Resources Information Center

Hughes, Christina

2011-01-01

This article explores pleasure in terms of the values of independent judgement, writerly authority, originality and singularity associated with doctoral study. It also considers how pleasure can be understood as a mode of experience that acts as a force for change. Here, the article takes a broad Deleuzian approach that is concerned with our…

Trotter's limit formula for the Schrödinger equation with singular potential

NASA Astrophysics Data System (ADS)

Nathanson, Ekaterina S.; Jørgensen, Palle E. T.

2017-12-01

We discuss the Schrödinger equation with singular potentials. Our focus is non-relativistic Schrödinger operators H with scalar potentials V defined on R d, hence covering such quantum systems as atoms, molecules, and subatomic particles whether free, bound, or localized. By a "singular potential" V, we refer to the case when the corresponding Schrödinger operators H, with their natural minimal domain in L2(R d), are not essentially self-adjoint. Since V is assumed real valued, the corresponding Hermitian symmetric operator H commutes with the conjugation in L2(R d), and so (by von Neumann's theorem), H has deficiency indices (n, n). The case of singular potentials V refers to when n > 0. Hence, by von Neumann's theory, we know the full variety of all the self-adjoint extensions. Since the Trotter formula is restricted to the case when n = 0, and here n > 0, two questions arise: (i) existence of the Trotter limit and (ii) the nature of this limit. We answer (i) affirmatively. Our answer to (ii) is that when n > 0, the Trotter limit is a strongly continuous contraction semigroup; so it is not time-reversible.

Quantum propagation across cosmological singularities

NASA Astrophysics Data System (ADS)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

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.

Analytic Evolution of Singular Distribution Amplitudes in QCD

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

Tandogan Kunkel, Asli

2014-08-01

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standardmore » method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.« less

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

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

Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of Tmore » due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.« less

Singular value decomposition approach to the yttrium occurrence in mineral maps of rare earth element ores using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Romppanen, Sari; Häkkänen, Heikki; Kaski, Saara

2017-08-01

Laser-induced breakdown spectroscopy (LIBS) has been used in analysis of rare earth element (REE) ores from the geological formation of Norra Kärr Alkaline Complex in southern Sweden. Yttrium has been detected in eudialyte (Na15 Ca6(Fe,Mn)3 Zr3Si(Si25O73)(O,OH,H2O)3 (OH,Cl)2) and catapleiite (Ca/Na2ZrSi3O9·2H2O). Singular value decomposition (SVD) has been employed in classification of the minerals in the rock samples and maps representing the mineralogy in the sampled area have been constructed. Based on the SVD classification the percentage of the yttrium-bearing ore minerals can be calculated even in fine-grained rock samples.

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.

Using Rényi parameter to improve the predictive power of singular value decomposition entropy on stock market

NASA Astrophysics Data System (ADS)

Jiang, Jiaqi; Gu, Rongbao

2016-04-01

This paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of Rényi entropy. We analyze the predictive power of the entropy based on trajectory matrix using Shanghai Composite Index and Dow Jones Index data in both static test and dynamic test. In the static test on SCI, results of global granger causality tests all turn out to be significant regardless of orders selected. But this entropy fails to show much predictability in American stock market. In the dynamic test, we find that the predictive power can be significantly improved in SCI by our generalized method but not in DJI. This suggests that noises and errors affect SCI more frequently than DJI. In the end, results obtained using different length of sliding window also corroborate this finding.

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.

Singular value decomposition of received ultrasound signal to separate tissue, blood flow, and cavitation signals

NASA Astrophysics Data System (ADS)

Ikeda, Hayato; Nagaoka, Ryo; Lafond, Maxime; Yoshizawa, Shin; Iwasaki, Ryosuke; Maeda, Moe; Umemura, Shin-ichiro; Saijo, Yoshifumi

2018-07-01

High-intensity focused ultrasound is a noninvasive treatment applied by externally irradiating ultrasound to the body to coagulate the target tissue thermally. Recently, it has been proposed as a noninvasive treatment for vascular occlusion to replace conventional invasive treatments. Cavitation bubbles generated by the focused ultrasound can accelerate the effect of thermal coagulation. However, the tissues surrounding the target may be damaged by cavitation bubbles generated outside the treatment area. Conventional methods based on Doppler analysis only in the time domain are not suitable for monitoring blood flow in the presence of cavitation. In this study, we proposed a novel filtering method based on the differences in spatiotemporal characteristics, to separate tissue, blood flow, and cavitation by employing singular value decomposition. Signals from cavitation and blood flow were extracted automatically using spatial and temporal covariance matrices.

An analytic formula for H-infinity norm sensitivity with applications to control system design

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Lim, Kyong B.

1992-01-01

An analytic formula for the sensitivity of singular value peak variation with respect to parameter variation is derived. As a corollary, the derivative of the H-infinity norm of a stable transfer function with respect to a parameter is presented. It depends on some of the first two derivatives of the transfer function with respect to frequency and the parameter. For cases when the transfer function has a linear system realization whose matrices depend on the parameter, analytic formulas for these first two derivatives are derived, and an efficient algorithm for calculating them is discussed. Examples are given which provide numerical verification of the H-infinity norm sensitivity formula and which demonstrate its utility in designing control systems satisfying H-infinity norm constraints. In the appendix, derivative formulas for singular values are paraphrased.

High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities

NASA Astrophysics Data System (ADS)

Britt, Darrell Steven, Jr.

Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is because the FD scheme is only consistent for classical solutions of the PDE. For this reason, we implement the method of singularity subtraction as a means for restoring the design accuracy of the scheme in the presence of singularities at the boundary. While this method is well studied for low order methods and for problems in which singularities arise from the geometry (e.g., corners), we adapt it to our high-order scheme for curved boundaries via a conformal mapping and show that it can also be used to restore accuracy when the singularity arises from the BCs rather than the geometry. Altogether, the proposed methodology for 2D boundary value problems is computationally efficient, easily handles a wide class of boundary conditions and boundary shapes that are not aligned with the discretization grid, and requires little modification for solving new problems.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

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').

Optical effects related to Keplerian discs orbiting Kehagias-Sfetsos naked singularities

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Schee, Jan

2014-10-01

We demonstrate possible optical signatures of the Kehagias-Sfetsos (KS) naked singularity spacetimes representing a spherically symmetric vacuum solution of the modified Hořava gravity. In such spacetimes, accretion structures significantly different from those present in standard black hole spacetimes occur due to the ‘antigravity’ effect, which causes an internal static sphere surrounded by Keplerian discs. We focus our attention on the optical effects related to the Keplerian accretion discs, constructing the optical appearance of the Keplerian discs, the spectral continuum due to their thermal radiation, and the spectral profiled lines generated in the innermost parts of such discs. The KS naked singularity signature is strongly encoded in the characteristics of predicted optical effects, especially in cases where the spectral continuum and spectral lines are profiled by the strong gravity of the spacetimes due to the vanishing region of the angular velocity gradient influencing the effectiveness of the viscosity mechanism. We can conclude that optical signatures of KS naked singularities can be well distinguished from the signatures of standard black holes.

Spatial Dimension as a Variable in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Doren, Douglas James

Several approximation methods potentially useful in electronic structure calculations are developed. These methods all treat the spatial dimension, D, as a variable. In an Introduction, the motivations for these methods are described, with special attention to the semiclassical 1/D expansion. Several terms in this expansion have been calculated for two-electron atoms. The results have qualitative appeal but poor convergence properties when D = 3. Chapter 1 shows that this convergence problem is due to singularities in the energy at D = 1 and a method of removing their effects is demonstrated. Chapter 2 treats several model problems, showing how to identify special dimensions at which the energy becomes singular or the Hamiltonian simplifies. Expansions are developed about these special finite values of D which are quite accurate at low order, regardless of the physical parameters of the Hamiltonian. In Chapter 3, expansions about singular points in the energy at finite values of D are used to resum the 1/D series in cases where its leading orders are not sufficient. This leads to a hybrid expansion which typically improves on both the 1/D and the finite D series. These methods are applied in Chapter 4 to two -electron atoms. The ground state energy of few-electron systems is dominated by the presence of a pole when D = 1. The residue of this pole is determined by the eigenvalue of a simple limiting Schrodinger equation. The limit and first order correction are determined for both unapproximated nonrelativistic two-electron atoms and the Hartree-Fock approximation to them. The hybrid expansion using only the first few terms in the 1/D series determines the energy at arbitrary D, providing estimates accurate to four or five figures when D = 3. Degeneracies between D = 3 states and those in nonphysical dimensions are developed in Chapter 5 which provide additional applications for this series. Chapter 6 illustrates these methods in an application to the H(' -) ion, an especially stringent test case. Proposals for future work in this field are described in the final chapter.

Structure-Based Low-Rank Model With Graph Nuclear Norm Regularization for Noise Removal.

PubMed

Ge, Qi; Jing, Xiao-Yuan; Wu, Fei; Wei, Zhi-Hui; Xiao, Liang; Shao, Wen-Ze; Yue, Dong; Li, Hai-Bo

2017-07-01

Nonlocal image representation methods, including group-based sparse coding and block-matching 3-D filtering, have shown their great performance in application to low-level tasks. The nonlocal prior is extracted from each group consisting of patches with similar intensities. Grouping patches based on intensity similarity, however, gives rise to disturbance and inaccuracy in estimation of the true images. To address this problem, we propose a structure-based low-rank model with graph nuclear norm regularization. We exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure. With the manifold structure information, a graph nuclear norm regularization is established and incorporated into a low-rank approximation model. We then prove that the graph-based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular-value thresholding algorithm. Extensive experiments on additive white Gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state-of-the-art algorithms.

Modeling Coherent Structures in Canopy Flows

NASA Astrophysics Data System (ADS)

Luhar, Mitul

2017-11-01

It is well known that flows over vegetation canopies are characterized by the presence of energetic coherent structures. Since the mean profile over dense canopies exhibits an inflection point, the emergence of such structures is often attributed to a Kelvin-Helmholtz instability. However, though stability analyses provide useful mechanistic insights into canopy flows, they are limited in their ability to generate predictions for spectra and coherent structure. The present effort seeks to address this limitation by extending the resolvent formulation (McKeon and Sharma, 2010, J. Fluid Mech.) to canopy flows. Under the resolvent formulation, the turbulent velocity field is expressed as a superposition of propagating modes, identified via a gain-based (singular value) decomposition of the Navier-Stokes equations. A key advantage of this approach is that it reconciles multiple mechanisms that lead to high amplification in turbulent flows, including modal instability, transient growth, and critical-layer phenomena. Further, individual high-gain modes can be combined to generate more complete models for coherent structure and velocity spectra. Preliminary resolvent-based model predictions for canopy flows agree well with existing experiments and simulations.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Plasma-Sheath Model

NASA Astrophysics Data System (ADS)

Riemann, Karl-Ulrich

2012-10-01

In typical gas discharges a quasineutral plasma is shielded from a negativ absorbing wall by a thin positive sheath that is nearly planar and collision-free. The subdivision of ``plasma'' and ``sheath'' was introduced by Langmuir and is based on a small ratio of the electron Debye lenghth λD to the dominant competing characteristic plasma length l. Depending on the special conditions, l may represent, e.g., the plasma extension, the ionization length, the ion mean free path, the ion gyro radius, or a geometric length. Strictly speaking, this subdivion is possible only in the asymptotic limit λD/l->0. The asymptotic analysis results in singularities at the ``sheath edge'' closely related to the ``Bohm criterion.'' Due to these singularities a direct smooth matching of the separate plasma and sheath soltions is not possible. To obtain a consistent smooth transition, the singular sheath edge must be bridged by an additinal narrow ``intermediate'' model zone accounting both for plasma processes (e.g., collisions) and for the first build up of space charge. Due to this complexity and to different interpretations of the ``classical'' papers by Langmuir and Bohm, the asymptotic plasma-sheath concept and the definition of the sheath edge were questioned and resulted in controversies during the last two decades. We discuss attempts to re-define the sheath edge, to account for finite values of λD/l in the Bohm criterion, and demonstrate the consistent matching of plasma and sheath. The investigations of the plasma-sheath transition discussed so far are based on a simplified fluid analysis that cannot account for the essential inhomogeneity of the boundary layer and for the dominant role of slow ions in space charge formation. Therefore we give special emphasis to the kinetic theory of the plasma-sheath transition. Unfortunately this approach results in an additional mathematical difficulty caused by ions with zero velocity. We discuss attempts to avoid this singularity by a modification of the kinetic Bohm criterion and investigate the influence of slow ions on the structure of the plasma-sheath transition. The most important conclusions are illustrated with selected examples.

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

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

Baker, G.; Siegel, M.; Tanveer, S.

1995-09-01

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. The situation is disastrous for numerical computation, as small roundoff errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. Themore » method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out. 47 refs., 10 figs., 1 tab.« less

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.

Impact of Complex-Valued Energy Function Singularities on the Behaviour of RAYLEIGH-SCHRöDINGER Perturbation Series. H_2CO Molecule Vibrational Energy Spectrum.

NASA Astrophysics Data System (ADS)

Duchko, Andrey; Bykov, Alexandr

2015-06-01

Nowadays the task of spectra processing is as relevant as ever in molecular spectroscopy. Nevertheless, existing techniques of vibrational energy levels and wave functions computation often come to a dead-lock. Application of standard quantum-mechanical approaches often faces inextricable difficulties. Variational method requires unimaginable computational performance. On the other hand perturbational approaches beat against divergent series. That's why this problem faces an urgent need in application of specific resummation techniques. In this research Rayleigh-Schrödinger perturbation theory is applied to vibrational energy levels calculation of excited vibrational states of H_2CO. It is known that perturbation series diverge in the case of anharmonic resonance coupling between vibrational states [1]. Nevertheless, application of advanced divergent series summation techniques makes it possible to calculate the value of energy with high precision (more than 10 true digits) even for highly excited states of the molecule [2]. For this purposes we have applied several summation techniques based on high-order Pade-Hermite approximations. Our research shows that series behaviour completely depends on the singularities of complex energy function inside unit circle. That's why choosing an approximation function modelling this singularities allows to calculate the sum of divergent series. Our calculations for formaldehyde molecule show that the efficiency of each summation technique depends on the resonant type. REFERENCES 1. J. Cizek, V. Spirko, and O. Bludsky, ON THE USE OF DIVERGENT SERIES IN VIBRATIONAL SPECTROSCOPY. TWO- AND THREE-DIMENSIONAL OSCILLATORS, J. Chem. Phys. 99, 7331 (1993). 2. A. V. Sergeev and D. Z. Goodson, SINGULARITY ANALYSIS OF FOURTH-ORDER MöLLER-PLESSET PERTURBATION THEORY, J. Chem. Phys. 124, 4111 (2006).

Prediction of monthly-seasonal precipitation using coupled SVD patterns between soil moisture and subsequent precipitation

Treesearch

Yongqiang Liu

2003-01-01

It was suggested in a recent statistical correlation analysis that predictability of monthly-seasonal precipitation could be improved by using coupled singular value decomposition (SVD) pattems between soil moisture and precipitation instead of their values at individual locations. This study provides predictive evidence for this suggestion by comparing skills of two...

Matrix Approach of Seismic Wave Imaging: Application to Erebus Volcano

NASA Astrophysics Data System (ADS)

Blondel, T.; Chaput, J.; Derode, A.; Campillo, M.; Aubry, A.

2017-12-01

This work aims at extending to seismic imaging a matrix approach of wave propagation in heterogeneous media, previously developed in acoustics and optics. More specifically, we will apply this approach to the imaging of the Erebus volcano in Antarctica. Volcanoes are actually among the most challenging media to explore seismically in light of highly localized and abrupt variations in density and wave velocity, extreme topography, extensive fractures, and the presence of magma. In this strongly scattering regime, conventional imaging methods suffer from the multiple scattering of waves. Our approach experimentally relies on the measurement of a reflection matrix associated with an array of geophones located at the surface of the volcano. Although these sensors are purely passive, a set of Green's functions can be measured between all pairs of geophones from ice-quake coda cross-correlations (1-10 Hz) and forms the reflection matrix. A set of matrix operations can then be applied for imaging purposes. First, the reflection matrix is projected, at each time of flight, in the ballistic focal plane by applying adaptive focusing at emission and reception. It yields a response matrix associated with an array of virtual geophones located at the ballistic depth. This basis allows us to get rid of most of the multiple scattering contribution by applying a confocal filter to seismic data. Iterative time reversal is then applied to detect and image the strongest scatterers. Mathematically, it consists in performing a singular value decomposition of the reflection matrix. The presence of a potential target is assessed from a statistical analysis of the singular values, while the corresponding eigenvectors yield the corresponding target images. When stacked, the results obtained at each depth give a three-dimensional image of the volcano. While conventional imaging methods lead to a speckle image with no connection to the actual medium's reflectivity, our method enables to highlight a chimney-shaped structure inside Erebus volcano with true positive rates ranging from 80% to 95%. Although computed independently, the results at each depth are spatially consistent, substantiating their physical reliability. The identified structure is therefore likely to describe accurately the internal structure of the Erebus volcano.

The singular behavior of massive QCD amplitudes

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Moch, Sven-Olaf

2007-05-01

We discuss the structure of infrared singularities in on-shell QCD amplitudes with massive partons and present a general factorization formula in the limit of small parton masses. The factorization formula gives rise to an all-order exponentiation of both, the soft poles in dimensional regularization and the large collinear logarithms of the parton masses. Moreover, it provides a universal relation between any on-shell amplitude with massive external partons and its corresponding massless amplitude. For the form factor of a heavy quark we present explicit results including the fixed-order expansion up to three loops in the small mass limit. For general scattering processes we show how our constructive method applies to the computation of all singularities as well as the constant (mass-independent) terms of a generic massive n-parton QCD amplitude up to the next-to-next-to-leading order corrections.

Light-cone singularities and transverse-momentum-dependent factorization at twist-3

NASA Astrophysics Data System (ADS)

Chen, A. P.; Ma, J. P.

2017-05-01

We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of αs. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.

SVD-aided pseudo principal-component analysis: A new method to speed up and improve determination of the optimum kinetic model from time-resolved data

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

Oang, Key Young; Yang, Cheolhee; Muniyappan, Srinivasan

Determination of the optimum kinetic model is an essential prerequisite for characterizing dynamics and mechanism of a reaction. Here, we propose a simple method, termed as singular value decomposition-aided pseudo principal-component analysis (SAPPA), to facilitate determination of the optimum kinetic model from time-resolved data by bypassing any need to examine candidate kinetic models. We demonstrate the wide applicability of SAPPA by examining three different sets of experimental time-resolved data and show that SAPPA can efficiently determine the optimum kinetic model. In addition, the results of SAPPA for both time-resolved X-ray solution scattering (TRXSS) and transient absorption (TA) data of themore » same protein reveal that global structural changes of protein, which is probed by TRXSS, may occur more slowly than local structural changes around the chromophore, which is probed by TA spectroscopy.« less

Ferromagnetism in the Hubbard Model with a Gapless Nearly-Flat Band

NASA Astrophysics Data System (ADS)

Tanaka, Akinori

2018-01-01

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.

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.

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

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.

Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

PubMed

Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

2017-03-01

Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Black holes in magnetic monopoles

NASA Technical Reports Server (NTRS)

Lee, Kimyeong; Nair, V. P.; Weinberg, Erick J.

1991-01-01

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs field vacuum expectation value v is less than or equal to a critical value v sub cr, which is of the order of the Planck mass. In the limiting case, the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For v less than v sub cr, we find additional solutions which are singular at f = 0, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of v and of the total mass M and their relation to the Reissner-Nordstrom solutions is discussed.

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.

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.

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance.

PubMed

Srivastava, Madhur; Freed, Jack H

2017-11-16

Regularization is often utilized to elicit the desired physical results from experimental data. The recent development of a denoising procedure yielding about 2 orders of magnitude in improvement in SNR obviates the need for regularization, which achieves a compromise between canceling effects of noise and obtaining an estimate of the desired physical results. We show how singular value decomposition (SVD) can be employed directly on the denoised data, using pulse dipolar electron spin resonance experiments as an example. Such experiments are useful in measuring distances and their distributions, P(r) between spin labels on proteins. In noise-free model cases exact results are obtained, but even a small amount of noise (e.g., SNR = 850 after denoising) corrupts the solution. We develop criteria that precisely determine an optimum approximate solution, which can readily be automated. This method is applicable to any signal that is currently processed with regularization of its SVD analysis.

Helicity and singular structures in fluid dynamics

PubMed Central

Moffatt, H. Keith

2014-01-01

Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described. PMID:24520175

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2016-10-31

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

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

Juan, Pierre -Alexandre; Dingreville, Remi

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Laser-ablative engineering of phase singularities in plasmonic metamaterial arrays for biosensing applications

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

Aristov, Andrey I.; Kabashin, Andrei V., E-mail: kabashin@lp3.univ-mrs.fr; Zywietz, Urs

2014-02-17

By using methods of laser-induced transfer combined with nanoparticle lithography, we design and fabricate large-area gold nanoparticle-based metamaterial arrays exhibiting extreme Heaviside-like phase jumps in reflected light due to a strong diffractive coupling of localized plasmons. When employed in sensing schemes, these phase singularities provide the sensitivity of 5 × 10{sup 4} deg. of phase shift per refractive index unit change that is comparable with best values reported for plasmonic biosensors. The implementation of sensor platforms on the basis of such metamaterial arrays promises a drastic improvement of sensitivity and cost efficiency of plasmonic biosensing devices.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

NASA Astrophysics Data System (ADS)

Mercan, Kadir; Demir, Çiǧdem; Civalek, Ömer

2016-01-01

In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

Recording 2-D Nutation NQR Spectra by Random Sampling Method

PubMed Central

Sinyavsky, Nikolaj; Jadzyn, Maciej; Ostafin, Michal; Nogaj, Boleslaw

2010-01-01

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution. PMID:20949121

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1994-01-01

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

NASA Astrophysics Data System (ADS)

García, Isaac A.; Hernández-Bermejo, Benito

2017-08-01

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

Does Grammatical Structure Accelerate Number Word Learning? Evidence from Learners of Dual and Non-Dual Dialects of Slovenian

PubMed Central

Plesničar, Vesna; Razboršek, Tina; Sullivan, Jessica; Barner, David

2016-01-01

How does linguistic structure affect children’s acquisition of early number word meanings? Previous studies have tested this question by comparing how children learning languages with different grammatical representations of number learn the meanings of labels for small numbers, like 1, 2, and 3. For example, children who acquire a language with singular-plural marking, like English, are faster to learn the word for 1 than children learning a language that lacks the singular-plural distinction, perhaps because the word for 1 is always used in singular contexts, highlighting its meaning. These studies are problematic, however, because reported differences in number word learning may be due to unmeasured cross-cultural differences rather than specific linguistic differences. To address this problem, we investigated number word learning in four groups of children from a single culture who spoke different dialects of the same language that differed chiefly with respect to how they grammatically mark number. We found that learning a dialect which features “dual” morphology (marking of pairs) accelerated children’s acquisition of the number word two relative to learning a “non-dual” dialect of the same language. PMID:27486802

Does Grammatical Structure Accelerate Number Word Learning? Evidence from Learners of Dual and Non-Dual Dialects of Slovenian.

PubMed

Marušič, Franc; Žaucer, Rok; Plesničar, Vesna; Razboršek, Tina; Sullivan, Jessica; Barner, David

2016-01-01

How does linguistic structure affect children's acquisition of early number word meanings? Previous studies have tested this question by comparing how children learning languages with different grammatical representations of number learn the meanings of labels for small numbers, like 1, 2, and 3. For example, children who acquire a language with singular-plural marking, like English, are faster to learn the word for 1 than children learning a language that lacks the singular-plural distinction, perhaps because the word for 1 is always used in singular contexts, highlighting its meaning. These studies are problematic, however, because reported differences in number word learning may be due to unmeasured cross-cultural differences rather than specific linguistic differences. To address this problem, we investigated number word learning in four groups of children from a single culture who spoke different dialects of the same language that differed chiefly with respect to how they grammatically mark number. We found that learning a dialect which features "dual" morphology (marking of pairs) accelerated children's acquisition of the number word two relative to learning a "non-dual" dialect of the same language.

Dopamine prediction error responses integrate subjective value from different reward dimensions

PubMed Central

Lak, Armin; Stauffer, William R.; Schultz, Wolfram

2014-01-01

Prediction error signals enable us to learn through experience. These experiences include economic choices between different rewards that vary along multiple dimensions. Therefore, an ideal way to reinforce economic choice is to encode a prediction error that reflects the subjective value integrated across these reward dimensions. Previous studies demonstrated that dopamine prediction error responses reflect the value of singular reward attributes that include magnitude, probability, and delay. Obviously, preferences between rewards that vary along one dimension are completely determined by the manipulated variable. However, it is unknown whether dopamine prediction error responses reflect the subjective value integrated from different reward dimensions. Here, we measured the preferences between rewards that varied along multiple dimensions, and as such could not be ranked according to objective metrics. Monkeys chose between rewards that differed in amount, risk, and type. Because their choices were complete and transitive, the monkeys chose “as if” they integrated different rewards and attributes into a common scale of value. The prediction error responses of single dopamine neurons reflected the integrated subjective value inferred from the choices, rather than the singular reward attributes. Specifically, amount, risk, and reward type modulated dopamine responses exactly to the extent that they influenced economic choices, even when rewards were vastly different, such as liquid and food. This prediction error response could provide a direct updating signal for economic values. PMID:24453218

Non-singular bounce transitions in the multiverse

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

Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu

2013-11-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition tomore » another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.« less

Rare regions and Griffiths singularities at a clean critical point: the five-dimensional disordered contact process.

PubMed

Vojta, Thomas; Igo, John; Hoyos, José A

2014-07-01

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.

Topological features of vector vortex beams perturbed with uniformly polarized light

PubMed Central

D’Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams. PMID:28079134

Topological features of vector vortex beams perturbed with uniformly polarized light

NASA Astrophysics Data System (ADS)

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow

PubMed Central

Saw, E. -W.; Kuzzay, D.; Faranda, D.; Guittonneau, A.; Daviaud, F.; Wiertel-Gasquet, C.; Padilla, V.; Dubrulle, B.

2016-01-01

The three-dimensional incompressible Navier–Stokes equations, which describe the motion of many fluids, are the cornerstones of many physical and engineering sciences. However, it is still unclear whether they are mathematically well posed, that is, whether their solutions remain regular over time or develop singularities. Even though it was shown that singularities, if exist, could only be rare events, they may induce additional energy dissipation by inertial means. Here, using measurements at the dissipative scale of an axisymmetric turbulent flow, we report estimates of such inertial energy dissipation and identify local events of extreme values. We characterize the topology of these extreme events and identify several main types. Most of them appear as fronts separating regions of distinct velocities, whereas events corresponding to focusing spirals, jets and cusps are also found. Our results highlight the non-triviality of turbulent flows at sub-Kolmogorov scales as possible footprints of singularities of the Navier–Stokes equation. PMID:27578459

Topological features of vector vortex beams perturbed with uniformly polarized light.

PubMed

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-12

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Removal of singularity in radial Langmuir probe models for non-zero ion temperature

NASA Astrophysics Data System (ADS)

Regodón, Guillermo Fernando; Fernández Palop, José Ignacio; Tejero-del-Caz, Antonio; Díaz-Cabrera, Juan Manuel; Carmona-Cabezas, Rafael; Ballesteros, Jerónimo

2017-10-01

We solve a radial theoretical model that describes the ion sheath around a cylindrical Langmuir probe with finite non-zero ion temperature in which singularity in an a priori unknown point prevents direct integration. The singularity appears naturally in fluid models when the velocity of the ions reaches the local ion speed of sound. The solutions are smooth and continuous and are valid from the plasma to the probe with no need for asymptotic matching. The solutions that we present are valid for any value of the positive ion to electron temperature ratio and for any constant polytropic coefficient. The model is numerically solved to obtain the electric potential and the ion population density profiles for any given positive ion current collected by the probe. The ion-current to probe-voltage characteristic curves and the Sonin plot are calculated in order to use the results of the model in plasma diagnosis. The proposed methodology is adaptable to other geometries and in the presence of other presheath mechanisms.

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.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

Physics and control of wall turbulence for drag reduction.

PubMed

Kim, John

2011-04-13

Turbulence physics responsible for high skin-friction drag in turbulent boundary layers is first reviewed. A self-sustaining process of near-wall turbulence structures is then discussed from the perspective of controlling this process for the purpose of skin-friction drag reduction. After recognizing that key parts of this self-sustaining process are linear, a linear systems approach to boundary-layer control is discussed. It is shown that singular-value decomposition analysis of the linear system allows us to examine different approaches to boundary-layer control without carrying out the expensive nonlinear simulations. Results from the linear analysis are consistent with those observed in full nonlinear simulations, thus demonstrating the validity of the linear analysis. Finally, fundamental performance limit expected of optimal control input is discussed.

A Computational Framework for Identifiability and Ill-Conditioning Analysis of Lithium-Ion Battery Models

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

López C, Diana C.; Wozny, Günter; Flores-Tlacuahuac, Antonio

2016-03-23

The lack of informative experimental data and the complexity of first-principles battery models make the recovery of kinetic, transport, and thermodynamic parameters complicated. We present a computational framework that combines sensitivity, singular value, and Monte Carlo analysis to explore how different sources of experimental data affect parameter structural ill conditioning and identifiability. Our study is conducted on a modified version of the Doyle-Fuller-Newman model. We demonstrate that the use of voltage discharge curves only enables the identification of a small parameter subset, regardless of the number of experiments considered. Furthermore, we show that the inclusion of a single electrolyte concentrationmore » measurement significantly aids identifiability and mitigates ill-conditioning.« less

The construction and assessment of a statistical model for the prediction of protein assay data.

PubMed

Pittman, J; Sacks, J; Young, S Stanley

2002-01-01

The focus of this work is the development of a statistical model for a bioinformatics database whose distinctive structure makes model assessment an interesting and challenging problem. The key components of the statistical methodology, including a fast approximation to the singular value decomposition and the use of adaptive spline modeling and tree-based methods, are described, and preliminary results are presented. These results are shown to compare favorably to selected results achieved using comparitive methods. An attempt to determine the predictive ability of the model through the use of cross-validation experiments is discussed. In conclusion a synopsis of the results of these experiments and their implications for the analysis of bioinformatic databases in general is presented.

Robust Flutter Margin Analysis that Incorporates Flight Data

NASA Technical Reports Server (NTRS)

Lind, Rick; Brenner, Martin J.

1998-01-01

An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.

Condensation of an ideal gas obeying non-Abelian statistics.

PubMed

Mirza, Behrouz; Mohammadzadeh, Hosein

2011-09-01

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.

Freezing transition of the random bond RNA model: Statistical properties of the pairing weights

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2007-03-01

To characterize the pairing specificity of RNA secondary structures as a function of temperature, we analyze the statistics of the pairing weights as follows: for each base (i) of the sequence of length N , we consider the (N-1) pairing weights wi(j) with the other bases (j≠i) of the sequence. We numerically compute the probability distributions P1(w) of the maximal weight wimax=maxj[wi(j)] , the probability distribution Π(Y2) of the parameter Y2(i)=∑jwi2(j) , as well as the average values of the moments Yk(i)=∑jwik(j) . We find that there are two important temperatures TcTgap , the distribution P1(w) vanishes at some value w0(T)<1 , and accordingly the moments Yk(i)¯ decay exponentially as [w0(T)]k in k . For T

Predictability of a Coupled Model of ENSO Using Singular Vector Analysis: Optimal Growth and Forecast Skill.

NASA Astrophysics Data System (ADS)

Xue, Yan

The optimal growth and its relationship with the forecast skill of the Zebiak and Cane model are studied using a simple statistical model best fit to the original nonlinear model and local linear tangent models about idealized climatic states (the mean background and ENSO cycles in a long model run), and the actual forecast states, including two sets of runs using two different initialization procedures. The seasonally varying Markov model best fit to a suite of 3-year forecasts in a reduced EOF space (18 EOFs) fits the original nonlinear model reasonably well and has comparable or better forecast skill. The initial error growth in a linear evolution operator A is governed by the eigenvalues of A^{T}A, and the square roots of eigenvalues and eigenvectors of A^{T}A are named singular values and singular vectors. One dominant growing singular vector is found, and the optimal 6 month growth rate is largest for a (boreal) spring start and smallest for a fall start. Most of the variation in the optimal growth rate of the two forecasts is seasonal, attributable to the seasonal variations in the mean background, except that in the cold events it is substantially suppressed. It is found that the mean background (zero anomaly) is the most unstable state, and the "forecast IC states" are more unstable than the "coupled model states". One dominant growing singular vector is found, characterized by north-south and east -west dipoles, convergent winds on the equator in the eastern Pacific and a deepened thermocline in the whole equatorial belt. This singular vector is insensitive to initial time and optimization time, but its final pattern is a strong function of initial states. The ENSO system is inherently unpredictable for the dominant singular vector can amplify 5-fold to 24-fold in 6 months and evolve into the large scales characteristic of ENSO. However, the inherent ENSO predictability is only a secondary factor, while the mismatches between the model and data is a primary factor controlling the current forecast skill.

Free energy of singular sticky-sphere clusters.

PubMed

Kallus, Yoav; Holmes-Cerfon, Miranda

2017-02-01

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a system of N spherical particles, and directly account for the singularities that arise in the sticky limit where the pairwise interaction is strong and short ranged. Although the contribution to the partition function from singular clusters diverges in the limit, its asymptotic value can be calculated and depends on only two parameters, characterizing the depth and range of the potential. The result holds for systems that are second-order rigid, a geometric characterization that describes all known ground-state (rigid) sticky clusters. To illustrate the applications of our theory we address the question of emergence: how does crystalline order arise in large systems when it is strongly disfavored in small ones? We calculate the partition functions of all known rigid clusters up to N≤21 and show the cluster landscape is dominated by hyperstatic clusters (those with more than 3N-6 contacts); singular and isostatic clusters are far less frequent, despite their extra vibrational and configurational entropies. Since the most hyperstatic clusters are close to fragments of a close-packed lattice, this underlies the emergence of order in sticky-sphere systems, even those as small as N=10.

Free energy of singular sticky-sphere clusters

NASA Astrophysics Data System (ADS)

Kallus, Yoav; Holmes-Cerfon, Miranda

2017-02-01

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a system of N spherical particles, and directly account for the singularities that arise in the sticky limit where the pairwise interaction is strong and short ranged. Although the contribution to the partition function from singular clusters diverges in the limit, its asymptotic value can be calculated and depends on only two parameters, characterizing the depth and range of the potential. The result holds for systems that are second-order rigid, a geometric characterization that describes all known ground-state (rigid) sticky clusters. To illustrate the applications of our theory we address the question of emergence: how does crystalline order arise in large systems when it is strongly disfavored in small ones? We calculate the partition functions of all known rigid clusters up to N ≤21 and show the cluster landscape is dominated by hyperstatic clusters (those with more than 3 N -6 contacts); singular and isostatic clusters are far less frequent, despite their extra vibrational and configurational entropies. Since the most hyperstatic clusters are close to fragments of a close-packed lattice, this underlies the emergence of order in sticky-sphere systems, even those as small as N =10 .

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

NASA Technical Reports Server (NTRS)

Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.

1993-01-01

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Quasiparticle interference in multiband superconductors with strong coupling

NASA Astrophysics Data System (ADS)

Dutt, A.; Golubov, A. A.; Dolgov, O. V.; Efremov, D. V.

2017-08-01

We develop a theory of the quasiparticle interference (QPI) in multiband superconductors based on the strong-coupling Eliashberg approach within the Born approximation. In the framework of this theory, we study dependencies of the QPI response function in the multiband superconductors with the nodeless s -wave superconductive order parameter. We pay special attention to the difference in the quasiparticle scattering between the bands having the same and opposite signs of the order parameter. We show that at the momentum values close to the momentum transfer between two bands, the energy dependence of the quasiparticle interference response function has three singularities. Two of these correspond to the values of the gap functions and the third one depends on both the gaps and the transfer momentum. We argue that only the singularity near the smallest band gap may be used as a universal tool to distinguish between the s++ and s± order parameters. The robustness of the sign of the response function peak near the smaller gap value, irrespective of the change in parameters, in both the symmetry cases is a promising feature that can be harnessed experimentally.

Fluctuation removal around spectral and temporal constancy limits via use of an extended space expectation value weight function for singular quantum systems

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

Kalay, Berfin; Demiralp, Metin

2015-03-10

This work is a new extension to our a very recent work whose paper will appear in the proceedings of a very recent international conference. What we have done in the previous work is the use of a weight operator to suppress the singularities causing nonexistence of some of temporal Maclaurin expansion coefficients. The weight operator has been constructed in such a way that certain number of expectation values of position operator’s first positive integer powers with and without the chosen weight operator match. Therein this match has not been considered for the momentum operator’s corresponding power expectation values andmore » a finite linear combination of the spatial variable’s first reciprocal powers has been used in the construction of the weight operator. Here, that approach is extended to the case where matches for both position and momentum operators are considered and the weight operator involves finite linear combinations of the spatial variable’s both positive integer powers and their reciprocals.« less

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.

Flavor structure in F-theory compactifications

NASA Astrophysics Data System (ADS)

Hayashi, Hirotaka; Kawano, Teruhiko; Tsuchiya, Yoichi; Watari, Taizan

2010-08-01

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of righthanded neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N gen = 3 or the number of singularity points of certain types. If there is a geometry with only one E 6 type point and one D 6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N gen × N gen CKM matrix is predicted to have only N gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. The hierarchy among the Yukawa eigenvalues of the down-type and charged lepton sector is predicted to be smaller than that of the up-type sector, and the Majorana masses of left-handed neutrinos generated through the see-saw mechanism have small hierarchy. All of these predictions agree with what we observe in the real world. We also obtained a precise description of zero mode wavefunctions near the E 6 type singularity points, where the up-type Yukawa couplings are generated.

Modeling and Application of Piezoelectric Materials in Repair of Engineering Structures

NASA Astrophysics Data System (ADS)

Wu, Nan

The shear horizontal wave propagation and vibration of piezoelectric coupled structures under an open circuit electrical boundary condition are studied. Following the studies on the dynamic response of piezoelectric coupled structures, the repair of both crack/notch and delaminated structures using piezoelectric materials are conducted. The main contribution was the proposed the active structural repair design using piezoelectric materials for different structures. An accurate model for the piezoelectric effect on the shear wave propagation is first proposed to guide the application of piezoelectric materials as sensors and actuators in the repair of engineering structures. A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. The mechanical models and solutions for the wave propagation and vibration analysis of piezoelectric coupled structures are established based on the Kirchhoff plate model and Maxwell equation. Following the studies of the dynamic response of piezoelectric coupled structures, a close-loop feedback control repair methodology is proposed for a vibrating delaminated beam structure by using piezoelectric patches. The electromechanical characteristic of the piezoelectric material is employed to induce a local shear force above the delamination area via an external actuation voltage, which is designed as a feedback of the deflection of a vibrating beam and a delaminated plate, to reduce the stress singularity around the delamination tips. Furthermore, an experimental realization of an effective repair of a notched cantilever beam structure subjected to a dynamic loading by use of piezoelectric patches is reported. A small piezoelectric patch used as a sensor is placed on the notch position to monitor the severity of the stress singularity around the notch area by measuring the charge output on the sensor, and a patch used as an actuator is located around the notch area to generate a required bending moment by employing an actuation voltage to reduce the stress singularity at the notch position. The actuation voltage on the actuator is designed from a feedback circuit process. Through the analytical model, FEM simulation and experimental studies, the active structural repair method using piezoelectric materials is realized and proved to be feasible and practical.

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.

Local properties and global structure of McVittie spacetimes with non-flat Friedmann-Lemaître-Robertson-Walker backgrounds

NASA Astrophysics Data System (ADS)

Nolan, Brien C.

2017-11-01

McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter) spacetime in an isotropic, Friedmann-Lemaître-Robertson-Walker (FLRW) background universe. The global structure of such spacetimes is well understood when the FLRW background is spatially flat. In this paper, we study the global structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. We derive some basic results on the metric, curvature and matter content of these spacetimes and provide a representation of the metric that makes the study of their global properties possible. In the closed case, we find that at each instant of time, the spacetime is confined to a region bounded by a (positive) minimum and a maximum area radius, and is bounded either to the future or to the past by a scalar curvature singularity. This allowed region only exists when the background scale factor is above a certain minimum, and so is bounded away from the Big Bang singularity, as in the flat case. In the open case, the situation is different, and we focus mainly on this case. In K<0 McVittie spacetimes, radial null geodesics originate in finite affine time in the past at a boundary formed by the union of the Big Bang singularity of the FLRW background and a hypersurface (of varying causal character) which is non-singular in the sense of scalar curvature. Furthermore, in the case of eternally expanding open universes with Λ≥slant0 , we prove that black holes are ubiquitous: ingoing radial null geodesics extend in finite affine time to a hypersurface that forms the boundary of the region from which photons can escape to future null infinity. We determine the structure of the conformal diagrams that can arise in the open case. Finally, we revisit the black hole interpretation of McVittie spacetimes in the spatially flat case, and show that this interpretation holds also in the case of a vanishing cosmological constant, contrary to a previous claim of ours.

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.

Recurrent noise-induced phase singularities in drifting patterns.

PubMed

Clerc, M G; Coulibaly, S; del Campo, F; Garcia-Nustes, M A; Louvergneaux, E; Wilson, M

2015-11-01

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.

Heating of the corona by magnetic singularities

NASA Technical Reports Server (NTRS)

Antiochos, Spiro K.

1990-01-01

Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

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.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model

NASA Astrophysics Data System (ADS)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Inflationary cosmology with Chaplygin gas in Palatini formalism

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

Borowiec, Andrzej; Wojnar, Aneta; Stachowski, Aleksander

2016-01-01

We present a simple generalisation of the ΛCDM model which on the one hand reaches very good agreement with the present day experimental data and provides an internal inflationary mechanism on the other hand. It is based on Palatini modified gravity with quadratic Starobinsky term and generalized Chaplygin gas as a matter source providing, besides a current accelerated expansion, the epoch of endogenous inflation driven by type III freeze singularity. It follows from our statistical analysis that astronomical data favors negative value of the parameter coupling quadratic term into Einstein-Hilbert Lagrangian and as a consequence the bounce instead of initialmore » Big-Bang singularity is preferred.« less

The approximation of anomalous magnetic field by array of magnetized rods

NASA Astrophysics Data System (ADS)

Denis, Byzov; Lev, Muravyev; Natalia, Fedorova

2017-07-01

The method for calculation the vertical component of an anomalous magnetic field from its absolute value is presented. Conversion is based on the approximation of magnetic induction module anomalies by the set of singular sources and the subsequent calculation for the vertical component of the field with the chosen distribution. The rods that are uniformly magnetized along their axis were used as a set of singular sources. Applicability analysis of different methods of nonlinear optimization for solving the given task was carried out. The algorithm is implemented using the parallel computing technology on the NVidia GPU. The approximation and calculation of vertical component is demonstrated for regional magnetic field of North Eurasia territories.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

[Fractal characteristics of the functional state of the brain in patients with anxious phobic disorders].

PubMed

Dik, O E; Sviatogor, I A; Ishinova, V A; Nozdrachev, A D

2012-01-01

The task of estimation of the functional state of the human brain during psychotherapeutic treatment of psychogenic pain in patients with anxious phobic disorders is examined. For solving the task the methods of spectral and multifractal analyses of EEG fragments are applied during the perception of psychogenic pain and its removal by the psychorelaxation technique. Contrary to power spectra singularity spectra allow to distinguish EEGs quanitatively in the examined functional states of the human brain. The pain suppression in patients with anxious phobic disorders during psychorelaxation is accompanied by changing the width of the singularity spectrum and approximation of this multifractal partameter to the value corresponding to a healthy subject.

DUALITY IN MULTIVARIATE RECEPTOR MODEL. (R831078)

EPA Science Inventory

Multivariate receptor models are used for source apportionment of multiple observations of compositional data of air pollutants that obey mass conservation. Singular value decomposition of the data leads to two sets of eigenvectors. One set of eigenvectors spans a space in whi...